Princeton Science Library

Beth Shapiro is professor of ecology and evolutionary biology at the University of California, Santa Cruz. She received a MacArthur Award in 2009. Twitter @bonesandbugs. An insider's view on bringing extinct species back to life Could extinct species, like mammoths and passenger pigeons, be brought back to life? In How to Clone a Mammoth, Beth Shapiro, an evolutionary biologist and pioneer in ancient DNA research, addresses this intriguing question by walking readers through the astonishing and controversial process of de-extinction. From deciding which species should be restored to anticipating how revived populations might be overseen in the wild, Shapiro vividly explores the extraordinary cutting-edge science that is being used to resurrect the past. Considering de-extinction's practical benefits and ethical challenges, Shapiro argues that the overarching goal should be the revitalization and stabilization of contemporary ecosystems. Looking at the very real and compelling science behind an idea once seen as science fiction, How to Clone a Mammoth demonstrates how de-extinction will redefine conservation's future. "A fascinating book."-Carl Zimmer, Wall Street Journal "An engaging, rigorous, and deeply thoughtful book."-Elizabeth Kolbert, author of The Sixth Extinction "At once an account of the state of the technology, a sketch of how to proceed, a barrage of as-yet unanswerable questions and a manifesto."-Olivia Judson, Financial Times "A thrilling tour of the science that might-might-recreate lost worlds from the not-too-distant past. . . . Sharp, witty, and impeccably-argued."-Riley Black, National Geographic.com "An entertaining and deeply informative read."-A. Rus Hoelzel, Science

"Winner of the 1994 Award for Best Professional/Scholarly Book in Chemistry, Association of American Publishers" Philip Ball, Associate Editor for Physical Sciences for Nature, has written on the new chemistry for both technical journals and popular magazines and newspapers. Some of the most exciting scientific developments in recent years have come not from theoretical physicists, astronomers, or molecular biologists but instead from the chemistry lab. Chemists have created superconducting ceramics for brain scanners, designed liquid crystal flat screens for televisions and watch displays, and made fabrics that change color while you wear them. They have fashioned metals from plastics, drugs from crude oil, and have pinpointed the chemical pollutants affecting our atmosphere and are now searching for remedies for the imperiled planet. Philip Ball, an editor for the prestigious magazine Nature, lets the lay reader into the world of modern chemistry. Here, for example, chemists find new uses for the improbable buckminsterfullerene molecules--60-atom carbon soccerballs, dubbed "buckyballs"--which seem to have applications for everything from lubrication to medicine to electronics. The book is not intended as an introduction to chemistry, but as an accessible survey of recent developments throughout many of the major fields allied with chemistry: from research in traditional areas such as crystallography and spectroscopy to entirely new fields of study such as molecular electronics, artificial enzymes, and "smart" polymer gels. Ball's grand tour along the leading edge of scientific discovery will appeal to all curious readers, with or without any scientific training, to chemistry students looking for future careers, and to practicing chemical researchers looking for information on other specialties within their discipline. "In this very readable and enjoyable book, Ball {offers} a whirlwind guided tour through some of the most exciting topics in modern chemistry, molecular physics, and materials science. . . . Lucidly written . . . with an acute awareness of recent advances and an excellent understanding of their intrinsic scientific content." "A tour de force of popular science writing."---John Postgate, The, Times Literary Supplement "This book is like a clean fresh breeze, and puts the image of chemistry back into proper perspective.... {It} should be used ... to help convey to students ... enthusiasm for modern research."---Rudolph Fahnenstich, Angewandte Chemie "It covers almost every possible recent development in chemistry in just the right amount of detail.... The old disciplines of organic, inorganic and physical chemistry of the stuffy textbooks are ploughed over and a new patchwork of fields created to fill their place."---David Bradley, New Scientist

Jacques Hadamard (1865-1963), an internationally known mathematician, was born in Versailles and lectured at universities throughout the world, including Hravard, Princeton, Stanford, and Columbia Universities, and at the Institute for Advanced Study. Fifty years ago when Jacques Hadamard set out to explore how mathematicians invent new ideas, he considered the creative experiences of some of the greatest thinkers of his generation, such as George Polya, Claude Lévi-Strauss, and Albert Einstein. It appeared that inspiration could strike anytime, particularly after an individual had worked hard on a problem for days and then turned attention to another activity. In exploring this phenomenon, Hadamard produced one of the most famous and cogent cases for the existence of unconscious mental processes in mathematical invention and other forms of creativity. Written before the explosion of research in computers and cognitive science, his book, originally titled The Psychology of Invention in the Mathematical Field, remains an important tool for exploring the increasingly complex problem of mental life. The roots of creativity for Hadamard lie not in consciousness, but in the long unconscious work of incubation, and in the unconscious aesthetic selection of ideas that thereby pass into consciousness. His discussion of this process comprises a wide range of topics, including the use of mental images or symbols, visualized or auditory words, "meaningless" words, logic, and intuition. Among the important documents collected is a letter from Albert Einstein analyzing his own mechanism of thought.

Edwin Abbott Abbott (1838-1926), the author of more than fifty books on classics, theology, history, and Shakespeare, was headmaster of the City of London School and one of the leading educators of his time. Thomas Banchoff is professor emeritus of mathematics at Brown University and author of Beyond the Third Dimension. In 1884, Edwin Abbott Abbott wrote a mathematical adventure set in a two-dimensional plane world, populated by a hierarchical society of regular geometrical figures-who think and speak and have all too human emotions. Since then Flatland has fascinated generations of readers, becoming a perennial science-fiction favorite. By imagining the contact of beings from different dimensions, the author fully exploited the power of the analogy between the limitations of humans and those of his two-dimensional characters. A first-rate fictional guide to the concept of multiple dimensions of space, the book will also appeal to those who are interested in computer graphics. This field, which literally makes higher dimensions seeable, has aroused a new interest in visualization. We can now manipulate objects in four dimensions and observe their three-dimensional slices tumbling on the computer screen. But how do we interpret these images? In his introduction, Thomas Banchoff points out that there is no better way to begin exploring the problem of understanding higher-dimensional slicing phenomena than reading this classic novel of the Victorian era. "One of the most imaginative, delightful and, yes, touching works of mathematics, this slender 1884 book purports to be the memoir of A. Square, a citizen of an entirely two-dimensional world." "Flatland has remained of interest for over a century precisely because of its ability to engage its readers on so many different planes in so many different dimensions." "This reprint of Abbott's Flatland adventures contains an Introduction by Thomas Banchoff which is worth reading on its own. So if you don't have yet this book at home, go ahead and buy this edition."

Richard L. Gregory (1923–2010) was a distinguished British psychologist and emeritus professor of neuropsychology at the University of Bristol. Since the publication of the first edition in 1966, Eye and Brain has established itself worldwide as an essential introduction to the basic phenomena of visual perception. Richard Gregory offers clear explanations of how we see brightness, movement, color, and objects, and he explores the phenomena of visual illusions to establish principles about how perception normally works and why it sometimes fails. Illusion continues to be a major theme in the book, which provides a comprehensive classification system. There are also sections on what babies see and how they learn to see, on motion perception, the relationship between vision and consciousness, and on the impact of new brain imaging techniques. "[A] hugely influential book. . . . It stands as the essential guide to Gregory's framework for perception, but also to a whole range of visual demonstrations, illusions, and puzzles that will have you captivated long after you have finished."---Iain D. Gilchrist, Perception "An excellent introduction to the psychology of vision. It presents what we know, what we don't know, and what we think. Gregory accomplishes this in an astonishingly succinct and successful book."---Steven M. Kastenbaum, Science Books & Films

"Honorable Mention for the 1994 Award for Best Professional/Scholarly Book in Mathematics, Association of American Publishers" Eli Maor is the author of Beautiful Geometry (with Eugen Jost), Venus in Transit, Trigonometric Delights, To Infinity and Beyond, and The Pythagorean Theorem: A 4,000-Year History (all Princeton). The interest earned on a bank account, the arrangement of seeds in a sunflower, and the shape of the Gateway Arch in St. Louis are all intimately connected with the mysterious number e. In this informal and engaging history, Eli Maor portrays the curious characters and the elegant mathematics that lie behind the number. Designed for a reader with only a modest mathematical background, this biography brings out the central importance of e to mathematics and illuminates a golden era in the age of science. "This is a gently paced, elegantly composed book, and it will bring its readers much pleasure. . . . Maor has written an excellent book that should be in every public and school library."---Ian Stewart, New Scientist "Maor wonderfully tells the story of e. The chronological history allows excursions into the lives of people involved with the development of this fascinating number. Maor hangs his story on a string of people stretching from Archimedes to David Hilbert. And by presenting mathematics in terms of the humans who produced it, he places the subject where it belongs--squarely in the centre of the humanities."---Jerry P. King, Nature "Maor has succeeded in writing a short, readable mathematical story. He has interspersed a variety of anecdotes, excursions, and essays to lighten the flow.... [The book] is like the voyages of Columbus as told by the first mate."---Peter Borwein, Science "Maor attempts to give the irrational number e its rightful standing alongside pi as a fundamental constant in science and nature; he succeeds very well.... Maor writes so that both mathematical newcomers and long-time professionals alike can thoroughly enjoy his book, learn something new, and witness the ubiquity of mathematical ideas in Western culture." "It can be recommended to readers who want to learn about mathematics and its history, who want to be inspired and who want to understand important mathematical ideas more deeply." "[A] very interesting story about the history of e, logarithms, and related matters, especially the history of calculus. . . . [A] useful complement to a course in calculus and analysis, shedding light on some fundamental topics."---Mehdi Hassani, MAA Reviews

A landmark account of the dynamics of living systems and the methods for studying them Random Walks in Biology provides a lucid, straightforward introduction to the concepts and techniques of statistical physics that students of biology, biochemistry, and biophysics must know. Howard Berg offers an essential foundation for understanding random motions of molecules, subcellular particles, and cells as well as the processes that are affected by such motions. Using the concept of "random walks" of individual particles, Berg illuminates the physics involved in diffusion, sedimentation, electrophoresis, chromatography, and cell motility. With an engaging foreword by theoretical biophysicist William Bialek, this Princeton Science Library edition can serve as a supplementary text for courses on biochemistry, molecular biology, biomechanics, physiology, biophysics, and physical chemistry. It is also an ideal reference volume. Howard C. Berg (1934–2021) was the Herchel Smith Professor of Physics and professor of molecular and cellular biology at Harvard University. William Bialek is the John Archibald Wheeler/Battelle Professor in Physics at Princeton University. "A unique work. Marvelous pithiness-and the scholarship is impeccable."-Steven Vogel, author of Comparative Biomechanics: Life's Physical World "A scholarly and pedagogically masterly introduction to diffusion, its physics and its statistics."---Charles DeLisi, Nature "I very strongly recommend this excellent book to students as a supplementary textbook in courses on biochemistry, physiology, and biophysics. Moreover, research scientists and scholars should enjoy reading it."---Akira Okubo, Quarterly Review of Biology

Julian Havil is the author of Gamma: Exploring Euler's Constant, Nonplussed!: Mathematical Proof of Implausible Ideas, Impossible?: Surprising Solutions to Counterintuitive Conundrums, and John Napier: Life, Logarithms, and Legacy (all Princeton). He is a retired former master at Winchester College, England, where he taught mathematics for more than three decades. An entertaining and enlightening history of irrational numbers, from ancient Greece to the twenty-first century The ancient Greeks discovered them, but it wasn't until the nineteenth century that irrational numbers were properly understood and rigorously defined, and even today not all their mysteries have been revealed. In The Irrationals, the first popular and comprehensive book on the subject, Julian Havil tells the story of irrational numbers and the mathematicians who have tackled their challenges, from antiquity to the twenty-first century. Along the way, he explains why irrational numbers are surprisingly difficult to define-and why so many questions still surround them. Fascinating and illuminating, this is a book for everyone who loves math and the history behind it. "The insides of this book are as clever and compelling as the subtitle on the cover. Havil, a retired former master at Winchester College in England, where he taught math for decades, takes readers on a history of irrational numbers--numbers, like v2 or p, whose decimal expansion 'is neither finite nor recurring.' We start in ancient Greece with Pythagoras, whose thinking most likely helped to set the path toward the discovery of irrational numbers, and continue to the present day, pausing to ponder such questions as, 'Is the decimal expansion of an irrational number random?'"---Anna Kuchment, Scientific American "The Irrationals is a true mathematician's and historian's delight."---Robert Schaefer, New York Journal of Books "From its lively introduction straight through to a rousing finish this is a book which can be browsed for its collection of interesting facts or studied carefully by anyone with an interest in numbers and their history. . . . This is a wonderful book which should appeal to a broad audience. Its level of difficulty ranges nicely from ideas accessible to high school students to some very deep mathematics. Highly recommended!"---Richard Wilders, MAA Reviews "It is a book that can be warmly recommended to any mathematician or any reader who is generally interested in mathematics. One should be prepared to read some of the proofs. Skipping all the proofs would do injustice to the concept, leaving just a skinny skeleton, but skipping some of the most advanced ones is acceptable. The style, the well documented historical context and quotations mixed with references to modern situations make it a wonderful read."---A. Bultheel, European Mathematical Society "To follow the mathematical sections of the book, the reader should have at least a second-year undergraduate mathematical background, as the author does not shrink from providing some detailed arguments. However, the presentation of historical material is given in modern mathematical form. Many readers will encounter unfamiliar and surprising material in this field in which much remains to be explored."---E. J. Barbeau, Mathematical Reviews Clippings "This is a well-written book to which senior high school students who do not intend to study mathematics at university should be exposed in their last two years at school. The ideas are challenging and provocative, with numerous clear diagrams. The topics are presented with numerous examples, and unobtrusive humour which renders the exposition even more palatable. The book would be an ideal source of ideas in a mathematics course within a liberal arts college because it links not only with the historical source of mathematics problems, but also with some of the great ideas of philosophy."---A. G. Shannon, Notes on Number Theory and Discrete Mathematics "Mathematicians and se

Humanity's ongoing quest to unlock the secrets of dark matter and dark energy Heart of Darkness describes the incredible saga of humankind's quest to unravel the deepest secrets of the universe. Over the past forty years, scientists have learned that two little-understood components-dark matter and dark energy-comprise most of the known cosmos, explain the growth of all cosmic structure, and hold the key to the universe's fate. The story of how evidence for the so-called "Lambda-Cold Dark Matter" model of cosmology has been gathered by generations of scientists throughout the world is told here by one of the pioneers of the field, Jeremiah Ostriker, and his coauthor Simon Mitton. From humankind's early attempts to comprehend Earth's place in the solar system, to astronomers' exploration of the Milky Way galaxy and the realm of the nebulae beyond, to the detection of the primordial fluctuations of energy from which all subsequent structure developed, this book explains the physics and the history of how the current model of our universe arose and has passed every test hurled at it by the skeptics. Throughout this rich story, an essential theme is emphasized: how three aspects of rational inquiry-the application of direct measurement and observation, the introduction of mathematical modeling, and the requirement that hypotheses should be testable and verifiable-guide scientific progress and underpin our modern cosmological paradigm. This monumental puzzle is far from complete, however, as scientists confront the mysteries of the ultimate causes of cosmic structure formation and the real nature and origin of dark matter and dark energy. Jeremiah P. Ostriker is professor of astrophysical sciences at Princeton University. His books include Formation of Structure in the Universe and Unsolved Problems in Astrophysics (Princeton). Simon Mitton is affiliated research scholar in the history and philosophy of science and a fellow of St. Edmund's College, University of Cambridge. His books include Fred Hoyle: A Life in Science and The Young Oxford Book of Astronomy. "The invisible rules the visible while the infinitesimal determines the cosmic. This is not fuzzy mysticism. It is the clear-eyed logic of the world observed by astronomers, described here with precision and verve by Ostriker and Mitton. Read this book and let them guide you to enlightenment."-Robert P. Kirshner, author of The Extravagant Universe "If you want a clear and fair assessment of the astonishing recent progress in understanding the cosmos-and of the mysteries that remain to be addressed-then this is the book for you. Ostriker and Mitton write with authority, and with style as well."-Martin Rees, Master of Trinity College, University of Cambridge, and Astronomer Royal "Heart of Darkness offers an engaging historical perspective on cosmology, and fluently moves onto the key modern issues in the dark sector. It is full of anecdotes and insights that will intrigue a general readership."-Joseph Silk, author of On the Shores of the Unknown: A Short History of the Universe "Heart of Darkness offers a fresh perspective on the development of cosmology from one of its pioneers and most original thinkers, Jeremiah Ostriker, in collaboration with an exceptional science writer, Simon Mitton. This engaging history introduces nonexperts to the discoveries and basic concepts behind our current understanding of the universe."-Abraham Loeb, author of How Did the First Stars and Galaxies Form? "Heart of Darkness is a penetrating and thorough narrative of how humans discovered the universe. Ostriker and Mitton are strong advocates for the tenacity and creativity of physicists and astronomers. This is an upbeat and inspiring story, told with vigor and enthusiasm."-Alan Dressler, author of Voyage to the Great Attractor: Exploring Intergalactic Space "In this stimulating study, the Princeton astrophysics professor and the University of Ca

Brian Greene is professor of physics and of mathematics at Columbia University. He is the author of the best-selling The Elegant Universe and The Fabric of the Cosmos. In 1921, five years after the appearance of his comprehensive paper on general relativity and twelve years before he left Europe permanently to join the Institute for Advanced Study, Albert Einstein visited Princeton University, where he delivered the Stafford Little Lectures for that year. These four lectures constituted an overview of his then-controversial theory of relativity. Princeton University Press made the lectures available under the title The Meaning of Relativity, the first book by Einstein to be produced by an American publisher. As subsequent editions were brought out by the Press, Einstein included new material amplifying the theory. A revised version of the appendix "Relativistic Theory of the Non-Symmetric Field," added to the posthumous edition of 1956, was Einstein's last scientific paper. "A condensed unified presentation intended for one who has already gone through a standard text and digested the mechanics of tensor theory and the physical basis of relativity. Einstein's little book then serves as an excellent tying-together of loose ends and as a broad survey of the subject."

Julian Havil is a retired former master at Winchester College, England, where he taught mathematics for thirty-three years. He received a Ph.D. in mathematics from Oxford University. Freeman Dyson is professor emeritus of physics at the Institute for Advanced Study in Princeton. He is the author of several books, including Disturbing the Universe and Origins of Life. Among the many constants that appear in mathematics, π, e, and i are the most familiar. Following closely behind is y, or gamma, a constant that arises in many mathematical areas yet maintains a profound sense of mystery. In a tantalizing blend of history and mathematics, Julian Havil takes the reader on a journey through logarithms and the harmonic series, the two defining elements of gamma, toward the first account of gamma's place in mathematics. Introduced by the Swiss mathematician Leonhard Euler (1707-1783), who figures prominently in this book, gamma is defined as the limit of the sum of 1 + 1/2 + 1/3 + . . . Up to 1/n, minus the natural logarithm of n--the numerical value being 0.5772156. . . . But unlike its more celebrated colleagues π and e, the exact nature of gamma remains a mystery--we don't even know if gamma can be expressed as a fraction. Among the numerous topics that arise during this historical odyssey into fundamental mathematical ideas are the Prime Number Theorem and the most important open problem in mathematics today--the Riemann Hypothesis (though no proof of either is offered!). Sure to be popular with not only students and instructors but all math aficionados, Gamma takes us through countries, centuries, lives, and works, unfolding along the way the stories of some remarkable mathematics from some remarkable mathematicians. "[A] wonderful book. . . . Havil's emphasis on historical context and his conversational style make this a pleasure to read. . . . Gamma is a gold mine of irresistible mathematical nuggets. Anyone with a serious interest in maths will find it richly rewarding."---Ben Longstaff, New Scientist "This book is a joy from start to finish."---Gerry Leversha, Mathematical Gazette "Wonderful. . . . Havil's emphasis on historical context and his conversational style make this a pleasure to read. . . .Gammais a gold mine of irresistible mathematical nuggets. Anyone with a serious interest in math will find it richly rewarding."--New Scientist"A joy from start to finish."--Mathematical Gazette"[Gamma] is not a book about mathematics, but a book of mathematics. . . . [It] is something like a picaresque novel; the hero, Euler's constantg, serves as the unifying motif through a wide range of mathematical adventures." "[Gamma] is enjoyable for many reasons. Here are just two. First, the explanations are not only complete, but they have the right amount of generality. . . . Second, the pleasure Havil has in contemplating this material is infectious." "It is only fitting that someone should write a book about gamma, or Euler's constant. Havil takes on this task and does an excellent job." "Mathematics is presented throughout as something connected to reality. . . . Many readers will find in [Gamma] exactly what they have been missing."---Mohammad Akbar, Plus Magazine "This book is written in an informal, engaging, and often amusing style. The author takes pains to make the mathematics clear. He writes about the mathematical geniuses of the past with reverence and awe. It is especially nice that the mathematical topics are discussed within a historical context."---Ward R. Stewart, Mathematics Teacher "I like this book very much. So much, in fact, that I found myself muttering 'neat stuff!' all the way through. While it is about an important topic, there isn't a single competitor. This amazing oversight by past authors is presumably the result of the topic requiring an author with a pretty sophisticated mathematical personality. Havil clearly has that. His skillful weaving of mathematics and history makes t

"Winner of the 2002 Award for Best Professional/Scholarly Book in Physics and Astronomy, Association of American Publishers" "Finalist for the 2003 Aventis General Prize" Robert P. Kirshner is the Clowes Professor of Science at Harvard University. The Extravagant Universe tells the story of a remarkable adventure of scientific discovery. One of the world's leading astronomers, Robert Kirshner, takes readers inside a lively research team on the quest that led them to an extraordinary cosmological discovery: the expansion of the universe is accelerating under the influence of a dark energy that makes space itself expand. In addition to sharing the story of this exciting discovery, Kirshner also brings the science up-to-date in a new epilogue. He explains how the idea of an accelerating universe--once a daring interpretation of sketchy data--is now the standard assumption in cosmology today. This measurement of dark energy--a quality of space itself that causes cosmic acceleration--points to a gaping hole in our understanding of fundamental physics. In 1917, Einstein proposed the "cosmological constant" to explain a static universe. When observations proved that the universe was expanding, he cast this early form of dark energy aside. But recent observations described first-hand in this book show that the cosmological constant--or something just like it--dominates the universe's mass and energy budget and determines its fate and shape. Warned by Einstein's blunder, and contradicted by the initial results of a competing research team, Kirshner and his colleagues were reluctant to accept their own result. But, convinced by evidence built on their hard-earned understanding of exploding stars, they announced their conclusion that the universe is accelerating in February 1998. Other lines of inquiry and parallel supernova research now support a new synthesis of a cosmos dominated by dark energy but also containing several forms of dark matter. We live in an extravagant universe with a surprising number of essential ingredients: the real universe we measure is not the simplest one we could imagine. "Kirshner is a talented writer, and both experts and general readers will find his book a consistently enjoyable read. . . . The Extravagant Universe is a personal book. . . . For the general reader interested in the excitement of how science is done, this strategy makes for a fascinating account. . . . The story . . . is irresistible in its own right, and is related with verve and good humor. . . . Books like this one will help inspire the next generation of physicists."---Sean Carroll, Nature "An extravagant and thoroughly enjoyable account of our amazing universe."---Michael S. Turner, Science "Robert Kirshner has written an excellent insider's account of the race to discover the fate of the cosmos. . . . Kirshner shows an impressively deft touch with complex explanations, and he doesn't hesitate to bridge gaps in the reader's knowledge with an apt metaphor. . . . The Extravagant Universe delivers the promise of its subtitle extremely well, and should serve as the definitive insider's story of how Kirshner led his motley group of astronomers to glory in their search to find the fate of the universe."---Donald Goldsmith, Natural History "Fellow astronomers--and generations of Harvard undergraduates--have long appreciated [Kirshner] as a raconteur of exceptional eloquence, so it is hard to imagine anyone better suited to give us the inside story on the new discoveries. [He] does not disappoint. He tells, in large part, a story of how improved technology has enabled astronomers to look farther into the distance and thus further into the past."---Laurence Marschall, Discover Magazine "The Extravagant Universe is hugely enjoyable. . . . It's wonderful . . . an entertaining and witty account of one of the biggest scientific stories of the past 10 years: how exploding supernovae show that the expansion of the Universe is accelerat

"One of Choice's Outstanding Academic Titles for 1999" "Honorable Mention for the 1998 Award for Best Professional/Scholarly Book in Mathematics, Association of American Publishers" Paul J. Nahin is professor emeritus of electrical engineering at the University of New Hampshire and the author of many best-selling popular math books, including The Logician and the Engineer and Will You Be Alive 10 Years from Now? (both Princeton). Today complex numbers have such widespread practical use--from electrical engineering to aeronautics--that few people would expect the story behind their derivation to be filled with adventure and enigma. In An Imaginary Tale, Paul Nahin tells the 2000-year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i. He recreates the baffling mathematical problems that conjured it up, and the colorful characters who tried to solve them. In 1878, when two brothers stole a mathematical papyrus from the ancient Egyptian burial site in the Valley of Kings, they led scholars to the earliest known occurrence of the square root of a negative number. The papyrus offered a specific numerical example of how to calculate the volume of a truncated square pyramid, which implied the need for i. In the first century, the mathematician-engineer Heron of Alexandria encountered I in a separate project, but fudged the arithmetic; medieval mathematicians stumbled upon the concept while grappling with the meaning of negative numbers, but dismissed their square roots as nonsense. By the time of Descartes, a theoretical use for these elusive square roots--now called "imaginary numbers"--was suspected, but efforts to solve them led to intense, bitter debates. The notorious i finally won acceptance and was put to use in complex analysis and theoretical physics in Napoleonic times. Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts and mathematical discussions, including the application of complex numbers and functions to important problems, such as Kepler's laws of planetary motion and ac electrical circuits. This book can be read as an engaging history, almost a biography, of one of the most evasive and pervasive "numbers" in all of mathematics. Some images inside the book are unavailable due to digital copyright restrictions. "A book-length hymn of praise to the square root of minus one."---Brian Rotman, Times Literary Supplement "An Imaginary Tale is marvelous reading and hard to put down. Readers will find that Nahin has cleared up many of the mysteries surrounding the use of complex numbers."---Victor J. Katz, Science "[An Imaginary Tale] can be read for fun and profit by anyone who has taken courses in introductory calculus, plane geometry and trigonometry."---William Thompson, American Scientist "Someone has finally delivered a definitive history of this 'imaginary' number. . . . A must read for anyone interested in mathematics and its history."---D. S. Larson, Choice "Attempting to explain imaginary numbers to a non-mathematician can be a frustrating experience. . . . On such occasions, it would be most useful to have a copy of Paul Nahin's excellent book at hand."---A. Rice, Mathematical Gazette "Imaginary numbers! Threeve! Ninety-fifteen! No, not those kind of imaginary numbers. If you have any interest in where the concept of imaginary numbers comes from, you will be drawn into the wonderful stories of how i was discovered."---Rebecca Russ, Math Horizons "There will be something of reward in this book for everyone."---R.G. Keesing, Contemporary Physics "Nahin has given us a fine addition to the family of books about particular numbers. It is interesting to speculate what the next member of the family will be about. Zero? The Euler constant? The square root of two? While we are waiting, we can enjoy An Imaginary Tale."---Ed Sandifer, MAA Online "Paul Nahin's book is a delightf

The remarkable scientific story of how Earth became an oxygenated planet The air we breathe is twenty-one percent oxygen, an amount higher than on any other known world. While we may take our air for granted, Earth was not always an oxygenated planet. How did it come to be this way? Donald Canfield covers this vast history, emphasizing its relationship to the evolution of life and the evolving chemistry of Earth. He guides readers through the various lines of scientific evidence, considers some of the wrong turns and dead ends along the way, and highlights the scientists and researchers who have made key discoveries in the field. Now with an incisive new preface by the author, Oxygen takes readers on an astonishing journey of discovery, telling the story of how our planet became oxygenated. Donald E. Canfield is professor of ecology at the University of Southern Denmark and a member of the National Academy of Sciences. "With humor and humanity, Oxygen captures the excitement of scientific discovery and describes the amazing natural history of how Earth's oxygenated atmosphere came to be."-Ed DeLong, Massachusetts Institute of Technology "A fascinating, accessible tour through the history of atmospheric oxygen, written by one of the world's top geobiologists. Canfield takes the reader from the anaerobic early Archean Earth up through the modern highly oxygenated environment, providing pointers to the relevant scientific literature along the way. Even experts in this field will learn things from his book."-James Kasting, author of How to Find a Habitable Planet "In Oxygen, Don Canfield recounts two epics in one-the evolution of breathable air over the entirety of Earth history, and the equally engaging account of how scientists have reconstructed this history from chemical details in ancient rocks. Even those who know the story well, or think they do, will find much food for thought."-Andrew Knoll, Harvard University, author of Life on a Young Planet: The First Three Billion Years of Evolution on Earth "Canfield takes us on a journey through the discovery of what produces oxygen, how oxygen evolved on the planet, and how that evolution influenced other aspects of planetary evolution. An enjoyable book."-Lee Kump, coauthor of The Earth System "This is a wonderful introduction to the most important event in Earth history-the rise of oxygen in the atmosphere. Canfield shares his broad and deep grasp of the field, his research leadership, his respect and admiration for the work of others, and his excitement and healthy skepticism about what we know-and still need to know."-Timothy W. Lyons, University of California, Riverside "[Canfield's] excellent descriptions of the scientific process show how competing hypotheses, and the scientists who present them, vie for supremacy. Canfield also offers a philosophical perspective: scientific understanding provides true insight into the structure of the natural world." "An engaging and authoritative primer on oxygen." "Concise and easily read, Oxygen provides an ideal starting block for those interested in learning about Earth's O2 history and, more broadly, the function and history of biogeochemical cycles. . . . The endnotes provide valuable entries for readers who wish to explore particular points in greater depth and, in other cases, enable brief digressions for interesting personal notes without disrupting the logical thread of a given concept. And the detailed bibliography captures a vast swath of the relevant primary literature. I highly recommend Canfield's book for anyone with even a remote interest in Earth history, as O2 singularly encompasses much of what makes our planet special."---Woodward W. Fischer, Science "This is the sort of science writing we would all do well to read more of. . . . Engage[s] with the ambiguity of a world where evidence is imperfect, knowledge evolves, and mistakes can be made in interpreting the data."---Ian Schef

"Winner of the 2006 Book Award in Science, Phi Beta Kappa" William F. Ruddiman is a paleoclimatologist and professor emeritus at the University of Virginia. The impact on climate from 200 years of industrial development is an everyday fact of life, but did humankind's active involvement in climate change really begin with the industrial revolution, as commonly believed? Plows, Plagues, and Petroleum has sparked lively scientific debate since it was first published--arguing that humans have actually been changing the climate for some 8,000 years--as a result of the earlier discovery of agriculture. The "Ruddiman Hypothesis" will spark intense debate. We learn that the impact of farming on greenhouse-gas levels, thousands of years before the industrial revolution, kept our planet notably warmer than if natural climate cycles had prevailed--quite possibly forestalling a new ice age. Plows, Plagues, and Petroleum is the first book to trace the full historical sweep of human interaction with Earth's climate. Ruddiman takes us through three broad stages of human history: when nature was in control; when humans began to take control, discovering agriculture and affecting climate through carbon dioxide and methane emissions; and, finally, the more recent human impact on climate change. Along the way he raises the fascinating possibility that plagues, by depleting human populations, also affected reforestation and thus climate--as suggested by dips in greenhouse gases when major pandemics have occurred. While our massive usage of fossil fuels has certainly contributed to modern climate change, Ruddiman shows that industrial growth is only part of the picture. The book concludes by looking to the future and critiquing the impact of special interest money on the global warming debate. In the afterword, Ruddiman explores the main challenges posed to his hypothesis, and shows how recent investigations and findings ultimately strengthen the book's original claims. "[A]n excellent book summarizing and placing in context the age-old influence of humans on atmospheric composition, climate and global warming." "If you're not familiar with Ruddiman's hypothesis, you should be. . . . Plows, Plagues, and Petroleum is excellent reading for scientist and nonscientist alike."---James White, Science "Ruddiman's argument makes it clear that there is no 'natural' baseline of climate in the late Holocene from which to reckon the human impact of the past two centuries."---Wolfgang H. Berger, American Scientist "What is most remarkable about Ruddiman's work is the evidence it provides for an initial disruption to the climate system that occurred long before the industrial revolution--around 8,000 years ago. . . . Ruddiman's realisation that the gaseous composition of Earth's atmosphere is an exquisitely sensitive barometer of changes to life itself represents a great breakthrough."---Tim Flannery, Guardian "William Ruddiman's provocative but plausible conclusion is that the economic behavior of humans began to profoundly influence global climate roughly 8000 years ago. . . . Ruddiman's book has already begun to spark an important debate--a debate which economic historians should be eager to follow and join."---Robert Whaples, EH.net "This well-written book does a great job of summarizing complex topics through simple calculations and examples, and provides the right balance of cultural background and scientific data."---Matthew S. Lachniet, Geotimes "The book by Ruddiman is very enjoyable and easy to read. It also takes quite a unique perspective on the relationship between human societies and climate. For Ruddiman, rather than the climate being a determinant of the course of human events, the argument is turned on its head making human economic behavior a cause of climate change, even well into distant antiquity."---Arlene Miller Rosen, Nature and Culture "Ruddiman's short book is an excellent primer on the various influences on global climate. He

The first popular history of irrational numbers and their discoverers, from ancient Greece to the twenty-first century The ancient Greeks discovered them, but it wasn't until the nineteenth century that irrational numbers were properly understood and rigorously defined, and even today not all their mysteries have been revealed. In The Irrationals, the first popular and comprehensive book on the subject, Julian Havil tells the story of irrational numbers and the mathematicians who have tackled their challenges, from antiquity to the twenty-first century. Along the way, he explains why irrational numbers are surprisingly difficult to define-and why so many questions still surround them. Fascinating and illuminating, this is a book for everyone who loves math and the history behind it.

Robin Wilson is emeritus professor of pure mathematics at the Open University and emeritus professor of geometry at Gresham College, London. He has written and edited many books on topics ranging from graph theory and combinatorics, via sudoku, philately, and the Gilbert and Sullivan operas, to the history of mathematics. He is currently president of the British Society for the History of Mathematics. On October 23, 1852, Professor Augustus De Morgan wrote a letter to a colleague, unaware that he was launching one of the most famous mathematical conundrums in history--one that would confound thousands of puzzlers for more than a century. This is the amazing story of how the "map problem" was solved. The problem posed in the letter came from a former student: What is the least possible number of colors needed to fill in any map (real or invented) so that neighboring counties are always colored differently? This deceptively simple question was of minimal interest to cartographers, who saw little need to limit how many colors they used. But the problem set off a frenzy among professional mathematicians and amateur problem solvers, among them Lewis Carroll, an astronomer, a botanist, an obsessive golfer, the Bishop of London, a man who set his watch only once a year, a California traffic cop, and a bridegroom who spent his honeymoon coloring maps. In their pursuit of the solution, mathematicians painted maps on doughnuts and horseshoes and played with patterned soccer balls and the great rhombicuboctahedron. It would be more than one hundred years (and countless colored maps) later before the result was finally established. Even then, difficult questions remained, and the intricate solution--which involved no fewer than 1,200 hours of computer time--was greeted with as much dismay as enthusiasm. Providing a clear and elegant explanation of the problem and the proof, Robin Wilson tells how a seemingly innocuous question baffled great minds and stimulated exciting mathematics with far-flung applications. This is the entertaining story of those who failed to prove, and those who ultimately did prove, that four colors do indeed suffice to color any map. This new edition features many color illustrations. It also includes a new foreword by Ian Stewart on the importance of the map problem and how it was solved. "The simplicity of the four-color conjecture is deceptive. Just how deceptive is made clear by Robin Wilson's delightful history of the quest to resolve it. . . . Four Colors Suffice is strewn with good anecdotes, and the author . . . proves himself skillful at making the mathematics accessible."---Jim Holt, New York Review of Books "Wilson's lucid history weaves together lively anecdotes, biographical sketches, and a non-technical account of the mathematics." "Earlier books . . . relate some of the relevant history in their introductions, but they are primarily technical. In contrast, Four Colors Suffice is a blend of history anecdotes and mathematics. Mathematical arguments are presented in a clear, colloquial style, which flows gracefully."---Daniel S. Silver, American Scientist "Robin Wilson appeals to the mathematical novice with an unassuming lucidity. It's thrilling to see great mathematicians fall for seductively simple proofs, then stumble on equally simple counter-examples. Or swallow their pride."---Jascha Hoffman, The Boston Globe "A thoroughly accessible history of attempts to prove the four-color theorem. Wilson defines the problem and explains some of the methods used by those trying to solve it. His descriptions of the contributions made by dozens of dedicated, and often eccentric, mathematicians give a fascinating insight into how mathematics moves forward, and how approaches have changed over the past 50 years. . . . It's comforting to know that however indispensable computers become, there will always be a place for the delightfully eccentric mathematical mind. Let's hope that Robin

Martin Rees is Astronomer Royal of Great Britain, a Fellow of Trinity College, Cambridge, a former director of the Cambridge Institute of Astronomy and author, most recently, of the bestselling Just Six Numbers: The Deep Forces That Shape the Universe. Our universe seems strangely ''biophilic,'' or hospitable to life. Is this happenstance, providence, or coincidence? According to cosmologist Martin Rees, the answer depends on the answer to another question, the one posed by Einstein's famous remark: ''What interests me most is whether God could have made the world differently.'' This highly engaging book explores the fascinating consequences of the answer being ''yes.'' Rees explores the notion that our universe is just a part of a vast ''multiverse,'' or ensemble of universes, in which most of the other universes are lifeless. What we call the laws of nature would then be no more than local bylaws, imposed in the aftermath of our own Big Bang. In this scenario, our cosmic habitat would be a special, possibly unique universe where the prevailing laws of physics allowed life to emerge. Rees begins by exploring the nature of our solar system and examining a range of related issues such as whether our universe is or isn't infinite. He asks, for example: How likely is life? How credible is the Big Bang theory? Rees then peers into the long-range cosmic future before tracing the causal chain backward to the beginning. He concludes by trying to untangle the paradoxical notion that our entire universe, stretching 10 billion light-years in all directions, emerged from an infinitesimal speck. As Rees argues, we may already have intimations of other universes. But the fate of the multiverse concept depends on the still-unknown bedrock nature of space and time on scales a trillion trillion times smaller than atoms, in the realm governed by the quantum physics of gravity. Expanding our comprehension of the cosmos, Our Cosmic Habitat will be read and enjoyed by all those--scientists and nonscientists alike--who are as fascinated by the universe we inhabit as is the author himself. "[This book] has an informal style and breadth of coverage that make it a joy to read. . . . Rees's explanations are exactly right."---William G. Unruh, Science "Rees provides a nice summary of how we got here, how the universe began and how it might end. . . . Lay readers will appreciate Rees' clear, uncomplicated prose, even when dealing with tough stuff that leaves most physicists tongue-tied. Most welcome of all, he explains how scientists know what they claim to know."---K.C. Cole, Los Angeles Times "[An] awe-inspiring survey. . . . Rees is not only a world-class cosmologist but one of our best living science writers."---John Cornwell, Sunday Times "Probably the clearest and most easily understandable account of our Universe available."---Ian Morison, New Scientist "Our very own Astronomer Royal blasts off into space, in velvety, friendly prose. His musings on the possibilities of alien life and of time travel, the necessity to colonise space, and a vision of the far future make for a pleasingly concise and always intriguing tour d'horizon."---Steven Poole, The Guardian "In the crowded field of popular writing about the universe, Rees is genuinely in the forefront--an accomplished scientist with the superior writing skills. . . . He exudes the instinctual curiosity we all possess when looking upward, and he focuses that wonderment on the narrow range of cosmological numbers that allow us to ruminate about it all. A wonderfully appealing presentation." "There is a lot of stuff in the universe--the estimated number of stars is 10 followed by 22 zeros. But as to whether there are other planets with life like Earth's, Rees says the chance of two similar ecologies is less than the chance of two randomly typing monkeys producing the same Shakespearean play."---George F. Will, The Washington Post "In the instant after the big bang, there was only a o

In It's About Time, N. David Mermin asserts that relativity ought to be an important part of everyone's education-after all, it is largely about time, a subject with which all are familiar. The book reveals that some of our most intuitive notions about time are shockingly wrong, and that the real nature of time discovered by Einstein can be rigorously explained without advanced mathematics. This readable exposition of the nature of time as addressed in Einstein's theory of relativity is accessible to anyone who remembers a little high school algebra and elementary plane geometry. The book evolved as Mermin taught the subject to diverse groups of undergraduates at Cornell University, none of them science majors, over three and a half decades. Mermin's approach is imaginative, yet accurate and complete. Clear, lively, and informal, the book will appeal to intellectually curious readers of all kinds, including even professional physicists, who will be intrigued by its highly original approach.

Paul G. Falkowski holds the Bennett L. Smith Chair in Business and Natural Resources at Rutgers University, where he studies how microbes have shaped the history of Earth. The marvelous microbes that made life on Earth possible and support our very existence For almost four billion years, microbes had the primordial oceans all to themselves. The stewards of Earth, these organisms transformed the chemistry of our planet to make it habitable for plants, animals, and us. Life's Engines takes readers deep into the microscopic world to explore how these marvelous creatures made life on Earth possible-and how human life today would cease to exist without them. Paul Falkowski looks "under the hood" of microbes to find the engines of life, the actual working parts that do the biochemical heavy lifting for every living organism on Earth. With insight and humor, he explains how these miniature engines are built-and how they have been appropriated by and assembled like Lego sets within every creature that walks, swims, or flies. Falkowski shows how evolution works to maintain this core machinery of life, and how we and other animals are veritable conglomerations of microbes. A vibrantly entertaining book about the microbes that support our very existence, Life's Engines will inspire wonder about these elegantly complex nanomachines that have driven life since its origin. It also issues a timely warning about the dangers of tinkering with that machinery to make it more "efficient" at meeting the ever-growing demands of humans in the coming century. "A work full of surprises. . . . Immensely rewarding."---Tim Flannery, New York Review of Books "Entertaining, easy-to-read and historically rich."---Adrian Woolfson, Nature "Personal stories, hard facts, and illuminative illustrations each contribute to this engaging examination of our microbial overlords . . . Paul Falkowski's decades of study in various earth and life sciences fuel this excellent addition. . . . Falkowski effectively uses analogies to convey abstract and complicated ideas."---Rachel Jagareski, Foreword Reviews "Falkowski's loving examination sets out, life on this planet is organized by and for bacteria--the rest of us are just along for the ride."---Brian Bethune, Macleans "Falkowski brings a formidable breadth of scientific understanding to the task of explaining this, having worked as a biologist, an oceanographer and an astrobiologist. He moves easily between biological and earth sciences to help us understand the steps microscopic single-celled organisms took to make the planet habitable." "{The} wonderful and awe-inspiring universe of the microbes, unseen creatures that have shaped the planet such that we may live in it, is engagingly presented by Paul Falkowski in a remarkable text entitled Life's Engines. . . . The book's success is its utter simplicity. It tells the story of the history of life on our planet from a very personal perspective. . . . I was so enthralled by this book from the get-go that I invite you to have a short taste of it."---Roberto Kolter, Cell "A pleasure to read, the book touches on virtually every topic covered in a college biology curriculum by seamlessly weaving concepts with personal anecdotes and analogies. Presenting scientific facts and the fascinating history of their discovery, Falkowski (Rutgers Univ.) intersperses evolutionary theory with biochemistry, ecology, microbiology, molecular biology, anatomy, and even anthropology and economics. He also presents a fact-based, nonpolitical vision for the future of biotechnology. . . . This reviewer came away inspired to learn more. Easily understood by anyone with a passing knowledge of science, this volume poses innumerable questions for further investigation." "What is known about the hidden world of the microbes and their fundamental roles in sustaining planetary habitability is insightfully revealed by Paul Falkowski in this authoritative, comprehensive, and delightful book

Claus Emmeche, a Danish theoretical biologist, is a Research Fellow at the Center of Cognitive Science, University of Roskilde. He is also Guest Scientist and a reader at the Niels Bohr Institute, University of Copenhagen, and is the author of several books on biology. What is life? Is it just the biologically familiar--birds, trees, snails, people--or is it an infinitely complex set of patterns that a computer could simulate? What role does intelligence play in separating the organic from the inorganic, the living from the inert? Does life evolve along a predestined path, or does it suddenly emerge from what appeared lifeless and programmatic? In this easily accessible and wide-ranging survey, Claus Emmeche outlines many of the challenges and controversies involved in the dynamic and curious science of artificial life. Emmeche describes the work being done by an international network of biologists, computer scientists, and physicists who are using computers to study life as it could be, or as it might evolve under conditions different from those on earth. Many artificial-life researchers believe that they can create new life in the computer by simulating the processes observed in traditional, biological life-forms. The flight of a flock of birds, for example, can be reproduced faithfully and in all its complexity by a relatively simple computer program that is designed to generate electronic "boids." Are these "boids" then alive? The central problem, Emmeche notes, lies in defining the salient differences between biological life and computer simulations of its processes. And yet, if we can breathe life into a computer, what might this mean for our other assumptions about what it means to be alive? The Garden in the Machine touches on every aspect of this complex and rapidly developing discipline, including its connections to artificial intelligence, chaos theory, computational theory, and studies of emergence. Drawing on the most current work in the field, this book is a major overview of artificial life. Professionals and nonscientists alike will find it an invaluable guide to concepts and technologies that may forever change our definition of life. "Emmeche's account goes beyond describing (with appropriate awe) the accomplishments of computer biology to raise the crucial question of whether the new metaphor of the machine can be extended ... to the whole of nature." "A serious, sensible introduction to an exciting new field. It is not every day that one can see science fiction clash with natural philosophy in such a civilized fashion." "Can life be synthesized? Emmeche suggests in his fascinating book an approach to this question by means of computer simulation of living processes ... {and} tackles the posed questions with great insight."

Stephen R. Palumbi is Professor of Biology at Stanford University. Anthony R. Palumbi, Stephen's son, is a science writer and novelist whose work has appeared in the Atlantic and other publications. A thrilling tour of the sea's most extreme species, coauthored by one of the world's leading marine scientists The ocean teems with life that thrives under difficult situations in unusual environments. The Extreme Life of the Sea takes readers to the absolute limits of the ocean world-the fastest and deepest, the hottest and oldest creatures of the oceans. It dives into the icy Arctic and boiling hydrothermal vents-and exposes the eternal darkness of the deepest undersea trenches-to show how marine life thrives against the odds. This thrilling book brings to life the sea's most extreme species, and tells their stories as characters in the drama of the oceans. Coauthored by Stephen Palumbi, one of today's leading marine scientists, The Extreme Life of the Sea tells the unforgettable tales of some of the most marvelous life forms on Earth, and the challenges they overcome to survive. Modern science and a fluid narrative style give every reader a deep look at the lives of these species. The Extreme Life of the Sea shows you the world's oldest living species. It describes how flying fish strain to escape their predators, how predatory deep-sea fish use red searchlights only they can see to find and attack food, and how, at the end of her life, a mother octopus dedicates herself to raising her batch of young. This wide-ranging and highly accessible book also shows how ocean adaptations can inspire innovative commercial products-such as fan blades modeled on the flippers of humpback whales-and how future extremes created by human changes to the oceans might push some of these amazing species over the edge. "This gem of a book by marine biologist Stephen Palumbi and his son, science writer Anthony Palumbi, finds enough weirdness in the ocean to feed creativity for generations to come. . . . The Palumbis' writing is a wonderful mix of meticulous science and creative panache. . . . A joy whether read at one sitting, or dipped in and out of to prolong the pleasure."---Callum Roberts, Nature "From 'immortal' jellyfish that age in reverse, to zombie bone worms that eat the skeletons of dead whales, the ocean is full of bizarre characters. Biologist Stephen Palumbi and his science writer son, Anthony, profile the most unusual specimens. Chapters cover the smallest, the oldest, the hottest and the coldest species, among others, and the landscape of strange creatures is brought to life by charming writing."---Clara Moskowitz, Scientific American "The Palumbis probe life in the depths of the oceans and in tide waters in successive chapters spotlighting the long-lived Bowhead whale; sea species that adapt to extremely high temperatures and others to cold; clownfish, which change gender, becoming male or female as circumstances dictate; and much more. The authors end with a warning that the oceans contain a complex ecology in which each species 'thrives in its easily disrupted specialized niche.'. . . A sparkling appreciation of the wonderful variety of marine life that also communicates an important message." "The book reads like an action-adventure novel. . . . This approach is a pleasant departure from dull textbook prose. It will delight readers who lack scientific credentials but yearn to understand the diversity of life in the oceans. The text demystifies, mystifies, and amazes."---Geraldine Richards, ForeWord Reviews "Highlighting the strangest cases in animate sea life, marine ecologist S.R. Palumbi exudes a palpable and contagious sense of delight as he enlists his writer son's help to fill the 'gap in character development' in the story of the ocean's robust yet fragile ecosystems. . . . By showing how each creature is so tightly tied to its environment, the authors are able to effectively demonstrate how small human-d

Laurence A. Marschall is Professor of Physics at Gettysburg College and the editor of CCD Astronomy. He is a contributor to The Sciences, Astronomy, Harper's, The New York Times Book Review, and Air and Space. Astronomers believe that a supernova is a massive explosion signaling the death of a star, causing a cosmic recycling of the chemical elements and leaving behind a pulsar, black hole, or nothing at all. In an engaging story of the life cycles of stars, Laurence Marschall tells how early astronomers identified supernovae, and how later scientists came to their current understanding, piecing together observations and historical accounts to form a theory, which was tested by intensive study of SN 1987A, the brightest supernova since 1006. He has revised and updated The Supernova Story to include all the latest developments concerning SN 1987A, which astronomers still watch for possible aftershocks, as well as SN 1993J, the spectacular new event in the cosmic laboratory. "Marschall's supernova book is a superb piece of writing; it reads almost as easily as a good novel." "A wondrous romp through astro-physics written by an expert guide." "This is a wonderful book about science, about astronomy, and, of course, about supernovae." "A superb piece of writing; it reads almost as easily as a good novel."

Pierre Duhem (1861-1916) is best known in science for his work in thermodynamics and in history of science for his treatment of the Middle Ages. He was Professor of Physics at the University of Bordeaux This classic work in the philosophy of physical science is an incisive and readable account of the scientific method. Pierre Duhem was one of the great figures in French science, a devoted teacher, and a distinguished scholar of the history and philosophy of science. This book represents his most mature thought on a wide range of topics. "The central proposition of this famous book is that physical theories are conventions serving to economize scientific thought rather than descriptions or explanations of the way the world is made. The work remains intensely alive in a climate of opinion in which strong skepticism about scientific realism is motivated by social and political considerations that could scarcely be more at variance with Duhem's ultra-Catholic conservatism. The introduction by Jules Vuillemin, at once expository and critical, is the clearest commentary on Duhem's philosophy of science that I have had the pleasure of reading. Duhem's phenomenalism, Vuillemin points out, distinguishes between humanity and nature and opposes the naturalism that would make reason merely an aspect of the natural processes it studies."-Charles C. Gillispie, Da}ton-Stockton Professor of History of Science Emeritus, Princeton University,

Geerat J. Vermeij is Distinguished Professor of Earth and Planetary Sciences at the University of California, Davis. He is the author of The Evolutionary World: How Adaptation Explains Everything from Seashells to Civilization; Privileged Hands: A Scientific Life; Nature: An Economic History (Princeton); and Evolution and Escalation: An Ecological History of Life (Princeton). From "one of the master naturalists of our time" (American Scientist), a fascinating exploration of what seashells reveal about biology, evolution, and the history of life Geerat Vermeij wrote this "celebration of shells" to share his enthusiasm for these supremely elegant creations and what they can teach us about nature. Most popular books on shells emphasize the identification of species, but Vermeij uses shells as a way to explore major ideas in biology. How are shells built? How do they work? And how did they evolve? With lucidity and charm, the MacArthur-winning evolutionary biologist reveals how shells give us insights into the lives of animals today and in the distant geological past. "Vermeij provides an elegantly written and beautifully illustrated account of shell construction, function and evolution, while showing how these molluscan houses give us insights into ecology and the history of life. A book that will be treasured by scientists and lay readers alike." "A fascinating biological view of shells as the products of living organisms. . . . We come to appreciate and understand the diverse wonders of economy, function and construction that can be seen in shells."---Douglas Palmer, New Scientist "This is a pleasingly different book. Most other popular books on shells help one to identify them. In this book Vermeij uses shells to help understand the ecology, evolution, and history of snails, clams, and other Mollusca, the phylum of animals that construct 'shells.' . . . This book uses both contemporary and fossil shells to explore many ideas and processes in general biology. . . . I have been seeking this book for years." "I was swept away by the world of molluscs and found myself fascinated and informed. . . . By the end of the book I was convinced that anyone with a passion for their subject would enjoy and be educated by Vermeij's obvious passion for his."

The late John Napier was a physician specializing in hands, and was also a professor and writer on primates and evolution. Russell H. Tuttle is Professor of Anthropology at the University of Chicago. Intended for all readers--including magicians, detectives, musicians, orthopedic surgeons, and anthropologists--this book offers a thorough account of that most intriguing and most human of appendages: the hand. In this illustrated work, John Napier explores a wide range of absorbing subjects such as fingerprints, handedness, gestures, fossil remains, and the making and using of tools. "Maybe Newton was right about the thumb [that it was evidence of God's existence], but there is far more to arouse wonder in the hand than he knew, and Dr. Napier indicates its scope with authority and imagination." "[John Napier's] book is deliberately 'not too technical,' light and full of wit. . . . Fingerprints, gestures, nerves, bone, hand hair--all are given attention . . . in this interesting survey." "Each fascinating chapter in this book is a conjured mixture of anecdote, entertainment, and instruction."

"One of Times Higher Education's Best Books of 2015" Gary Marcus is professor emeritus of psychology and neural science at New York University. His books include Guitar Zero: The Science of Becoming Musical at Any Age and Kluge: The Haphazard Evolution of the Human Mind. Jeremy Freeman is a neuroscientist at the Howard Hughes Medical Institute's Janelia Farm Research Campus. The world's top experts take readers to the very frontiers of brain science Includes a chapter by 2014 Nobel laureates May-Britt Moser and Edvard Moser An unprecedented look at the quest to unravel the mysteries of the human brain, The Future of the Brain takes readers to the absolute frontiers of science. Original essays by leading researchers such as Christof Koch, George Church, Olaf Sporns, and May-Britt and Edvard Moser describe the spectacular technological advances that will enable us to map the more than eighty-five billion neurons in the brain, as well as the challenges that lie ahead in understanding the anticipated deluge of data and the prospects for building working simulations of the human brain. A must-read for anyone trying to understand ambitious new research programs such as the Obama administration's BRAIN Initiative and the European Union's Human Brain Project, The Future of the Brain sheds light on the breathtaking implications of brain science for medicine, psychiatry, and even human consciousness itself. Contributors include: Misha Ahrens, Ned Block, Matteo Carandini, George Church, John Donoghue, Chris Eliasmith, Simon Fisher, Mike Hawrylycz, Sean Hill, Christof Koch, Leah Krubitzer, Michel Maharbiz, Kevin Mitchell, Edvard Moser, May-Britt Moser, David Poeppel, Krishna Shenoy, Olaf Sporns, Anthony Zador. "An awe-inspiring treasure trove of progress reports, frank opinions and exciting predictions from eminent neuroscientists of all genres."---Georgina Rippon, Times Higher Education "Thought-provoking arguments for the future of the brain and the implications on ethics and human behavior. . . . A fascinating book for readers of all levels." "Dispatches from the scientific minds at the forefront of the quest to map and understand the myriad neural connections that constitute evolution's most curious creation, the essays that make up The Future of the Brain serve as great primers in topics scientific and logistical: from memory and consciousness to the computer modeling of neural complexities to big-data analysis."---Bob Grant, The Scientist "A book called The Future of the Brain: Essays by the World's Leading Neuroscientists cannot have modest ambitions. The editors and authors of this collection of essays do not disappoint on that score, taking a broad, well-informed view of recent and potential advances in neuroscience and their implications for the field."---Sandra Aamodt, Nature Neuroscience "{The Future of the Brain} will leave readers both amazed and full of questions."---Richard Cytowic, New York Journal of Books "The Future of the Brain offers a broad spectrum of introductions to different fields of current neuroscience research, perfect for readers interested in going beyond basic neuroscience."---Chris Kaperak, The Daily "A wonderful way to launch yourself into the exciting world of twenty-first-century neuroscience, whether you are a scientist or an intellectually curious layperson. The power in this sampler is that the coverage is not just technical but conceptual: the essays probe the ways in which an understanding of the brain will and won't illuminate the mind, and they do so with depth and balance rather than the usual breathless hype."-Steven Pinker, author of The Language Instinct and How the Mind Works "Have you ever wondered what's coming around the bend in terms of new insights into how the brain works? Open the pages of The Future of the Brain to find out. Gary Marcus and Jeremy Freeman have brought together some of the leading thinkers and researchers to share their vision of where we are headed. It

In Reinventing Discovery, Michael Nielsen argues that we are living at the dawn of the most dramatic change in science in more than 300 years. This change is being driven by powerful new cognitive tools, enabled by the internet, which are greatly accelerating scientific discovery. There are many books about how the internet is changing business or the workplace or government. But this is the first book about something much more fundamental: how the internet is transforming the nature of our collective intelligence and how we understand the world. Reinventing Discovery tells the exciting story of an unprecedented new era of networked science. We learn, for example, how mathematicians in the Polymath Project are spontaneously coming together to collaborate online, tackling and rapidly demolishing previously unsolved problems. We learn how 250,000 amateur astronomers are working together in a project called Galaxy Zoo to understand the large-scale structure of the Universe, and how they are making astonishing discoveries, including an entirely new kind of galaxy. These efforts are just a small part of the larger story told in this book--the story of how scientists are using the internet to dramatically expand our problem-solving ability and increase our combined brainpower. This is a book for anyone who wants to understand how the online world is revolutionizing scientific discovery today--and why the revolution is just beginning.

David S. Richeson is professor of mathematics at Dickinson College. How a simple equation reshaped mathematics Leonhard Euler's polyhedron formula describes the structure of many objects-from soccer balls and gemstones to Buckminster Fuller's buildings and giant all-carbon molecules. Yet Euler's theorem is so simple it can be explained to a child. From ancient Greek geometry to today's cutting-edge research, Euler's Gem celebrates the discovery of Euler's beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. Using wonderful examples and numerous illustrations, David Richeson presents this mathematical idea's many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map. Filled with a who's who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem's development, Euler's Gem will fascinate every mathematics enthusiast. This paperback edition contains a new preface by the author. "Everything in the book is very well illustrated with insightful graphics that, together with the text, make results almost like being obvious."---Adhemar Bultheel, European Mathematical Society "The author has achieved a remarkable feat, introducing a naïve reader to a rich history without compromising the insights and without leaving out a delicious detail. . . . An awe-inspiring experience."-Choice "This is an excellent book about a great man and a timeless formula."-Charles Ashbacher, Journal of Recreational Mathematics "It was a pleasure reading this book, and I recommend it to everyone who is not afraid of mathematical arguments and has ever wondered what this field of 'rubbersheet geometry' is about. You will not be disappointed."-Jeanine Daems, Mathematical Intelligencer "David Richeson's Euler's Gem does an outstanding job of explaining serious mathematics to a general audience. . . . The book succeeds at showing the reader a lot of attractive mathematics with a well-chosen level of technical detail."-Jeremy L. Martin, Notices of the AMS

"Winner of the 2011 Award for Excellence in Biology & Life Sciences, Association of American Publishers" "One of Choice's Outstanding Academic Titles for 2012" Patricia S. Churchland is professor emerita of philosophy at the University of California, San Diego, and an adjunct professor at the Salk Institute. Her books include Brain-Wise and Neurophilosophy. A provocative new account of how morality evolved What is morality? Where does it come from? And why do most of us heed its call most of the time? In Braintrust, neurophilosophy pioneer Patricia Churchland argues that morality originates in the biology of the brain. She describes the "neurobiological platform of bonding" that, modified by evolutionary pressures and cultural values, has led to human styles of moral behavior. The result is a provocative genealogy of morals that asks us to reevaluate the priority given to religion, absolute rules, and pure reason in accounting for the basis of morality. Moral values, Churchland argues, are rooted in a behavior common to all mammals-the caring for offspring. The evolved structure, processes, and chemistry of the brain incline humans to strive not only for self-preservation but for the well-being of allied selves-first offspring, then mates, kin, and so on, in wider and wider "caring" circles. Separation and exclusion cause pain, and the company of loved ones causes pleasure; responding to feelings of social pain and pleasure, brains adjust their circuitry to local customs. In this way, caring is apportioned, conscience molded, and moral intuitions instilled. A key part of the story is oxytocin, an ancient body-and-brain molecule that, by decreasing the stress response, allows humans to develop the trust in one another necessary for the development of close-knit ties, social institutions, and morality. A major new account of what really makes us moral, Braintrust challenges us to reconsider the origins of some of our most cherished values. "{Patricia Churchland} finds that morality is all about empathy. . . . Churchland is also 'biological' about morality, seeing it as an adaptation that our brains have evolved in order to cement social ties. With a series of examples, she rejects the idea that morality is a set of rules and codes handed down from on high, without which we would all behave badley."---Matt Ridley, Wall Street Journal "Churchland's discussion puts . . . areas of research prone to over-interpretation into much-needed perspective. . . . In my view, by illuminating the biological foundations on which caring, cooperation and social understanding are based, and by arguing against simplistic views about innateness and divine ordination, Churchland has delineated the conceptual space still to be navigated concerning which actions are morally right, how we come to those decisions, and how we justify them."---Adina L. Roskies, Nature "Churchland provides an important service in Braintrust by applying recent scientific research to moral concerns."---Richard S. Mathis, Science "Intriguing. . . . The puzzle that concerns {Churchland} above all is whether morality can be explained or justified by science."---Margaret A. Boden, Times Higher Education "Churchland's superbly written, dense-with-thinking book is fiercely alert to what can and cannot justifiably be inferred from modern science. She is a brilliantly precise (and often slyly funny) demolisher of exaggerated claims."---Steven Poole, Guardian "Churchland, by insisting that morality is neither an innate instinct nor an abstract system, but rather a tough, practical problem posed by our instincts, is bringing together the best in both neuroscientific and philosophical thinking."---Josh Rothman, Boston Globe's Brainiac blog "What is morality? Where does it come from? According to neurophilosopher Patricia S. Churchland in her book Braintrust, morality originates in the brain. She argues that over time the human brain evolved to feel social pain and pleasure.

"One of Choice's Outstanding Academic Titles for 1997" Florin Diacu is Associate Professor of Mathematics at the University of Victoria in Canada. Philip Holmes, a Fellow of the American Academy of Arts and Sciences, is Professor of Mechanics and Applied Mathematics at Princeton University, where he directs the Program in Applied and Computational Mathematics. Celestial Encounters is for anyone who has ever wondered about the foundations of chaos. In 1888, the 34-year-old Henri Poincaré submitted a paper that was to change the course of science, but not before it underwent significant changes itself. "The Three-Body Problem and the Equations of Dynamics" won a prize sponsored by King Oscar II of Sweden and Norway and the journal Acta Mathematica, but after accepting the prize, Poincaré found a serious mistake in his work. While correcting it, he discovered the phenomenon of chaos. Starting with the story of Poincaré's work, Florin Diacu and Philip Holmes trace the history of attempts to solve the problems of celestial mechanics first posed in Isaac Newton's Principia in 1686. In describing how mathematical rigor was brought to bear on one of our oldest fascinations--the motions of the heavens--they introduce the people whose ideas led to the flourishing field now called nonlinear dynamics. In presenting the modern theory of dynamical systems, the models underlying much of modern science are described pictorially, using the geometrical language invented by Poincaré. More generally, the authors reflect on mathematical creativity and the roles that chance encounters, politics, and circumstance play in it. "{S}tories about the history of celestial mechanics are the subject of this delightful book. The authors interweave numerous anecdotes about the personalities involved in the discoveries with technical details of the mathematical ideas themselves. . . . a pleasant mix of things technical and things historical. . . . written in a lively and informative way."---Robert L. Devaney, Science "This book, which should be required reading for every nonspecialist astronomer, may well be headed toward becoming a classic." "A particular strength of Celestial Encounters is the impression, conveyed with a deft touch, that mathematics is an international and collective effort made by real people for real reasons in the real world. All the players in the drama, alive or dead, come over as human beings who happen to have a passion for mathematics and an ability to fulfill that passion. This feature alone justifies buying the book."---Ian Stewart, New Scientist "A lively introduction to the fascinating story of celestial mechanics."---Jacques Laskar, Nature "Throughout the book one finds a vital quality that derives from the authors' real success in presenting mathematics as a human endeavor.... A valuable and accessible contribution to the chaos literature."---June Barrow-Green, Isis "A pleasant mix of things technical and things historical.... Written in a lively and informative way."---Robert Devaney, Science "An excellent book combining scientific integrity and popular appeal."-Steve Smale, City University of Hong Kong

Niles Eldredge is the Curator of the Department of Invertebrates at the American Museum of Natural History. Like the bird whose death signaled dangerous conditions in a mine, the demise of animals that once flourished should give humans pause. How is our fate linked to the earth's creatures, and the cycle of flourishing and extinction? Which are the simple workings of nature's order, and which are omens of ecological disaster? Does human activity accelerate extinction? What really causes it? In an illuminating and elegantly written account of the widespread reduction of the world's wildlife, renowned paleontologist Niles Eldredge poses these questions and examines humankind's role in the larger life cycles of the earth, composing a provocative general theory of extinction. "A powerfully impassioned plea for awareness--awareness of what we are doing, of what the consequences will be, and of what we can still do to reduce the biotic holocaust ahead." "It is clear that we are witnessing a mass extinction that is almost entirely the result of human activities. Eldredge is surely right that this is largely the consequence of habitat destruction rather than direct slaughter, but the consequences are nonetheless dire for our own species as well as others."

Award-winning scientist François Jacob's “The Logic of Life” is a landmark book in the history of biology and science. Focusing on heredity, which Jacob considers the fundamental feature of living things, he shows how, since the sixteenth century, the scientific understanding of inherited traits has moved not in a linear, progressive way, from error to truth, but instead through a series of frameworks. He reveals how these successive interpretive approaches-focusing on visible structures, internal structures (especially cells), evolution, genes, and DNA and other molecules, each have their own power but also limitations. Fundamentally challenging how the history of biology is told, much as Thomas Kuhn's “Structure of Scientific Revolutions” did for the history of science as a whole, “The Logic of Life” has greatly influenced the way scientists and historians view the past, present, and future of biology.

Michael Nielsen is one of the pioneers of quantum computing. He is an essayist, speaker, and advocate of open science. He lives in Toronto. How the internet and powerful online tools are democratizing and accelerating scientific discovery Reinventing Discovery argues that we are living at the dawn of the most dramatic change in science in more than three hundred years. This change is being driven by powerful cognitive tools, enabled by the internet, which are greatly accelerating scientific discovery. There are many books about how the internet is changing business, the workplace, or government. But this is the first book about something much more fundamental: how the internet is transforming our collective intelligence and our understanding of the world. From the collaborative mathematicians of the Polymath Project to the amateur astronomers of Galaxy Zoo, Reinventing Discovery tells the exciting story of the unprecedented new era in networked science. It will interest anyone who wants to learn about how the online world is revolutionizing scientific discovery-and why the revolution is just beginning. "Reinventing Discovery will frame serious discussion and inspire wild, disruptive ideas."-Chris Lintott, Nature "{Nielsen's} easy-to-read and enthusiastic narrative integrates a set of ideas that could, indeed, revolutionize knowledge creation."-Stephen M. Fiore, Science "Nielsen believes that mass collaboration is the future of science, and his book may be the most interesting piece of nonfiction I read this year."-Anthony Doerr, Boston Globe "The most compelling manifesto yet for the transformative power of networked science."-James Wilsdon, Financial Times "Timely and important."-Jack Stilgoe, Guardian

David P. Billington (1927–2018) was the Gordon Y. S. Wu Professor of Engineering Emeritus at Princeton University. His many books include Robert Maillart's Bridges and Power, Speed, and Form (both Princeton). An essential exploration of the engineering aesthetics of celebrated structures from long-span bridges to high-rise buildings What do structures such as the Eiffel Tower, the Brooklyn Bridge, and the concrete roofs of Pier Luigi Nervi have in common? According to The Tower and the Bridge, all are striking examples of structural art, an exciting area distinct from either architecture or machine design. Aided by stunning photographs, David Billington discusses the technical concerns and artistic principles underpinning the well-known projects of leading structural engineer-artists, including Othmar Ammann, Félix Candela, Gustave Eiffel, Fazlur Khan, Robert Maillart, John Roebling, and many others. A classic work, The Tower and the Bridge introduces readers to the fundamental aesthetics of engineering. "Billington is clearly moved by great structures. . . . This is a book on structural engineering that sees its subject as part of the larger drama of history and culture, and for the breadth of this stance alone, it is impressive."-Paul Goldberger, New York Times Book Review "Elegant modern structures are often described as beautiful, and Billington, with the love of an artist, the patience of a historian, and the knowledge of a first-rate structuralist, has presented the achievements of the new age in a language of such lucidity and accuracy as to make them understandable to the interested layman."-Mario Salvadori, American Scientist

Everybody knows that mathematics is indispensable to physics--imagine where we'd be today if Einstein and Newton didn't have the math to back up their ideas. But how many people realize that physics can be used to produce many astonishing and strikingly elegant solutions in mathematics? Mark Levi shows how in this delightful book, treating readers to a host of entertaining problems and mind-bending puzzlers that will amuse and inspire their inner physicist. Levi turns math and physics upside down, revealing how physics can simplify proofs and lead to quicker solutions and new theorems, and how physical solutions can illustrate why results are true in ways lengthy mathematical calculations never can. Did you know it's possible to derive the Pythagorean theorem by spinning a fish tank filled with water? Or that soap film holds the key to determining the cheapest container for a given volume? Or that the line of best fit for a data set can be found using a mechanical contraption made from a rod and springs? Levi demonstrates how to use physical intuition to solve these and other fascinating math problems. More than half the problems can be tackled by anyone with precalculus and basic geometry, while the more challenging problems require some calculus. This one-of-a-kind book explains physics and math concepts where needed, and includes an informative appendix of physical principles. The Mathematical Mechanic will appeal to anyone interested in the little-known connections between mathematics and physics and how both endeavors relate to the world around us.

Trigonometry has always been an underappreciated branch of mathematics. It has a reputation as a dry and difficult subject, a glorified form of geometry complicated by tedious computation. In this book, Eli Maor draws on his remarkable talents as a guide to the world of numbers to dispel that view. Rejecting the usual arid descriptions of sine, cosine, and their trigonometric relatives, he brings the subject to life in a compelling blend of history, biography, and mathematics. He presents both a survey of the main elements of trigonometry and a unique account of its vital contribution to science and social development. Woven together in a tapestry of entertaining stories, scientific curiosities, and educational insights, the book more than lives up to the title Trigonometric Delights. Maor, whose previous books have demystified the concept of infinity and the unusual number "e," begins by examining the "proto-trigonometry" of the Egyptian pyramid builders. He shows how Greek astronomers developed the first true trigonometry. He traces the slow emergence of modern, analytical trigonometry, recounting its colorful origins in Renaissance Europe's quest for more accurate artillery, more precise clocks, and more pleasing musical instruments. Along the way, we see trigonometry at work in, for example, the struggle of the famous mapmaker Gerardus Mercator to represent the curved earth on a flat sheet of paper; we see how M. C. Escher used geometric progressions in his art; and we learn how the toy Spirograph uses epicycles and hypocycles. Maor also sketches the lives of some of the intriguing figures who have shaped four thousand years of trigonometric history. We meet, for instance, the Renaissance scholar Regiomontanus, who is rumored to have been poisoned for insulting a colleague, and Maria Agnesi, an eighteenth-century Italian genius who gave up mathematics to work with the poor-but not before she investigated a special curve that, due to mistranslation, bears the unfortunate name "the witch of Agnesi." The book is richly illustrated, including rare prints from the author's own collection. Trigonometric Delights will change forever our view of a once dreaded subject.

Nobel Prize–winning physicist Roger Penrose questions some of the most fashionable ideas in physics today, including string theory What can fashionable ideas, blind faith, or pure fantasy possibly have to do with the scientific quest to understand the universe? Surely, theoretical physicists are immune to mere trends, dogmatic beliefs, or flights of fancy? In fact, acclaimed physicist and bestselling author Roger Penrose argues that researchers working at the extreme frontiers of physics are just as susceptible to these forces as anyone else. In this provocative book, he argues that fashion, faith, and fantasy, while sometimes productive and even essential in physics, may be leading today's researchers astray in three of the field's most important areas-string theory, quantum mechanics, and cosmology. Arguing that string theory has veered away from physical reality by positing six extra hidden dimensions, Penrose cautions that the fashionable nature of a theory can cloud our judgment of its plausibility. In the case of quantum mechanics, its stunning success in explaining the atomic universe has led to an uncritical faith that it must also apply to reasonably massive objects, and Penrose responds by suggesting possible changes in quantum theory. Turning to cosmology, he argues that most of the current fantastical ideas about the origins of the universe cannot be true, but that an even wilder reality may lie behind them. Finally, Penrose describes how fashion, faith, and fantasy have ironically also shaped his own work, from twistor theory, a possible alternative to string theory that is beginning to acquire a fashionable status, to "conformal cyclic cosmology," an idea so fantastic that it could be called "conformal crazy cosmology." The result is an important critique of some of the most significant developments in physics today from one of its most eminent figures. Roger Penrose, one the world's foremost theoretical physicists, has won numerous prizes, including the Nobel Prize and the Albert Einstein Medal, for his fundamental contributions to general relativity and cosmology. He is the bestselling author, with Stephen Hawking, of The Nature of Space and Time (Princeton). Penrose's other books include Cycles of Time: An Extraordinary New View of the Universe and The Road to Reality: A Complete Guide to the Laws of the Universe (both Vintage). He is the Rouse Ball Professor of Mathematics Emeritus at the University of Oxford and lives in Oxford, England. "This gem of a book is vintage Roger Penrose: eloquently argued and deeply original on every page. His perspective on the present crisis and future promise of physics and cosmology provides an important corrective to fashionable thinking at this crucial moment in science. This book deserves the widest possible hearing among specialists and the public alike."-Lee Smolin, author of Time Reborn: From the Crisis in Physics to the Future of the Universe "Physics has been at an awkward impasse for the past century. Two theories--quantum mechanics and general relativity--are widely believed to be true. . . . But they contradict each other in basic ways--they cannot both be entirely true. In Fashion, Faith, and Fantasy in the New Physics of the Universe . . . Roger Penrose, an elder statesman of physics, considers the problem. As intellectually offbeat as he is eminent . . . He ventures here some novel ways in which the two theories might be reconciled." "Penrose gets to the heart of modern physics' problem with subjectivity in this insightful and provocative pop-sci title. . . . [A] rewarding discussion of scientific stumbles in the search for truth." "It is always inspiring to read Penrose's uncompromisingly independent perspec­tive on physics."---Richard Dawid, Nature "An extremely original, rich, and thoughtful survey of today's most fashionable attempts to decipher the cosmos on its smallest and largest scales." "I can't recommend [Fashion, Faith, and Fantasy in

The world's top experts take readers to the very frontiers of brain science Includes a chapter by 2014 Nobel laureates May-Britt Moser and Edvard Moser An unprecedented look at the quest to unravel the mysteries of the human brain, The Future of the Brain takes readers to the absolute frontiers of science. Original essays by leading researchers such as Christof Koch, George Church, Olaf Sporns, and May-Britt and Edvard Moser describe the spectacular technological advances that will enable us to map the more than eighty-five billion neurons in the brain, as well as the challenges that lie ahead in understanding the anticipated deluge of data and the prospects for building working simulations of the human brain. A must-read for anyone trying to understand ambitious new research programs such as the Obama administration's BRAIN Initiative and the European Union's Human Brain Project, The Future of the Brain sheds light on the breathtaking implications of brain science for medicine, psychiatry, and even human consciousness itself. Contributors include: Misha Ahrens, Ned Block, Matteo Carandini, George Church, John Donoghue, Chris Eliasmith, Simon Fisher, Mike Hawrylycz, Sean Hill, Christof Koch, Leah Krubitzer, Michel Maharbiz, Kevin Mitchell, Edvard Moser, May-Britt Moser, David Poeppel, Krishna Shenoy, Olaf Sporns, Anthony Zador. Gary Marcus is professor emeritus of psychology and neural science at New York University. His books include Guitar Zero: The Science of Becoming Musical at Any Age and Kluge: The Haphazard Evolution of the Human Mind. Jeremy Freeman is a neuroscientist at the Howard Hughes Medical Institute's Janelia Farm Research Campus. "A wonderful way to launch yourself into the exciting world of twenty-first-century neuroscience, whether you are a scientist or an intellectually curious layperson. The power in this sampler is that the coverage is not just technical but conceptual: the essays probe the ways in which an understanding of the brain will and won't illuminate the mind, and they do so with depth and balance rather than the usual breathless hype."-Steven Pinker, author of The Language Instinct and How the Mind Works "Have you ever wondered what's coming around the bend in terms of new insights into how the brain works? Open the pages of The Future of the Brain to find out. Gary Marcus and Jeremy Freeman have brought together some of the leading thinkers and researchers to share their vision of where we are headed. It's a fun, readable book full of insights."-Joseph LeDoux, author of The Emotional Brain and Synaptic Self "A deep, intriguing view into the most exciting advances in neuroscience. The Future of the Brain is a nuanced and thought-provoking guide to what we do and don't know about the human brain-and what we may or may not one day find out."-Maria Konnikova, author of Mastermind: How to Think Like Sherlock Holmes "Understanding, theorizing, and simulating the human brain are essential goals for twenty-first-century science and engineering. Surfing the fine line between science and science fiction, this book is a treasure trove of daring ideas."-Stanislas Dehaene, author of Consciousness and the Brain: Deciphering How the Brain Codes Our Thoughts "The brain is a complicated thing, and progress in understanding how it works may seem slow. Will creating huge research teams, collecting more data at higher resolutions, and sharing data more widely and openly kick-start a new wave of progress? Or does the field still need to make conceptual leaps before the results would even make sense? Brilliant minds on both sides describe their visions of the future of neuroscience in this collection of short, engaging essays."-Christopher Chabris, coauthor of The Invisible Gorilla: How Our Intuitions Deceive Us "Massive technological advances promise rapid and profound discoveries in neuroscience, with very broad implications for our understanding of behavior, ethics,

Henry Petroski (1942–2023) was the Aleksandar S. Vesic Distinguished Professor Emeritus of Civil Engineering at Duke University. His many books include To Engineer Is Human, The Evolution of Useful Things, The Pencil, and The Toothpick. From the acclaimed author and engineer, an engaging and lively account of the surprising secret of great design Design pervades our lives. Everything from drafting a PowerPoint presentation to planning a state-of-the-art bridge embodies this universal human activity. But what makes a great design? In this compelling and wide-ranging look at the essence of invention, distinguished engineer and author Henry Petroski argues that, time and again, we have built success on the back of failure-not through easy imitation of success. Success through Failure shows us that making something better-by carefully anticipating and thus averting failure-is what invention and design are all about. Petroski explores the nature of invention and the character of the inventor through an unprecedented range of both everyday and extraordinary examples-illustrated lectures, child-resistant packaging for drugs, national constitutions, medical devices, the world's tallest skyscrapers, long-span bridges, and more. Stressing throughout that there is no surer road to eventual failure than modeling designs solely on past successes, he sheds new light on spectacular failures, from the destruction of the Tacoma Narrows Bridge in 1940 and the space shuttle disasters of recent decades, to the collapse of the World Trade Center in 2001. Petroski also looks at the prehistoric and ancient roots of many modern designs. The historical record, especially as embodied in failures, reveals patterns of human social behavior that have implications for large structures like bridges and vast organizations like NASA. Success through Failure-which will fascinate anyone intrigued by design, including engineers, architects, and designers themselves-concludes by speculating on when we can expect the next major bridge failure to occur, and the kind of bridge most likely to be involved. "From {Petroski's} vantage point, failures in design and construction present perfect teaching opportunities. They are object lessons in the history and practice and beauty of engineering."---Cornelia Dean, New York Times "The moral Petroski draws-success breeds hubris and catastrophe, failure nurtures humility and insight-is worth pondering." "Success through Failure is insightful and accessible."---J. M. Ottino, Nature "Petroski's main message deserves notice. He points out that failure is an inherent part of success when it comes to design and innovation, and failure can come in many forms."---Martin Ince, Times Higher Education Supplement "An excellent read." "This is a book about human nature in design settings and its role in the development of products and our built environment. . . . Ingenuity is explored as a pendulum that swings between success and failure, driven by design philosophy and practices in a given place and time." "From ancient Roman engineers dismayed at the failure of stone-arch bridges to twenty-first-century American architects stunned by the collapse of the Twin Towers, designers have frequently learned valuable principles through hard tutelage. Lucid and concise, this study invites nonspecialists to share in the challenge of trial-and-error engineering."---Bryce Christensen, Booklist "Petroski tells iconic tales to demonstrate that mistakes are not obnoxious by-products of innovation but fundamental clues to the ideal." "{An} engaging and readable book. . . . Petroski uses countless interesting case histories to show how failure motivates technological advancement. . . . I recommend you keep a copy of Petroski's book on hand and flip through it next time you're feeling seduced by success."---Steven Cass, IEEE Spectrum "Success through Failure is an insightful and accessible foray into design. The book is a page-

"One of New York Times Notable Books for 1997" Walter Alvarez is professor of geology at the University of California, Berkeley. Sixty-five million years ago, a comet or asteroid larger than Mount Everest slammed into the Earth, inducing an explosion equivalent to the detonation of a hundred million hydrogen bombs. Vaporized detritus blasted through the atmosphere upon impact, falling back to Earth around the globe. Disastrous environmental consequences ensued: a giant tsunami, continent-scale wildfires, darkness, and cold, followed by sweltering greenhouse heat. When conditions returned to normal, half the plant and animal genera on Earth had perished. This horrific chain of events is now widely accepted as the solution to a great scientific mystery: what caused the extinction of the dinosaurs? Walter Alvarez, one of the Berkeley scientists who discovered evidence of the impact, tells the story behind the development of the initially controversial theory. It is a saga of high adventure in remote locations, of arduous data collection and intellectual struggle, of long periods of frustration ended by sudden breakthroughs, of friendships made and lost, and of the exhilaration of discovery that forever altered our understanding of Earth's geological history. "[D]eft and readable . . . T. rex and the Crater of Doom gets the facts across in a lighthearted, almost playful manner. But it's also solid science, a clear and efficient exposition that conveys plenty of cogent detail while keeping an eye on the subtle interplay of thought, action, and personality that makes scientific research such arresting human behavior. . . . [An] estimable account from the world's leading authority on death from above."---Timothy Ferris, New York Times Book Review "A geologist (who happens to be a kind of working philosopher) gives a deft, readable explanation of the extinction of the dinosaurs." "The book is very well written and so engrossing that a reader with little or no background in the earth's geologic history will enjoy an easy and vastly entertaining summary of how we came to our present understanding of the past. It is a wonderful adventure in science."---Dale Russell, The Los Angeles Times Book Review "An unfolding story told by its leading protagonist. . . . Very clearly and entertainingly written, and illustrated with fascinating colour plates, it is accessible even to nonspecialists."---Arthur C. Clarke, The Times Higher Education Supplement "A fascinating proof of a once ridiculed theory. In fitting together the puzzle of dino demise, Alvarez excitingly shapes the story for the widest audience." "Every library with geology holdings will want to have this book. . . . Alvarez offers a great detective story. . . ." "A first-rate, swiftly paced tale of how science can propel its participants down avenues of surprising discovery to breathtaking conclusions."---Charles Petit, San Francisco Examiner & Chronicle "This personal account of the search for a geological Excalibur makes fascinating reading. . . . [It] reads like Arthurian legend, full of temptations which lead the hero astray and distract him and his followers from the true path."---Douglas Palmer, New Scientist "Alvarez's book recounts this scientific detective story in an authoritative yet consistently engaging manner. Once considered absurd, the idea that extraterrestrial factors were involved in some of the great crises in the history of life has become widely accepted."---Hans-Dieter Sues, Toronto Globe and Mail "A nicely told and well-written tale of scientific discovery." "Appealing and accessible, an excellent introduction to the subject." "Reading Alvarez's book is a bit like reading a letter from an old friend you haven't seen for 30 years. . . . Serious passages are offset by cheeky commentary and humble asides that keep the book from becoming overly solemn or preachy."---Rachel Berstein, Berkeley Science Review "If you love mysteries and enjoy science, this is a won

Didier Sornette is professor of entrepreneurial risks at the Swiss Federal Institute of Technology in Zurich, professor of finance at the Swiss Finance Institute in Geneva, and the director of the Financial Crisis Observatory at ETH Zurich. The scientific study of complex systems has transformed a wide range of disciplines in recent years, enabling researchers in both the natural and social sciences to model and predict phenomena as diverse as earthquakes, global warming, demographic patterns, financial crises, and the failure of materials. In this book, Didier Sornette boldly applies his varied experience in these areas to propose a simple, powerful, and general theory of how, why, and when stock markets crash. Most attempts to explain market failures seek to pinpoint triggering mechanisms that occur hours, days, or weeks before the collapse. Sornette proposes a radically different view: the underlying cause can be sought months and even years before the abrupt, catastrophic event in the build-up of cooperative speculation, which often translates into an accelerating rise of the market price, otherwise known as a "bubble." Anchoring his sophisticated, step-by-step analysis in leading-edge physical and statistical modeling techniques, he unearths remarkable insights and some predictions--among them, that the "end of the growth era" will occur around 2050. Sornette probes major historical precedents, from the decades-long "tulip mania" in the Netherlands that wilted suddenly in 1637 to the South Sea Bubble that ended with the first huge market crash in England in 1720, to the Great Crash of October 1929 and Black Monday in 1987, to cite just a few. He concludes that most explanations other than cooperative self-organization fail to account for the subtle bubbles by which the markets lay the groundwork for catastrophe. Any investor or investment professional who seeks a genuine understanding of looming financial disasters should read this book. Physicists, geologists, biologists, economists, and others will welcome Why Stock Markets Crash as a highly original "scientific tale," as Sornette aptly puts it, of the exciting and sometimes fearsome--but no longer quite so unfathomable--world of stock markets. "While it's difficult to pinpoint what type of trader would enjoy this book the most, I think there's something for everyone, whether you're a quaint, technical trader or a fundamentalist. . . . I feel that I'm smarter after finishing this book; I thoroughly enjoyed the lengthy journey, and would recommend this to any stock market enthusiast."---Jeff Pierce, Seeking Alpha "A highly recommended, enjoyable, well-researched, and thought-provoking book for anyone interested in stock markets and the modeling of financial processes."---Rick Gorvett, Journal of Risk and Insurance "The book is written in a readable style and does not require technical knowledge. Any reader interested in a serious approach to the origin and possible prediction of financial bubbles will enjoy reading it."---Josep M. Porra, Journal of Statistical Physics "Sornette's book is not just about finance and economics; it is also a mesmerizing introduction to game theory, fractals, catastrophe theory, critical phenomena, and much more. No prior knowledge of finance or economics is needed to understand the book. . . . Throughout the book, Sornette makes numerous, vivid comparisons with many other fields in which the various mathematical tools he describes can be applied."---Frank Cuypers, , Physics Today "Fascinating, and mind-expanding, reading."-Robert Shiller, author of Irrational Exuberance "Didier Sornette's insights into why markets behave as they do are fresh, productive, and provocative. This work is bound to become an important baseline for anyone trying to understand what will happen next in the stock and currency markets not only in the U.S. but in Europe and Asia as well."-Richard N. Foster, director, McKinsey & Company "This is

Frans de Waal is the C. H. Candler Professor of Psychology at Emory University and director of the Living Links Center at the Yerkes National Primate Center in Atlanta. Can virtuous behavior be explained by nature, and not by human rational choice? "It's the animal in us," we often hear when we've been bad. But why not when we're good? Primates and Philosophers tackles this question by exploring the biological foundations of one of humanity's most valued traits: morality. In this provocative book, renowned primatologist Frans de Waal argues that modern-day evolutionary biology takes far too dim a view of the natural world, emphasizing our "selfish" genes and reinforcing our habit of labeling ethical behavior as humane and the less civilized as animalistic. Seeking the origin of human morality not in evolution but in human culture, science insists that we are moral by choice, not by nature. Citing remarkable evidence based on his extensive research of primate behavior, de Waal attacks "Veneer Theory," which posits morality as a thin overlay on an otherwise nasty nature. He explains how we evolved from a long line of animals that care for the weak and build cooperation with reciprocal transactions. Drawing on Darwin, recent scientific advances, and his extensive research of primate behavior, de Waal demonstrates a strong continuity between human and animal behavior. He probes issues such as anthropomorphism and human responsibilities toward animals. His compelling account of how human morality evolved out of mammalian society will fascinate anyone who has ever wondered about the origins and reach of human goodness. Based on the Tanner Lectures de Waal delivered at Princeton University's Center for Human Values in 2004, Primates and Philosophers includes responses by the philosophers Peter Singer, Christine M. Korsgaard, and Philip Kitcher and the science writer Robert Wright. They press de Waal to clarify the differences between humans and other animals, yielding a lively debate that will fascinate all those who wonder about the origins and reach of human goodness. "Frans de Waal defends against philosopher critics his view that the roots of morality can be seen in the social behavior of monkeys and apes. . . . [H]e argues that human morality would be impossible without certain emotional buildings blocks that are clearly at work in chimps and monkey societies. . . . Dr. de Waal sees human morality as having grown out of primate sociality, but with two extra levels of sophistication. People enforce their society's moral codes much more rigorously with rewards, punishments and reputation building. They also apply a degree of judgment and reason, for which there are no parallels in animals."---Nicholas Wade, The New York Times "De Waal is one of the world's foremost authorities on nonhuman primates, and his thoughtful contribution to Primates and Philosophers is enriched by decades of close observation of their behavior. . . . He argues that humans are like their closest evolutionary kin in being moral by nature. . . . [A]n impressively well-focused collection of essays."---John Gray, New York Review of Books "Celebrated primatologist Frans de Waal . . . demonstrates through his empirical work with primates the evolutionary basis for ethics." "Frans de Waal . . . argues that . . . morality is actually a gift from animal ancestors and that people are good not by choice but by nature. . . . He argues that . . . critics fail to recognize that while animals are not human, humans are animals." "Dutch-born psychologist, ethologist and primatologist Frans de Waal has spent his career watching the behavior of apes and monkeys, mostly captive troupes in zoos. . . . His work . . . has helped lift Darwin's conjectures about the evolution of morality to a new level. . . . [De Waal argues that] sympathy, empathy, right and wrong are feelings that we share with other animals; even the best part of human nature, the par

"Winner of the 2001 Book Award in Science, Phi Beta Kappa" "One of Choices Outstanding Academic Titles for 2001" Richard B. Alley is the Evan Pugh Professor of Geosciences at Pennsylvania State University and a member of the National Academy of Sciences. The author of more than 240 scientific papers, he was also the host of the PBS miniseries Earth: The Operators' Manual. In the 1990s Richard B. Alley and his colleagues made headlines with the discovery that the last ice age came to an abrupt end over a period of only three years. In The Two-Mile Time Machine, Alley tells the fascinating history of global climate changes as revealed by reading the annual rings of ice from cores drilled in Greenland. He explains that humans have experienced an unusually temperate climate compared to the wild fluctuations that characterized most of prehistory. He warns that our comfortable environment could come to an end in a matter of years and tells us what we need to know in order to understand and perhaps overcome climate changes in the future. In a new preface, the author weighs in on whether our understanding of global climate change has altered in the years since the book was first published, what the latest research tells us, and what he is working on next. "Although not all scientists will agree with Alley's conclusions, [this] engaging book--a brilliant combination of scientific thriller, memoir and environmental science--provides instructive glimpses into our climatic past and global future . . ." "Alley's . . . striking finding is that the earth's climate has always been wildly variable and subject to dramatic swings--except during the past 10,000 years. So the period during which humankind has established itself across the globe and made the transition from grubby bands of hunter-gatherers to the dubious majesty of global capitalism corresponds exactly to a freakishly stable period in the earth's climate."---Angus Clarke, The Times of London "With a highly readable style designed to capture and stimulate the imagination of his students, Alley explains some of the complexities of Earth system science with a minimum of jargon. This book is not just for students: it will be readily accessible to a wide audience that should be aware of its contents."---David Peel, New Scientist "[A] provocative little book . . . a compelling tale of climate sleuthing . . .[Alley] is authoritative without being dogmatic, concerned without being alarmist."---Robert C. Cowen, Christian Science Monitor "A fascinating journey into the geologic past and the history of the Earth's climate . . . Alley ends his entertaining book by polishing his crystal ball, envisioning what the future climate will be, and what we might do about it."---J.A. Rial, American Scientist "A superlative account of a complex topic . . . It is refreshingly straightforward to read, often humorous, yet still deadly serious, complete with anecdotes and understandable explanations of complex processes." "Books in which scientists write about their professional experience and describe in lay terms the stuff that makes them excited about science rarely disappoint. Richard Alley's The Two Mile Time Machine is no exception. It describes a fascinating journey into the geologic past and the history of the Earth's climate. . . . Alley ends his entertaining book by polishing his crystal ball, envisioning what the future climate will be, and what we might do about it."---J.A. Rial, American Scientist "[A] superb book. . . . Alley demonstrates that the scientific understanding of climate is both a lot more complex, and a lot simpler, than public perceptions might indicate. . . .The Two-Mile Time Machine restores some of the joy of discovery that has always been present in scientific work, but is often lost amidst today's furious research pace and compressed news cycles."---Cathering H. Crouch, Books and Culture "A fascinating first-hand story. . . . [A]n engaging narrative about the processes o

"Winner of the Organisation Internationale de la Vigne et du Vin Grand Prize, History, Literature and Fine Arts Category" "Winner of the Research Prize, Asociación Internacional de Historia y Civilización de la Vid y el Vino" "Honorable Mention for the Award for Best Professional/Scholarly Book in Geology and Earth Sciences Professional/Scholarly Award, Association of American Publishers" Patrick E. McGovern is scientific director of the Biomolecular Archaeology Project for Cuisine, Fermented Beverages, and Health at the University of Pennsylvania Museum of Archaeology and Anthropology. He is the author of Uncorking the Past and Ancient Brews and has collaborated with Dogfish Head Brewery to recreate a series of ancient ales. A richly illustrated account of the story of ancient viniculture The history of civilization is, in many ways, the history of wine. This book is the first comprehensive account of the earliest stages of the history and prehistory of viniculture, which extends back into the Neolithic period and beyond. Elegantly written and richly illustrated, Ancient Wine opens up whole new chapters in the fascinating story of wine by drawing on recent archaeological discoveries, molecular and DNA sleuthing, and the writings and art of ancient peoples. In a new afterword, the author discusses exciting recent developments in the understanding of ancient wine, including a new theory of how viniculture came to central and northern Europe. "Remarkable."-Adam Gopnik, New Yorker "Riveting, informative and thought-provoking."-James C. Wright, American Scientist "No one is better qualified to sift through the widely scattered clues {to the origins of winemaking} than McGovern, a skilled scientific sleuth who wields the most powerful tools of modern chemistry in his search for the roots of ancient wines."-J. Madeleine Nash, Time Magazine "A rich treasury of lore on viticulture. . . . {W}ill likely remain a standard in every serious wine-lover's library for a long time."-Laurence A. Marschall, Natural History "Patrick McGovern serves us a magnificent feast of science and history that melds sophisticated chemistry with good, old-fashioned historical sleuthing. His innovative research has revolutionized our knowledge of the origins of one of humanity's greatest pleasures. This is an archaeological and gustatory delight for specialist and general reader alike."-Brian Fagan, author of The Little Ice Age

William Dunham is a Research Associate in Mathematics at Bryn Mawr College. He is the author of Journey Through Genius: The Great Theorems of Mathematics, The Mathematical Universe, and Euler: The Master of Us All, and is a co-editor (along with Jerry Alexanderson and Don Albers) of The G.H. Hardy Reader. He received the Mathematical Association of America's George Polya, Trevor Evans, and Lester R. Ford awards, as well as its Beckenbach Prize for expository writing. More than three centuries after its creation, calculus remains a dazzling intellectual achievement and the gateway to higher mathematics. This book charts its growth and development by sampling from the work of some of its foremost practitioners, beginning with Isaac Newton and Gottfried Wilhelm Leibniz in the late seventeenth century and continuing to Henri Lebesgue at the dawn of the twentieth. Now with a new preface by the author, this book documents the evolution of calculus from a powerful but logically chaotic subject into one whose foundations are thorough, rigorous, and unflinching-a story of genius triumphing over some of the toughest, subtlest problems imaginable. In touring The Calculus Gallery, we can see how it all came to be. "This is a book that should be part of the personal library of any mathematician."---Mark Hunacek, Mathematical Gazette "The Calculus Gallery is a wonderful book. The style is inviting; the explanations are clear and accessible…. Mathematicians, scientists, and historians alike can learn much that is interesting, much that is mathematically significant, and a good deal that is both."-Judith V. Grabiner, Science "If a better historical treatment of the development of the calculus is available, this reviewer has yet to see it…. Essential."-Choice "{A} brilliant book…. I predict that Dunham's book will itself come to be considered a masterpiece in its field."-Victor J. Katz, American Scientist "A joy to read…. {The Calculus Gallery} is a lovely and engaging gallery of the 'masters' that belongs in the library of everyone who seriously teaches or studies the subject."-Diane M. Spresser, Mathematics Teacher

Paul J. Nahin is the author of many popular math books, including How to Fall Slower Than Gravity and Hot Molecules, Cold Electrons (both Princeton). He is professor emeritus of electrical engineering at the University of New Hampshire. A mathematical journey through the most fascinating problems of extremes and how to solve them What is the best way to photograph a speeding bullet? How can lost hikers find their way out of a forest? Why does light move through glass in the least amount of time possible? When Least Is Best combines the mathematical history of extrema with contemporary examples to answer these intriguing questions and more. Paul Nahin shows how life often works at the extremes-with values becoming as small (or as large) as possible-and he considers how mathematicians over the centuries, including Descartes, Fermat, and Kepler, have grappled with these problems of minima and maxima. Throughout, Nahin examines entertaining conundrums, such as how to build the shortest bridge possible between two towns, how to vary speed during a race, and how to make the perfect basketball shot. Moving from medieval writings and modern calculus to the field of optimization, the engaging and witty explorations of When Least Is Best will delight math enthusiasts everywhere. "Nahin has written a beautifully clear, fascinating book on a topic which is truly vital to so many areas of science and I would recommend anyone who enjoys puzzle solving and having new tools to tackle old (or new) problems should read it."---Jonathan Shock, Mathemafrica "Terrific fun to read!"-Bonnie Shulman, MAA Online "A tour de force."-Dennis S. Bernstein, IEEE Control Systems Magazine "Highly recommended."-Clark Kimberling, Mathematical Intelligencer "A valuable and stimulating introduction to problems that have fascinated mathematicians and physicists for millennia."-D. R. Wilkins, Contemporary Physics "Anyone with a modest command of calculus, a curiosity about how mathematics developed, and a pad of paper for calculations will enjoy Nahin's lively book."-Donald R. Sherbert, SIAM Review

John MacCormick is associate professor of computer science at Dickinson College and a leading teacher, researcher, and writer in his field. His books include What Can Be Computed? A Practical Guide to the Theory of Computation (Princeton). Nine revolutionary algorithms that power our computers and smartphones Every day, we use our computers to perform remarkable feats. A simple web search picks out a handful of relevant needles from the world's biggest haystack. Uploading a photo to Facebook transmits millions of pieces of information over numerous error-prone network links, yet somehow a perfect copy of the photo arrives intact. Without even knowing it, we use public-key cryptography to transmit secret information like credit card numbers, and we use digital signatures to verify the identity of the websites we visit. How do our computers perform these tasks with such ease? John MacCormick answers this question in language anyone can understand, using vivid examples to explain the fundamental tricks behind nine computer algorithms that power our PCs, tablets, and smartphones. "A great way to find out what computer science is really about. . . . MacCormick provides a taste of why we computer scientists get so excited about algorithms."-Paul Curzon, Science "Excellent. . . . This is an unusually well-written text suitable for anyone with an interest in how today's information systems really work."-John Gilbey, Times Higher Education "MacCormick leaves the reader with a sense of the engine that powers the networked world."-Kevin Slavin, New Scientist "There's likely no better account of the software that underpins everything from Amazon to Facebook."-Brett Szmajda, Cosmos