Galileo and the Science Deniers

2020, Simon and Schuster

A fresh interpretation of the life of Galileo Galilei, one of history’s greatest and most fascinating scientists, that sheds new light on his discoveries and how he was challenged by science deniers. “We really need this story now, because we’re living through the next chapter of science denial” (Bill McKibben).

Galileo’s story may be more relevant today than ever before. At present, we face enormous crises—such as the minimization of the dangers of climate change—because the science behind these threats is erroneously questioned or ignored. Galileo encountered this problem 400 years ago. His discoveries, based on careful observations and ingenious experiments, contradicted conventional wisdom and the teachings of the church at the time. Consequently, in a blatant assault on freedom of thought, his books were forbidden by church authorities.

Astrophysicist and bestselling author Mario Livio draws on his own scientific expertise to provide captivating insights into how Galileo reached his bold new conclusions about the cosmos and the laws of nature. A freethinker who followed the evidence wherever it led him, Galileo was one of the most significant figures behind the scientific revolution. He believed that every educated person should know science as well as literature, and insisted on reaching the widest audience possible, publishing his books in Italian rather than Latin.

Galileo was put on trial with his life in the balance for refusing to renounce his scientific convictions. He remains a hero and inspiration to scientists and all of those who respect science—which, as Livio reminds us in this gripping book, remains threatened even today.

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“It is fashionable to invoke Galileo on both sides of any debate to claim the mantle of truth. In Galileo and the Science Deniers, Livio teaches us the method by which Galileo found the truth--a process more powerful than rhetoric--examination. Today more than ever we need to understand what made Galileo synonymous with finding the truth."

— Dr. Adam Riess, Nobel Laureate in Physics 2011 and co-discoverer of the accelerating expansion of the universe

"Mario Livio is ideally qualified to interpret Galileo's ideas and philosophy. As a bonus, he offers parallels between 17th century interactions between science, religion and the public, and those we encounter today. This fascinating book deserves wide readership."

— Martin Rees, Astronomer Royal for the United Kingdom, and author of On the Future: Prospects for Humanity

“Every so often a reason arises to retell the life of Galileo. This year, as Mario Livio so forcefully demonstrates in Galileo and the Science Deniers, the 400-year Galileo Affair casts an urgent new light on the current climate crisis.”

— Dava Sobel, author of Longitude, Galileo’s Daughter, and The Glass Universe

"Mario Livio's Galileo is a beautifully written, enthralling, and insightful history of a courageous genius. Today scientists and indeed all of us have a much less fraught, but otherwise not that dissimilar task to struggle with those who deny evolution, climate change, and free thought generally. A fascinating read."

— John A. Paulos, Professor of Mathematics at Temple University and author of Innumeracy.

"One would have hoped that the Galileo story could be treated just as the fascinating history this book makes clear it is -- but we really need this story now, because we're living through the next chapter of science denial, with stakes that couldn't be higher."

— Bill McKibben, author of Falter: Has the Human Game Begun to Play Itself Out?

“Galileo and the Science Deniers is a brilliant, highly readable account of Galileo’s life and accomplishments. The book is a joy to read and provides an accurate and vivid reconstruction of the immense intellectual contributions of Galileo. Livio thoroughly succeeds in illustrating the many facets of Galileo’s versatile personality, and he offers wise and insightful reflections upon the necessity to overcome the division between the humanities and the sciences.”

— Michele Camerota, Galileo scholar and author of Galileo Galilei e la cultura scientifica nell’età della Controriforma.

"To better understand the perilous threat of science denialism today, Mario Livio looks back at the scientist who faced the greatest denial of them all: that the Earth revolves around the Sun. By offering us an astrophysicist's unique perspective on Galileo's life and fate, this engaging work is a must read for anyone who values the contributions of science to society."

--- Marcia Bartusiak, author of The Day We Found the Universe and Dispatches from Planet 3.

"Scientists have typically been fascinated and inspired by Galileo’s scientific achievements and by his struggle with the Catholic Church. In this book, astrophysicist Livio does an excellent job of conveying such fascination and inspiration in a manner that can be appreciated by scientists and nonscientists alike. An important lesson he emphasizes is Galileo’s bridging of the gap between the two cultures, namely the sciences and the humanities.”

--- Maurice A. Finocchiaro, author of On Trial for Reason: Science, Religion, and Culture in the Galileo Affair.

"Livio illuminates the parallels between the deniers of Galileo’s scientific findings and those today who ignore the evidence of climate change. Intriguing and accessible, and packed with clever insights, Livio’s latest gives readers plenty of think about.”

--- Publishers Weekly, Review.

"This is an insightful, riveting and deeply researched biography of Galileo Galilei that

reveals not just his complex character but also how he was truly intellectually

radical and well ahead of his time.”

--- Priyamvada Natarajan, Professor, Departments of Astronomy & Physics, Yale University, author of Mapping The Heavens: The Radical Scientific Ideas That Reveal the Cosmos

"Books on Galileo are not scarce, but the latest from astrophysicist Livio features the author’s unique insights as well as his concern about the current fashion for giving ideology priority over truth… The author truly excels in his explanations of Galileo’s findings as well as his descriptions of the culture of Renaissance Italy. Popular histories extol the scientist’s use of the just invented telescope to galvanize Europe with astronomical discoveries—the moons of Jupiter, phases of Venus, and the mountains on Earth’s moon—but Livio gives equal time to his revelations of the laws of motion, which marked the birth of modern physics. An expert life of a giant of science.”

--- Kirkus Reviews

"Rather than present a straight biography, Livio's goal is to explore the parallels between Galileo's fate and the science denialism happening today. He makes apt arguments and offers compelling reasons why science and religion shouldn't be at odds. Livio is an astrophysicist and his perspective on Galileo's importance as a professional scientist is particularly valuable… Livio argues that the distinction we make between the humanities and the sciences is false and damaging, and that Galileo illuminates a better balance between the two. A refreshing perspective on Galileo's legacy."

— John Keogh, Booklist

"The Galileo affair involved a complex interplay of ancient and novel scientific ideas, scriptural exegesis, entrenched theological and philosophical positions, intellectual turf battles, academic rivalries, flawed characters, personality clashes, and ecclesiastical and secular politics, all unfolding over two decades in the fevered atmosphere of the struggle between Reformation and Counter-Reformation and the Thirty Years War. Few historical episodes are more fraught with subtleties, ironies and ambiguities. To tell it properly requires an unusual breadth of knowledge and the gifts of a great storyteller. Fortunately, Mario Livio is fully equipped for the task. In “Galileo: And the Science Deniers,” his mastery not only of the science (which is to be expected of a highly accomplished astrophysicist), but of the cultural and historical context, is impressive. Even more impressive perhaps, given that he is not Catholic, is his relatively sophisticated grasp of some of the theological arguments and issues."

— Stephen M. Barr, The Washington Post

"Admirably clear and concise account of the Galileo affair."

— David Aaronovitch, The Times (London)

Why: What Makes Us Curious

2017, Simon and Schuster

Astrophysicist and author Mario Livio investigates perhaps the most human of all our characteristics—curiosity—as he explores our innate desire to know why.

Experiments demonstrate that people are more distracted when they overhear a phone conversation—where they can know only one side of the dialogue—than when they overhear two people talking and know both sides. Why does half a conversation make us more curious than a whole conversation?

In the ever-fascinating Why? Mario Livio interviewed scientists in several fields to explore the nature of curiosity. He examined the lives of two of history’s most curious geniuses, Leonardo da Vinci and Richard Feynman. He also talked to people with boundless curiosity: a superstar rock guitarist who is also an astrophysicist; an astronaut with degrees in computer science, biology, literature, and medicine. What drives these people to be curious about so many subjects?

Curiosity is at the heart of mystery and suspense novels. It is essential to other forms of art, from painting to sculpture to music. It is the principal driver of basic scientific research. Even so, there is still no definitive scientific consensus about why we humans are so curious, or about the mechanisms in our brain that are responsible for curiosity.

Mario Livio—an astrophysicist who has written about mathematics, biology, and now psychology and neuroscience—explores this irresistible subject in a lucid, entertaining way that will captivate anyone who is curious about curiosity.

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"Have you ever wondered why we wonder why? Mario Livio has, and he takes you on a fascinating quest to understand the origin and mechanisms of our curiosity. I thoroughly recommend it.”

— Dr. Adam Riess, Nobel Laureate in Physics 2011

"An energetic look at the psychology and neuroscience of our inquisitiveness."

— Dan Jones, Nature

"Filled with fascinating stories, tidbits, and psychological insights, Why? is a delightful romp through every aspect of human curiosity. It will surprise you, make you smarter, and put a spring in your step.”

— Steven Strogatz, Schurman Professor of Applied Mathematics, Cornell University, and author of The Joy of X

"A lively, expert, and definitely not dumbed-down account of why we're curious."

— Kirkus Reviews

"It’s impossible to imagine creativity or invention without curiosity, and one could hardly ask for a richer or more engaging exploration of human curiosity than the one provided by Mario Livio in Why?. This book is an intellectual feast for any curious person."

— Jeffrey M. Schwartz MD, Research Psychiatrist UCLA, co-author of The Mind and the Brain and You are Not Your Brain

"Whether in science or art, curiosity is essential to progress—but what is it, exactly? Mixing historical narratives with interviews, and throwing in a dash of neuroscience, Mario Livio explores whether we are inquisitive because curiosity feels good in itself or because finding out something new removes an irritation. It can be both, he concludes, and different types of curiosity serve different purposes. Livio's book doesn't pretend to have all the answers, but it might well spur your own curiosity.”

— David Lindley, author of Uncertainty: Einstein, Heisenberg, Bohr, and the Struggle for the Soul of Science

"This cogent book presents the scientific research on curiosity in understandable ways without too much jargon. It answers many (although not all) of our potential questions about curiosity—including what many originally believed killed the cat."

--- Joseph Peschel, Science

Brilliant Blunders

From Darwin to Einstein - Colossal Mistakes by Great Scientists That Changed Our Understanding of Life and the Universe

2014, Simon and Schuster

Drawing on the lives of five great scientists, this “scholarly, insightful, and beautifully written book” (Martin Rees, author of From Here to Infinity) illuminates the path to scientific discovery.

Charles Darwin, William Thomson (Lord Kelvin), Linus Pauling, Fred Hoyle, and Albert Einstein all made groundbreaking contributions to their fields—but each also stumbled badly. Darwin’s theory of natural selection shouldn’t have worked, according to the prevailing beliefs of his time. Lord Kelvin gravely miscalculated the age of the earth. Linus Pauling, the world’s premier chemist, constructed an erroneous model for DNA in his haste to beat the competition to publication. Astrophysicist Fred Hoyle dismissed the idea of a “Big Bang” origin to the universe (ironically, the caustic name he gave to this event endured long after his erroneous objections were disproven). And Albert Einstein speculated incorrectly about the forces of the universe—and that speculation opened the door to brilliant conceptual leaps. As Mario Livio luminously explains in this “thoughtful meditation on the course of science itself” (The New York Times Book Review), these five scientists expanded our knowledge of life on earth, the evolution of the earth, and the evolution of the universe, despite and because of their errors.

“Thoughtful, well-researched, and beautifully written” (The Washington Post), Brilliant Blunders is a wonderfully insightful examination of the psychology of five fascinating scientists—and the mistakes as well as the achievements that made them famous.

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“Mario Livio sets the discoveries of five great scientists who were also remarkable personalities in their social context, showing how they emerged from confusion and controversy. His archival research allows him to debunk several myths that have been given currency through less thorough biographies. You don’t need to be a scientist to be fascinated by this scholarly, insightful and beautifully written book.”

— Martin Rees, Astronomer Royal and author of From Here to Infinity: A Vision for the Future of Science

“After reading Livio's account, I look on the history of science in a new way. In every century and every science, I see brilliant blunders.”

— Freeman Dyson, The New York Review of Books

“Scientists make mistakes all the time, but those bumps in the road are often smoothed out in the legends that surround the greatest discoverers. . . . Thoughtful, well-researched and beautifully written, Brilliant Blunders offers a distinctive — and far more truthful — perspective on the journey to scientific discovery."

— Marcia Bartusiak, The Washington Post

“Enlightening. . . . For many people, being a great scientist means being above error. . . . Livio’s book is a valuable antidote to this skewed picture. . . . Thanks to his deep curiosity, Livio turns Brilliant Blunders into a thoughtful meditation on the course of science itself."

— Carl Zimmer, The New York Times Book Review

“It is said that genius is the ability to make all possible mistakes in the least amount of time. Livio’s genius is to show us just how much those mistakes have taught us.”

— Adam Riess, Thomas Barber Professor of Physics and Astronomy, Johns Hopkins University, Nobel Laureate in Physics 2011

“Mario Livio wears many hats: scientist, sleuth, storyteller. In Brilliant Blunders, a delightful intellectual synthesis, he reminds us that he’s also one of the best science writers in our galaxy.”

— Steven Strogatz, Schurman Professor of Applied Mathematics, Cornell University, and author of The Joy of X

“In Brilliant Blunders, Mario Livio leaves no historical detail untold, as we re-walk the error-filled pathways along which human understanding of the universe slowly emerged.”

--- Neil deGrasse Tyson, Astrophysicist, American Museum of Natural History, and author of Space Chronicles: Facing the Ultimate Frontier

“Mr. Livio is a gifted storyteller. . . .[He] shows how science works partly by feeding on past mistakes: Once recognized, the errors sparked creativity in other scientists. An incorrect view of the world is not simply a mistake; it's a catalyst that leads to better understanding."

--- Samuel Arbesman, The Wall Street Journal

Is God a Mathematician

2009, Simon and Schuster

Albert Einstein once wondered: “How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?” Indeed, Newton formulated a mathematical law of gravity which he himself could verify (given the observational results of his day) to an accuracy of no better than four percent. Yet, the law proved to be precise to better than one part in a million! How is that possible? Or take the example of knot theory – the mathematical theory of knots. It evolved as an obscure branch of pure mathematics. Amazingly, this abstract endeavor suddenly found extensive modern applications in topics ranging from the structure of the DNA to “string theory” – the candidate for an ultimate theory of the subatomic world.

And this is not all. The famous logician Bertrand Russell argued that logic and mathematics are really the same thing. “They differ as boy and man, ” he said, “logic is the youth of mathematics and mathematics is the manhood of logic.” So how can we explain these incredible powers of mathematics? How come that stock option pricing and the agitated motion of pollen suspended in water can be described by the same mathematical equation?

At an even more fundamental level, are we merely discovering mathematics, just as astronomers discover previously unknown galaxies? Or, is mathematics simply a human invention? These (and many more) are the questions that Mario Livio is attempting to answer in Is God A Mathematician? The book reviews the ideas of great thinkers from Plato and Archimedes to Galileo and Descartes, and on to Russell and Gödel. It offers a lively and original discussion of topics ranging from cosmology to the cognitive sciences, and from mathematics to religion. The focus on the scientific and practical applications of the fascinating insights of great minds will appeal to a wide audience.

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“Livio (The Golden Ratio) is concerned with the contentious question: is mathematics a human invention? Or is it the intricate design of the universe that we are slowly discovering? Scientists in past centuries have argued for the latter, Platonist position. In the last 50 years, however, many scientists, calling into question the whole idea of scientific discovery, maintain that we have invented mathematics. Livio gives as one example the famous golden ratio, which has fascinated Western mathematicians for millennia and was originally emphasized for its mystical symbolism. But Chinese mathematicians, not sharing that outlook, didn't discover it—or maybe they just didn't need to invent it. Livio hedges his bets. . . arguing that mathematics is partly discovered and partly invented. But Livio is a smooth writer. His fans will enjoy this book, and new ones may discover him. "

— Publishers Weekly

“Livio recognizes a profound mystery inherent in the formulas his colleagues employ so sedulously: Why does the universe harmonize so well with numbers accessible to human minds? Probing this mystery, Livio traces the evolution of mathematical reasoning from the ritual symbolism of the ancient Pythagoreans to the multilayered analyses of twenty-first-century string theorists. In the impressive parade of intellectual explorers, we encounter Archimedes pondering geometrical figures at the very moment of his death, Descartes overthrowing all of medieval philosophy with one audacious thought, and Gödel quashing the ambitions of system-building logicians. This wide-ranging inquiry, however, ultimately highlights far more than personalities. A sharp conflict emerges between platonically minded philosophers who view mathematical breakthroughs as transcendent discoveries and psychologically inclined thinkers who interpret these breakthroughs as merely human inventions. Testing the tensions between these views, Livio delivers an exhilarating foray into the founding premises of mathematical science.

— Bryce Christensen, Booklist

“Did you know that 365 -- the number of days in a year -- is equal to 10 times 10, plus 11 times 11, plus 12 times 12? Or that the sum of any successive odd numbers always equals a square number -- as in 1 + 3 = 4 (2 squared), while 1 + 3 + 5 = 9 (3 squared), and 1 + 3 + 5 + 7 = 16 (4 squared)? Those are just the start of a remarkable number of magical patterns, coincidences and constants in mathematics. No wonder philosophers and mathematicians have been arguing for centuries over whether math is a system that humans invented or a cosmic -- possibly divine -- order that we simply discovered. That's the fundamental question Mario Livio probes in his engrossing book Is God a Mathematician? Livio, an astrophysicist at the Hubble Space Telescope Science Institute in Baltimore, explains the invention-vs.-discovery debate largely through the work and personalities of great figures in math history, from Pythagoras and Plato to Isaac Newton, Bertrand Russell and Albert Einstein. The author acknowledges that some readers will find his inconclusive conclusion to be unsatisfying. I didn't. Sometimes the adventure, the intellectual ride, is more important than the final destination."

— Marc Kaufman, The Washington Post

Is God a Mathematician?

2009, Simon and Schuster

Albert Einstein once wondered: “How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?” Indeed, Newton formulated a mathematical law of gravity which he himself could verify (given the observational results of his day) to an accuracy of no better than four percent. Yet, the law proved to be precise to better than one part in a million! How is that possible? Or take the example of knot theory – the mathematical theory of knots. It evolved as an obscure branch of pure mathematics. Amazingly, this abstract endeavor suddenly found extensive modern applications in topics ranging from the structure of the DNA to “string theory” – the candidate for an ultimate theory of the subatomic world.

And this is not all. The famous logician Bertrand Russell argued that logic and mathematics are really the same thing. “They differ as boy and man, ” he said, “logic is the youth of mathematics and mathematics is the manhood of logic.” So how can we explain these incredible powers of mathematics? How come that stock option pricing and the agitated motion of pollen suspended in water can be described by the same mathematical equation?

At an even more fundamental level, are we merely discovering mathematics, just as astronomers discover previously unknown galaxies? Or, is mathematics simply a human invention? These (and many more) are the questions that Mario Livio is attempting to answer in Is God A Mathematician? The book reviews the ideas of great thinkers from Plato and Archimedes to Galileo and Descartes, and on to Russell and Gödel. It offers a lively and original discussion of topics ranging from cosmology to the cognitive sciences, and from mathematics to religion. The focus on the scientific and practical applications of the fascinating insights of great minds will appeal to a wide audience.

## REVIEWS:

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“Livio (The Golden Ratio) is concerned with the contentious question: is mathematics a human invention? Or is it the intricate design of the universe that we are slowly discovering? Scientists in past centuries have argued for the latter, Platonist position. In the last 50 years, however, many scientists, calling into question the whole idea of scientific discovery, maintain that we have invented mathematics. Livio gives as one example the famous golden ratio, which has fascinated Western mathematicians for millennia and was originally emphasized for its mystical symbolism. But Chinese mathematicians, not sharing that outlook, didn't discover it—or maybe they just didn't need to invent it. Livio hedges his bets. . . arguing that mathematics is partly discovered and partly invented. But Livio is a smooth writer. His fans will enjoy this book, and new ones may discover him. "

— Publishers Weekly

“Livio recognizes a profound mystery inherent in the formulas his colleagues employ so sedulously: Why does the universe harmonize so well with numbers accessible to human minds? Probing this mystery, Livio traces the evolution of mathematical reasoning from the ritual symbolism of the ancient Pythagoreans to the multilayered analyses of twenty-first-century string theorists. In the impressive parade of intellectual explorers, we encounter Archimedes pondering geometrical figures at the very moment of his death, Descartes overthrowing all of medieval philosophy with one audacious thought, and Gödel quashing the ambitions of system-building logicians. This wide-ranging inquiry, however, ultimately highlights far more than personalities. A sharp conflict emerges between platonically minded philosophers who view mathematical breakthroughs as transcendent discoveries and psychologically inclined thinkers who interpret these breakthroughs as merely human inventions. Testing the tensions between these views, Livio delivers an exhilarating foray into the founding premises of mathematical science.

— Bryce Christensen, Booklist

“Did you know that 365 -- the number of days in a year -- is equal to 10 times 10, plus 11 times 11, plus 12 times 12? Or that the sum of any successive odd numbers always equals a square number -- as in 1 + 3 = 4 (2 squared), while 1 + 3 + 5 = 9 (3 squared), and 1 + 3 + 5 + 7 = 16 (4 squared)? Those are just the start of a remarkable number of magical patterns, coincidences and constants in mathematics. No wonder philosophers and mathematicians have been arguing for centuries over whether math is a system that humans invented or a cosmic -- possibly divine -- order that we simply discovered. That's the fundamental question Mario Livio probes in his engrossing book Is God a Mathematician? Livio, an astrophysicist at the Hubble Space Telescope Science Institute in Baltimore, explains the invention-vs.-discovery debate largely through the work and personalities of great figures in math history, from Pythagoras and Plato to Isaac Newton, Bertrand Russell and Albert Einstein. The author acknowledges that some readers will find his inconclusive conclusion to be unsatisfying. I didn't. Sometimes the adventure, the intellectual ride, is more important than the final destination."

— Marc Kaufman, The Washington Post

The Equation That Couldn't Be Solved

How Mathematical Genius Discovered the Language of Symmetry

2005, Simon and Schuster

For thousands of years mathematicians solved progressively more difficult algebraic equations, from the simple quadratic to the more complex quartic equation, yielding important insights along the way. Then they were stumped by the quintic equation, which resisted solutions for three centuries until two great prodigies independently proved that quintic equations cannot be solved by simple formula. These geniuses, a young Norwegian named Niels Henrik Abel and an even younger Frenchman named Evariste Galois, both died tragically. Galois, in fact, spent the last night before his fatal duel (at the age of twenty) scribbling a brief summary of his proof, occasionally writing in the margin of his notebook “I have no time.” Some of the mysteries surrounding his death, which have lingered for more than 170 years, are finally resolved in this book.

Galois’ work gave rise to group theory, the “language” that describes symmetry. Group theory explains much about the esthetics of our world, from the choosing of mates to Rubik’s cube, Bach’s musical compositions, the physics of subatomic particles and the popularity of Anna Kournikova.

Released on September 2005, The Equation That Couldn’t Be Solved is the first popular level book to explore group theory, not through abstract formulas but in a beautifully written and dramatic account of the lives and work of some of the greatest mathematicians in history.

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“A wide-ranging exploration of the phenomenon of symmetry....There's math, yes, but there are also tales of love, violence, history -- and the whole, in this case, turns out to be greater than the sum of those parts."

— Mary Carmichael, Newsweek

“Fascinating. . . . [Livio] writes passionately about the role of symmetry in human perception and the arts."

— The Economist

“A lively and fascinating read for a broad audience."

— Nature

The Golden Ratio:

The Story of PHI, the World's Most Astonishing Number

2003, Simon and Schuster

Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. In this fascinating book, Mario Livio tells the tale of a number at the heart of that mystery: phi, or 1.6180339887...This curious mathematical relationship, widely known as "The Golden Ratio," was discovered by Euclid more than two thousand years ago because of its crucial role in the construction of the pentagram, to which magical properties had been attributed. Since then it has shown a propensity to appear in the most astonishing variety of places, from mollusk shells, sunflower florets, and rose petals to the shape of the galaxy. Psychological studies have investigated whether the Golden Ratio is the most aesthetically pleasing proportion extant, and it has been asserted that the creators of the Pyramids and the Parthenon employed it. It is believed to feature in works of art from Leonardo da Vinci's Mona Lisa to Salvador Dali's The Sacrament of the Last Supper, and poets and composers have used it in their works. It has even been found to be connected to the behavior of the stock market!

The Golden Ratio is a captivating journey through art and architecture, botany and biology, physics and mathematics. It tells the human story of numerous phi-fixated individuals, including the followers of Pythagoras who believed that this proportion revealed the hand of God; astronomer Johannes Kepler, who saw phi as the greatest treasure of geometry; such Renaissance thinkers as mathematician Leonardo Fibonacci of Pisa; and such masters of the modern world as Goethe, Cezanne, Bartok, and physicist Roger Penrose. Wherever his quest for the meaning of phi takes him, Mario Livio reveals the world as a place where order, beauty, and eternal mystery will always coexist.

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“[An] entertaining review of the history of mathematics . . . A nice mental workout."

— Linda Schlossberg, San Francisco Chronicle

“Engagingly enthusiastic . . . It’s hard not to feel inspired and even unsettled by the hidden order Livio reveals."

— New Scientist

“Numbers aficionados will delight in astrophysicist Livio's history of an irrational number whose fame is second only to that of pi. . . . Livio's encyclopedic selection of subjects, supported by dozens of illustrations, will snare anyone with a recreational interest in mathematics."

— Booklist

The Accelerating Universe

Infinite Expansion, the Cosmological Constant, and the Beauty of the Cosmos

2000, Simon and Schuster

In one of the most surprising and important findings in cosmology in the century, astronomers recently discovered that the universe may be expanding at an ever-increasing rate. This discovery of an “accelerating universe” stunned many cosmologists because it directly contradicts their most deeply held beliefs about the evolution and fate of the universe. The discovery has therefore ignited a new revolution in cosmology in which scientists are wrestling anew with the most fundamental questions and revisiting ideas that were dismissed long ago.

As leading astrophysicist Mario Livio explains in this elegantly written and timely book, most cosmologists have long believed that the universe will expand at a gradually decreasing rate until the expansion effectively stops. In this pleasing scenario, the universe is perfectly poised between expanding into oblivion or collapsing in a “big crash” and will continue on in this miraculously balanced state for eternity. The discovery that the expansion appears in fact to be speeding up – and therefore that the universe will keep expanding faster and faster for infinity – throws the view of a perfectly balanced “beautiful universe” into question. Even more troubling, it threatens the cherished belief that the fundamental laws governing the cosmos are in themselves exquisitely “beautiful,” a belief that has always been a guiding light of discovery in cosmology.

What can explain this accelerated expansion? Does the universe have much less mass than originally thought? Is there some exotic unknown force, or new kind of energy, causing acceleration? Was Einstein’s “greatest blunder” – his idea of a cosmological constant – the right idea after all? What will the ultimate fate of the universe be? Must there be beauty in all good theories of the cosmos? Or are some of the laws governing the universe “ugly”?

In an entertaining and lively exploration of the answers to all of these questions, Mario Livio introduces readers to the “old cosmology,” which culminated in the view of the perfectly balanced universe, and then presents all of the ideas being explored by cosmologists in the “new cosmology” as they come to terms with the discovery of acceleration. Offering extraordinarily clear explanations of all the key concepts and theoretical ideas, Livio is a marvelous guide through this most exciting frontier in science today.

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“The Accelerating Universe is not only an informative book about cosmology. It is rich storytelling and, above all, a celebration of the human mind on its quest for beauty in all things."

— Alan Lightman, bestselling author of Einstein's Dreams

“Far more than a puzzle for specialists, the struggle to reinterpret the cosmos raises fundamental questions about the human craving for order: Does this craving reflect deep cosmic harmonies that helped create our species? Or does it simply defy an irreducible chaos that we would rather not confront? Livio probes these questions with a daring sufficient to satisfy the hungriest curiosity."

— Booklist

“The reader will enter a 'garden of delights.'"

— Physics World