Bestselling author and astrophysicist Mario Livio examines the lives and theories of history’s greatest mathematicians to ask how—if mathematics is an abstract construction of the human mind—it can so perfectly explain the physical world. Nobel Laureate Eugene Wigner once wondered about “the unreasonable effectiveness of mathematics” in the formulation of the laws of nature. Is God a Mathematician? investigates why mathematics is as powerful as it is. From ancient times to the present, scientists and philosophers have marveled at how such a seemingly abstract discipline could so perfectly explain the natural world. More than that—mathematics has often made predictions, for example, about subatomic particles or cosmic phenomena that were unknown at the time, but later were proven to be true. Is mathematics ultimately invented or discovered? If, as Einstein insisted, mathematics is “a product of human thought that is independent of experience,” how can it so accurately describe and even predict the world around us? Physicist and author Mario Livio brilliantly explores mathematical ideas from Pythagoras to the present day as he shows us how intriguing questions and ingenious answers have led to ever deeper insights into our world. This fascinating book will interest anyone curious about the human mind, the scientific world, and the relationship between them.
Livio investigates curiosity through the lives of paragons of inquisitiveness as Leonardo da Vinci and Richard Feynman. He interviewed a range of exceptionally curious people from an astronaut with degrees in statistics, medicine, and literature to a rock guitarist with a PhD in astrophysics
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.
Drawing on the lives of five great scientists -- Charles Darwin, William Thomson (Lord Kelvin), Linus Pauling, Fred Hoyle and Albert Einstein -- scientist/author Mario Livio shows how even the greatest scientists made major mistakes and how science built on these errors to achieve breakthroughs, especially into the evolution of life and the universe"--
The author of The Golden Ratio tells the “lively and fascinating” story of two nineteenth-century mathematicians whose work revealed the laws of symmetry (Nature). What do Bach’s compositions, Rubik’s Cube, the way we choose our mates, and the physics of subatomic particles have in common? All are governed by the laws of symmetry, which elegantly unify scientific and artistic principles. Yet the mathematical language of symmetry—known as group theory—did not emerge from the study of symmetry at all, but from an equation that couldn’t be solved. For three centuries, the quintic equation resisted efforts by mathematicians to find a solution. Working independently, two great prodigies ultimately proved that it couldn’t be solved by a simple formula. These geniuses, a Norwegian named Niels Henrik Abel and a romantic Frenchman named Évariste Galois, both died tragically young. Their incredible labor, however, produced the origins of group theory. The first extensive, popular account of the mathematics of symmetry and order, The Equation That Couldn’t Be Solved is told not through abstract formulas but in a dramatic account of the lives and work of some of the greatest mathematicians in history.
What do the Parthenon in Greece, crosses in graveyards, the ratio of the height of a woman's navel to a woman's height, sunflowers and Leonardo da Vinci's Mona Lisa have in common? The answer is that these disparate elements share a geometrical proportion of ancient origin commonly known as the golden ratio, or expressed numerically as phi. fractals and DNA on the way, the author takes us into the heart of this extraordinary number. He gives an account of the phi-obsessed individuals who devoted their lives to discovering its secrets - from the Pythagoreans who believed that the study of the Golden Ratio would reveal the hand of God, to the astronomer Johannes Kepler who felt that phi was the greatest treasure of geometry, to the modern day scientists who are discovering ever more remarkable ramifications of this strange, almost mystical, number.
Advance Praise for The Accelerating Universe "The Accelerating Universe is not only an informative book about modern cosmology. It is rich storytelling and, above all, a celebration of the human mind in its quest for beauty in all things." —Alan Lightman, author of Einstein's Dreams "This is a wonderfully lucid account of the extraordinary discoveries that have made the last years a golden period for observational cosmology. But Mario Livio has not only given the reader one clear explanation after another of what astronomers are up to, he has used them to construct a provocative argument for the importance of aesthetics in the development of science and for the inseparability of science, art, and culture." —Lee Smolin, author of The Life of the Cosmos "What a pleasure to read! An exciting, simple account of the universe revealed by modern astronomy. Beautifully written, clearly presented, informed by scientific and philosophical insights." —John Bahcall, Institute for Advanced Study "A book with charm, beauty, elegance, and importance. As authoritative a journey as can be taken through modern cosmology." —Allan Sandage, Observatories of the Carnegie Institution of Washington
An “intriguing and accessible” (Publishers Weekly) 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 minimizing 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 and uses his “gifts as a great storyteller” (The Washington Post) to provide a “refreshing perspective” (Booklist) 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 “admirably clear and concise” (The Times, London) book, remains threatened everyday.
A New York Times–bestselling astrophysicist and a Nobel laureate describe the quest to discover how and where the universe breathed life into matter For a long time, scientists have wondered how life has emerged from inanimate chemistry, and whether Earth is the only place where it exists. Charles Darwin speculated about life on Earth beginning in a warm little pond. Some of his contemporaries believed that life existed on Mars. It once seemed inevitable that the truth would be known by now. It is not. For more than a century, the origins and extent of life have remained shrouded in mystery. But, as Mario Livio and Jack Szostak reveal in Is Earth Exceptional?, the veil is finally lifting. The authors describe how life’s building blocks—from RNA to amino acids and cells—could have emerged from the chaos of Earth’s early existence. They then apply the knowledge gathered from cutting-edge research across the sciences to the search for life in the cosmos: both life as we know it and life as we don’t. Why and where life exists are two of the biggest unsolved problems in science. Is Earth Exceptional? is the ultimate exploration of the question of whether life is a freak accident or a chemical imperative.
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