Great Feuds in Mathematics


Book Description

Praise for Hal Hellman Great Feuds in Mathematics "Those who think that mathematicians are cold, mechanical proving machines will do well to read Hellman's book on conflicts in mathematics. The main characters are as excitable and touchy as the next man. But Hellman's stories also show how scientific fights bring out sharper formulations and better arguments." -Professor Dirk van Dalen, Philosophy Department, Utrecht University Great Feuds in Technology "There's nothing like a good feud to grab your attention. And when it comes to describing the battle, Hal Hellman is a master." -New Scientist Great Feuds in Science "Unusual insight into the development of science . . . I was excited by this book and enthusiastically recommend it to general as well as scientific audiences." -American Scientist "Hellman has assembled a series of entertaining tales . . . many fine examples of heady invective without parallel in our time." -Nature Great Feuds in Medicine "This engaging book documents [the] reactions in ten of the most heated controversies and rivalries in medical history. . . . The disputes detailed are . . . fascinating. . . . It is delicious stuff here." -The New York Times "Stimulating." -Journal of the American Medical Association




A Strange Wilderness


Book Description

The international bestselling author of Fermat’s Last Theorem explores the eccentric lives of history’s foremost mathematicians. From Archimedes’s eureka moment to Alexander Grothendieck’s seclusion in the Pyrenees, bestselling author Amir Aczel selects the most compelling stories in the history of mathematics, creating a colorful narrative that explores the quirky personalities behind some of the most groundbreaking, influential, and enduring theorems. Alongside revolutionary innovations are incredible tales of duels, battlefield heroism, flamboyant arrogance, pranks, secret societies, imprisonment, feuds, and theft—as well as some costly errors of judgment that prove genius doesn’t equal street smarts. Aczel’s colorful and enlightening profiles offer readers a newfound appreciation for the tenacity, complexity, eccentricity, and brilliance of our greatest mathematicians.




Great Feuds in Mathematics


Book Description

From Descartes battling Fermat for the honour of inventing analytic geometry, to Poincaré wrangling with Russell over the logical foundations of mathematics, this text provides a fascinating look behind the numbers game.




Great Feuds in Science


Book Description

Controversy is central to scientific development. This book recounts ten major disputes that riled the world of intellectual research since the seventeenth century. It discusses Galileo's censure by the Catholic Church for his theories of astronomy, the furore over Darwin's proposals concerning evolution, and other historic quarrels about the nature of the universe.




Bernoulli's Fallacy


Book Description

There is a logical flaw in the statistical methods used across experimental science. This fault is not a minor academic quibble: it underlies a reproducibility crisis now threatening entire disciplines. In an increasingly statistics-reliant society, this same deeply rooted error shapes decisions in medicine, law, and public policy with profound consequences. The foundation of the problem is a misunderstanding of probability and its role in making inferences from observations. Aubrey Clayton traces the history of how statistics went astray, beginning with the groundbreaking work of the seventeenth-century mathematician Jacob Bernoulli and winding through gambling, astronomy, and genetics. Clayton recounts the feuds among rival schools of statistics, exploring the surprisingly human problems that gave rise to the discipline and the all-too-human shortcomings that derailed it. He highlights how influential nineteenth- and twentieth-century figures developed a statistical methodology they claimed was purely objective in order to silence critics of their political agendas, including eugenics. Clayton provides a clear account of the mathematics and logic of probability, conveying complex concepts accessibly for readers interested in the statistical methods that frame our understanding of the world. He contends that we need to take a Bayesian approach—that is, to incorporate prior knowledge when reasoning with incomplete information—in order to resolve the crisis. Ranging across math, philosophy, and culture, Bernoulli’s Fallacy explains why something has gone wrong with how we use data—and how to fix it.




Scientific Feuds


Book Description

Most science chronicles present a triumphant march through time, with revolutionary thinkers and their discoveries following in orderly progression. The truth, however, is somewhat different. Scientific Feuds is a collection of the most vicious battles among the greatest minds of our time. It features such contests as Huxley and Wilberforce's debate on Darwin's theory of evolution, Franklin and Wilkins' fight over the discovery of DNA, and the “War of Currents” between Tesla and Edison (which ended with Edison electrocuting dogs and horses in a vain attempt to discredit Tesla's work). From passionate competition to vindictive sniping, these rivalries prove that the world of science is far from cold and methodical.




Shape


Book Description

An instant New York Times Bestseller! “Unreasonably entertaining . . . reveals how geometric thinking can allow for everything from fairer American elections to better pandemic planning.” —The New York Times From the New York Times-bestselling author of How Not to Be Wrong—himself a world-class geometer—a far-ranging exploration of the power of geometry, which turns out to help us think better about practically everything. How should a democracy choose its representatives? How can you stop a pandemic from sweeping the world? How do computers learn to play Go, and why is learning Go so much easier for them than learning to read a sentence? Can ancient Greek proportions predict the stock market? (Sorry, no.) What should your kids learn in school if they really want to learn to think? All these are questions about geometry. For real. If you're like most people, geometry is a sterile and dimly remembered exercise you gladly left behind in the dust of ninth grade, along with your braces and active romantic interest in pop singers. If you recall any of it, it's plodding through a series of miniscule steps only to prove some fact about triangles that was obvious to you in the first place. That's not geometry. Okay, it is geometry, but only a tiny part, which has as much to do with geometry in all its flush modern richness as conjugating a verb has to do with a great novel. Shape reveals the geometry underneath some of the most important scientific, political, and philosophical problems we face. Geometry asks: Where are things? Which things are near each other? How can you get from one thing to another thing? Those are important questions. The word "geometry"comes from the Greek for "measuring the world." If anything, that's an undersell. Geometry doesn't just measure the world—it explains it. Shape shows us how.




The Shape of a Life


Book Description

A Fields medalist recounts his lifelong effort to uncover the geometric shape—the Calabi-Yau manifold—that may store the hidden dimensions of our universe. Harvard geometer Shing-Tung Yau has provided a mathematical foundation for string theory, offered new insights into black holes, and mathematically demonstrated the stability of our universe. In this autobiography, Yau reflects on his improbable journey to becoming one of the world’s most distinguished mathematicians. Beginning with an impoverished childhood in China and Hong Kong, Yau takes readers through his doctoral studies at Berkeley during the height of the Vietnam War protests, his Fields Medal–winning proof of the Calabi conjecture, his return to China, and his pioneering work in geometric analysis. This new branch of geometry, which Yau built up with his friends and colleagues, has paved the way for solutions to several important and previously intransigent problems. With complicated ideas explained for a broad audience, this book offers not only insights into the life of an eminent mathematician, but also an accessible way to understand advanced and highly abstract concepts in mathematics and theoretical physics. “The remarkable story of one of the world’s most accomplished mathematicians . . . Yau’s personal journey—from escaping China as a youngster, leading a gang outside Hong Kong, becoming captivated by mathematics, to making breakthroughs that thrust him on the world stage—inspires us all with humankind’s irrepressible spirit of discovery.” —Brian Greene, New York Times–bestselling author of The Elegant Universe “An unexpectedly intimate look into a highly accomplished man, his colleagues and friends, the development of a new field of geometric analysis, and a glimpse into a truly uncommon mind.” —The Boston Globe “Engaging, eminently readable. . . . For those with a taste for elegant and largely jargon-free explanations of mathematics, The Shape of a Life promises hours of rewarding reading.” —American Scientist




Great Physicists


Book Description

Here is a lively history of modern physics, as seen through the lives of thirty men and women from the pantheon of physics. William H. Cropper vividly portrays the life and accomplishments of such giants as Galileo and Isaac Newton, Marie Curie and Ernest Rutherford, Albert Einstein and Niels Bohr, right up to contemporary figures such as Richard Feynman, Murray Gell-Mann, and Stephen Hawking. We meet scientists--all geniuses--who could be gregarious, aloof, unpretentious, friendly, dogged, imperious, generous to colleagues or contentious rivals. As Cropper captures their personalities, he also offers vivid portraits of their great moments of discovery, their bitter feuds, their relations with family and friends, their religious beliefs and education. In addition, Cropper has grouped these biographies by discipline--mechanics, thermodynamics, particle physics, and others--each section beginning with a historical overview. Thus in the section on quantum mechanics, readers can see how the work of Max Planck influenced Niels Bohr, and how Bohr in turn influenced Werner Heisenberg. Our understanding of the physical world has increased dramatically in the last four centuries. With Great Physicists, readers can retrace the footsteps of the men and women who led the way.




Towards Higher Mathematics: A Companion


Book Description

Containing a large and varied set of problems, this rich resource will allow students to stretch their mathematical abilities beyond the school syllabus, and bridge the gap to university-level mathematics. Many proofs are provided to better equip students for the transition to university. The author covers substantial extension material using the language of sixth form mathematics, thus enabling students to understand the more complex material. Exercises are carefully chosen to introduce students to some central ideas, without building up large amounts of abstract technology. There are over 1500 carefully graded exercises, with hints included in the text, and solutions available online. Historical and contextual asides highlight each area of mathematics and show how it has developed over time.