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Great Feuds in Mathematics: Ten of the Liveliest Disputes Ever

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Mathematical disputes offer indisputable proof that great mathematical minds are calculating in more ways than one. Fueled by greed, jealousy, ambition, and ego, they have plots worthy of a soap opera, pitting brother against brother, father against son, and student against mentor.

In the sixteenth century, Cardano and Tartaglia battled over credit for finding a method for solving cubic and quadratic equations; the plots and counterplots ended when Tartaglia, using Cardano's son as an informant, turned Cardano over to the Spanish Inquisition. In later centuries, Descartes battled Fermat over analytic geometry and optics; Newton and Leibniz feuded bitterly over the credit for the calculus; the Bernoulli brothers fought over calculus problems; and Poincaré tussled with Russell over the logical foundations of mathematics. In a notable twentieth-century math conflict involving Hilbert and Brouwer, Einstein took a neutral stance and described the controversy as the War of the Frogs and the Mice.

Hal Hellman explores both the mathematics and the spirit of the times in this fascinating exposé. He draws from letters, articles, and books in which the debated ideas were propounded or refuted, and from the works of historians who have assessed the contributions of the participants to mathematics. Many of the ideas that sparked the feuds are prominent in mathematics today. For example, Hilbert's proof theory is a powerful mathematical tool, especially in computer science. Russell's logicism has modern-day proponents. And Cantor's set theory became the basis for today's topology and fractals and led to advances that provided a rigorous grounding for infinitesimal calculus.

Providing insight into math and history, and spiced with cunning, deception, and subterfuge, this book shows how great feuds propelled great progress in mathematics.

About the Author

HAL HELLMAN is the author of Great Feuds in Science, Great Feuds in Medicine, and Great Feuds in Technology, all from Wiley. He has published articles in the New York Times, Omni, Reader's Digest, Psychology Today, and Geo.

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