Mathematical Mountaintops: The Five Most Famous Problems of All Time

In Mathematical Mountaintops, John Casti brilliantly recreates the solutions to the five greatest mathematical problems of all time: The Four-Color Map Problem, Fermat's Last Theorem, The Continuum Hypothesis, Kepler's Conjecture, and Hilbert's Tenth Problem. Casti recounts these mathematical quests with great verve. In retelling the story of Hilbert's Tenth Problem, for instance, he sweeps from Britain to New York to Leningrad and introduces us to such luminaries as Alan Turing, before turning to the young Soviet researcher who credited his breakthrough to a 700-year-old Italian problem about rabbits. He describes how Fermat's Last Theorem tantalized generations of scientists, who tried for three centuries to answer it, and relates how the final solution was greeted with the unprecedented front-page headlines, prize money, and international celebration--before a flaw (soon resolved) turned up. Casti's account of the struggle to solve Kepler's Conjecture wittily reveals how the "proof of the obvious" sometimes eludes us for centuries. And his discussion of The Continuum Hypothesis movingly portrays the tragic figure of Georg Cantor, the troubled genius who created the first truly original mathematics since the Greeks, yet died insane in an institution. Casti closes with a preview of the "Magnificent Seven"--the greatest unsolved mathematical mysteries, each of which carries a million-dollar bounty from the Clay Mathematics Institute--including the Poincare Conjecture, the Yang-Mills Existence and Mass Gap (why physicists can't isolate quarks), and the Reimann Hypothesis ("the granddaddy of all mathematical mysteries"). Mathematical Mountaintops is a brilliant account of mathematicians in action--seeking hidden patterns and structures, forging elegant chains of reasoning--as they struggle with problems that challenged the greatest minds for decades, if not centuries.

John Casti is a professor at the Technical University of Vienna and at the Sante Fe Institute, in New Mexico. An eminent mathematician, he is also the author of popular science books, including Five Golden Rules: Great Theories of 20th-Century Mathematics--And Why They Matter and Godel: A Life of Logic, the Mind, and Mathematics.