The Honors Class: Hilbert鈥檚 problems and their solvers by Benjamin H. Yandell, A.K. Peters, 拢28, ISBN 1568811411
A SLIM set of problems, just 23 鈥渦nsettled questions鈥� in mathematics inspired many of the 20th-century leaps in the field. The eminent mathematician David Hilbert listed them in his address to the Second International Congress of Mathematicians, all the way back in 1900. Hilbert encouraged his colleagues to crack these conundrums as a way of resolving contradictions that lay 鈥渁t the foundations of mathematics鈥�. So they did just that.
Most of those problems are now done and dusted, but not all the solutions came out as he might have expected or desired. For example, Kurt G枚del鈥檚 incompleteness theorems dashed Hilbert鈥檚 hopes that all of mathematics could be proved true from a complete and consistent set of axioms.
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In The Honors Class Benjamin Yandell鈥檚 treatment of the mathematics itself is descriptive, but unavoidably difficult in places. Happily, such passages are short enough to skip without losing the thread. And for those seeking more detail, Hilbert鈥檚 speech is reproduced in an appendix, and there is an extensive bibliography.
But Yandell deftly combines discussions of the problems themselves with biographies of the people who solved them. It鈥檚 a rich tale, and fascinating to trace the networks of contacts and occasional coincidences that carried the complex work forward.