The Honors Class: Hilbert's Problems and Their SolversThis eminently readable book focuses on the people of mathematics and draws the reader into their fascinating world. In a monumental address, given to the International Congress of Mathematicians in Paris in 1900, David Hilbert, perhaps the most respected mathematician of his time, developed a blueprint for mathematical research in the new century. Jokingly called a natural introduction to thesis writing with examples, this collection of problems has indeed become a guiding inspiration to many mathematicians, and those who succeeded in solving or advancing their solutions form an Honors Class among research mathematicians of this century. In a remarkable labor of love and with the support of many of the major players in the field, Ben Yandell has written a fascinating account of the achievements of this Honors Class, covering mathematical substance and biographical aspects. |
Contents
Set Theory Anyone? | 25 |
How Many Real Numbers Are There? | 59 |
Cant We Do This with a Computer? | 85 |
Copyright | |
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Aleksandrov algebraic numbers algebraic topology analysis analytic arithmetic Arnold Artin axiom of choice axioms became Bieberbach Bolibruch Braun calculation calculus of variations called Cantor class field theory Cohen complete constructed continuum hypothesis countable Darboux David Hilbert Davis Dehn Dehn's differential equations diophantine equations elliptic ematicians ematics existence father Fermat's last theorem finite number formal Frankfurt Gelfond geometry German Gleason Gödel Göttingen Hasse Hilbert Hilbert's problems Hilbert's tenth problem Honda ideas infinite integral Julia Kolmogorov later lectures logic math mathematicians mathematics Matiyasevich method Montgomery Moscow Natascha natural numbers Nazi number theory paper physics Poincaré polynomial prime numbers Princeton prob probably professor proof proved published question real numbers Reid result Riemann rigorous Russian says Schneider set theory Siegel solution solved statement Takagi talk tenth problem theorem tion topology transcendental numbers University variables Weyl whole numbers writes wrote zeta function Zippin