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Hilbert took over from Poincare the title of the most famous mathematician in the world. His mathematical achievements are numerous and varied; Reid does a good job of providing an overview of the impact Hilbert had on many different fields, and of his style; his strengths and weaknesses. There is a good deal of coverage of the famous twenty-three Hilbert problems, presented to the Second International Congress of Mathematicians in Paris in 1900, including a large section of the talk Hilbert gave.
Reid paints a vivid picture of the mathematical circle at Gottingen, a luminous collection of talents. Minkowski and Hilbert were close friends; Klein was the director of the institute there; Emmy Noether was there; Hurwitz; Zermelo; Landau; the list is long and impressive. It's all the more sad to read about the way the Institute was destroyed by the Nazis in the name of racial purity. Almost without exception the leading mathematicians emigrated, one by one, to America. Hilbert, who had retired in 1930 (retirement at age 68 was mandatory) was forced to watch as the work of decades was dismantled. The last years, of age, fading memory and the privations of war, are mercifully given less than a dozen pages.
Hilbert's life leads from the great days of the mid-nineteenth century to the Nazis and the atomic bomb. Reid has done a wonderful job of capturing the feel of Germany over his long life, and the mathematic impact and importance of his work. A compulsory book for those interested in modern mathematical history.


ever!. He contributed to several branches of mathematics,
including functional analysis, mathematical physics,
calculus of variations, and algebraic number theory.
(Everyone knows what a Hilbert space is right!)
At the turn of the 20th century, Hilbert enumerated
23 unsolved problems of mathematics that he considered worthy
of further investigation. To this day, very few of these, including
the 10th problem, on the finite solvability of Diophantine
equations, have been resolved! (thanks to
Yuri Matiyasevich, Martin Davis and Julia Robinson!).
Besides, Hilbert was also a character (read the section
when Norbert Weiner of cybernetics fame, came to give
a talk at Gottingen, and .... :-)).
Incidentally the author Constance Reid is the sister of
Julia Robinson (of Hilbert's 10th problem fame!),
hence there can no one better to write about
Hilbert!. Besides Constance Reid is a well known chronicler
of mathematicians lives (this one is a tour de force and
her best!).
No one can can call himself/herself a mathematician without
having Reid's book on his/her bookshelf. Strongly
recommended!

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