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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.
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