The Hilbert Challenge

by Jeremy J. Gray

Few problems in mathematics have had the status of those posed by David Hilbert in 1900. Mathematicians have made their reputations by solving some of them like Fermat's last theorem, but several remain unsolved including the Riemann Hypotheses, which has eluded all the great minds of this century. A hundred years later, this book takes a fresh look at the problems, the man who set them, and the reasons for their lasting impact on the mathematics of the twentieth century. In this fascinating book, the authors consider what makes this the pre-eminent collection of problems in mathematics, what they tell us about what drives mathematicians, and the nature of reputation, influence and power in the world of modern mathematics. It is written in a clear and entertaining style and will appeal to anyone with interest in mathematics or those mathematicians willing to try their hand at these problems.

Genres: Mathematics, Science, Nonfiction

328 pages, Hardcover

First published November 23, 2000

Reviews

[Arthur Ryman · Rating 4 out of 5]

This is a very authoritative account of the 23 problems Hilbert challenged the mathematics world to solve at the beginning of the 20th century, an impressive number of which have been solved over the last 120 years. The author provides a lot of detail about the problems and relates them to the the interplay between pure and applied mathematicals, mathematics and the real world, and the philosophical foundations of mathematics. Well worth the read by anyone with more than a casual interest in mathematics.

[Silvio Curtis · Rating 5 out of 5]

A book about the history of the 23 problems which Hilbert listed in his talk at the International Congress of Mathematicians in 1900 as important questions for the mathematicians of the twentieth century. The perspective is wider than if it were about just one problem, but more focused than a comprehensive history of twentieth-century mathematics would be. What I liked best was that even though it mentions mathematicians' personalities, friendships, and rivalries, it only does so it can explain how they affected the development of mathematics, and not the other way round as books on the history of science almost always do. Almost all of the problems are solved now, though some of them aren't simple yes-or-no questions and the Riemann Hypothesis has outlasted the century.

[Daniela · Rating 4 out of 5]

Excellent book, detailing the 23 problems that Hilbert believed would occupy mathmatician's minds for the XX century. Some of these are already solved, and this book tells their history. Excellent for people who do not have a very extensive background in math but are interested.