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Open Problems in Mathematics

John Forbes Nash, Jr. and Michael Th. Rassias, editors
Publication Date: 
Number of Pages: 
[Reviewed by
Felipe Zaldivar
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At the turn of the century, to commemorate Hilbert’s celebrated overview of mathematics with a collection of problems covering a large portion of our science around 1900, several books were published. Some gave a historical perspective or reviewed the current status of Hilbert’s problems, such as B. H. Yandell’s The Honors Class: Hilbert's Problems and their Solvers (A K Peters, 2001) or J. Gray’s The Hilbert Challenge (Oxford, 2000). Others, following Hilbert’s guidance, collected sets of problems covering various portions of the mathematical landscape.

The book under review joins in the above trend with a twist: It presents a collection of open research problems in pure and applied mathematics, but each article is written by a different specialist.

There are some overlaps with other such collections, for example, the P vs. NP problem, the Birch and Swinnerton-Dyer conjecture, the Riemann hypothesis, the Navier-Stokes equations and the Hodge conjecture are part of The Millennium Prize Problems (CMI-AMS, 2006). But the overlap is only on the topics, because now different authors give different perspectives on these problems.

The other problems collected range from algebraic topology (Novikov’s conjecture, and the unknotting problem), number theory (Pair correlations of zeros of Riemann’s zeta function, or other L-functions, and energy levels of heavy nuclei, the generalized Fermat equation, the discrete logarithm problem, and Goldbach’s conjectures), differential geometry (minimal surfaces: Plateau’s problem), game theory (cooperative game theory) and combinatorics (a pair of Erdős’s conjectures, and two conjectures of Hadwiger).

Depending on your tastes, some of the presented problems may be more attractive than others, but certainly you may find some appealing and engaging presentations in this collection of problems that somehow got the attention of John Nash.

Felipe Zaldivar is Professor of Mathematics at the Universidad Autonoma Metropolitana-I, in Mexico City. His e-mail address is

See the table of contents in the publisher's webpage.