Mathematicians have received surprising attention in the last decade, some of this being negative and some positive. This book intends to give attention to a mathematician that is accurate as well as interesting. It succeeds in this in every way, and allows the reader an inside view of the mind of one of the most noted mathematicians of the twentieth century. It is now a cliche to say that when a book is good that one "cannot put it down", but this is what happened to me when I began to read it. It is a totally absorbing account of the life and mathematical discoveries of John Nash, and this is no doubt due to the fact that the biographer has solid technical competence. It would be very helpful to the entire mathematical community if the lives of the best of our mathematicians would be documented as well as Nash's is here. Even from a solely didactic point of view, the mathematics of the mathematician can be better understood when it is put in an organized, historical perspective.
There are many interesting insights and anedotes throughout the book. JN was apparently labeled as an "underachiever" by his elementary school teachers, with his worse grades being in music and mathematics. It is no surprise to learn that books were his best friends as a child, but it is interesting to learn that he spent much of his childhood performing experiments in his home laboratory. Mathematics is not really an empirical science, and Nash's mathematical achievements rank more as pure than applied. Widely read, he also evidently preferred solving problems "in his head" rather than via the ubiquitous pencil and paper.
The biographer also gives interesting insights into the kind of university Princeton was at the time JN entered. In the Princeton department of mathematics, "Grades meant nothing" she quotes Solomon Lefschetz as saying. Emily Artin, the famous algebraist at Princeton at the time, apparently did not like Nash, clashing with him frequently in the "common room", and recommended that Nash be thrown out of Princeton. Also, the reader learns that game theory was viewed as somewhat "declasse" at Princeton, which is even more interesting considering its importance now in business and in research in artificial intelligence. The formalist school of mathematics held center stage at the time, and the biographer labels Nash's paper on the topic "one of the first to apply the axiomatic method to a problem in the social sciences". John von Neumann apparently thought his results "trivial" though, says the biographer. A whole chapter is spent on Nash's determination to avoid military service, for reasons that entering the military would preclude the obtaining of a prominent academic position.
Nash's bisexuality is perhaps a surprise, if compared to the rest of the mathematical community, who are in general heterosexual, then and now. Attitudes about homosexuality cost him a job according to the biographer. In the current age of political correctness and diversity-with-bias, this would be unheard of. With reference to his personal life, Nash's relationship with Alicia was delineated beautifully by the biographer. Even a mind so given to abstractions as Nash's needs the concreteness and warmth of human interaction. The perplexing age anxiety of mathematicians is also brought out in the book. A perusal of the brilliant work of the over-40 Edward Witten and Andrew Wiles should of course put this (crippling) anxiety to rest. Nash's decision to work on the Riemann Hypothesis would perhaps, if he had continued to work on it, brought him to middle-age and beyond.
One could perhaps speculate on what Nash would have achieved mathematically if mental illness would not have crippled him. Such speculation is superfluous though, as the contributions he made are more than most individuals have or could have made. His life hitherto has been one of overwhelming success, and his mind to be viewed with quiet envy.
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A Beautiful Mind
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M Knight
Excellently executed account - don't bother with the film
Reviewed in the United Kingdom on May 29, 2013