The best mathematical biography books

Elegantly written, skillfully ornamented with personal reminiscences and anecdotes (some very funny), this is all that a biography should be. The subject, David Hilbert (1862-1943) was a mathematician of the first rank in the decades around 1900. He was also a champion of talent wherever it might be found. When, in 1915, the Senate of Göttingen University would not grant formal lecturer rank to Emmy Noether because of her sex, Hilbert protested that, “We are a Senate, not a bath-house.” He then announced lectures in his own name, but had Noether deliver them.

When my daughter acquired a pet hamster in 2005 I named him Hilbert. On his death the following year I posted an obituary poem, In Hilbertiam, which can still be read on the internet.

When I was asked to review this book, my first instinct was to decline. Newton (1642-1727) was a towering genius but a dull fellow, with no interest in other human beings. He often published anonymously for fear that, he explained: "Public esteem, were I able to acquire and maintain it … would perhaps increase my acquaintance, the thing which I chiefly study to decline." How can a biographer make such a person interesting?

The author dodges very nimbly around this problem, giving us an account, not so much of the man as of his reputation and influence. Perhaps this means that her book is not a true biography, but it is done with such skill and wit, I include it anyway.

Gödel (1906-1978) is, like Newton, an unpromising subject for biography. He was antisocial and mentally unstable. His obsessive fear of being poisoned led eventually to him starving himself to death. 

Rebecca Goldstein is a professor of philosophy with a deep interest in logic and the foundations of mathematical truth – the applecart that Gödel overturned in 1931 with his tremendous paper on the incompleteness of axiomatic systems. She is also an experienced novelist. This combination makes her just the right person to construct a gripping story out of Gödel’s weirdness and world-shaking importance.

This is a work of historical fiction by a master storyteller. I have been acquainted with Charles Kingsley (1819-1875) since being given The Water-Babies and Westward Ho! to read in childhood. Here he takes as his subject Hypatia of Alexandria (370-415), daughter of the mathematician and philosopher Theon. She was played by Rachel Weisz in the 2009 movie Agora.

Hypatia’s own contributions to mathematics are unclear. “All Hypatia's work is lost except for its titles and some references to it,” says her biographical entry in the MacTutor online history of math; but since she does have a MacTutor entry, I claim her as a mathematician.

Queen Victoria liked Hypatia so much she appointed Charles Kingsley personal tutor to her son, the future King Edward VII.

First published in 1937, this is a classic in its field: still, so far as I know, the most comprehensive one-volume collection of math biographies. Bell’s 42 subjects range from Zeno of Elea (fifth century B.C.) to Georg Cantor (1845-1918) and include all eight Bernoullis. Nor is the book as exclusionary as its title suggests: Sofia Kovalevskaya shares a chapter with Karl Weierstrass.

I read the book in my teens and retain that early affection. However, I love this book the way we love family members: with differences of opinion and occasional irritations (some of which I aired in Unknown Quantity). Bell is sometimes wrong -- e.g. about Galois -- and often opinionated. Still, he shapes the history of math in a way I have found true and useful overall.