100 books like Hilbert

Richard Feynman was unique. A brilliant theoretical physicist, humorous, eccentric, and independent.

Feynman’s genius gave him a certain freedom, which he exploited to the full. The book is autobiographical and shows his often irresponsible behavior but also a relentless curiosity, and willingness to try anything, the essence of a successful scientist.

One cannot hope to imitate Feynman (and perhaps we should not: he was often mischievous, even mildly malicious); but any scientist should envy the way he approached problems in engineering as well as science—and the book is fun!

First published in 1937, this lovely book is a true classic. In two volumes Bell brings to life 30 or so mathematicians, from Archimedes to Cantor. When first reading the book many years ago I had remembered some of the names from school and college, but only as labels to theorems or equations, and I felt taken into a delightful new realm of knowledge – I could now think of Fermat, Lagrange, Gauss, and Riemann as people. And I began to want to know more about the scientists whose names I had heard in school and college. Bell’s book had sparked a lifelong interest.

I found this beautiful book to be simultaneously uplifting and heartbreaking.

Often, science is taught as if it descended from heaven on stone tablets, devoid of the human drama involved in its discovery and explication. Sobel captures the agony and ecstasy of the drama in the life of Galileo, the father of experimental physics and the first astronomer to use the telescope.

Summoned late in life to face the Inquisition because of his unabashed promotion of heliocentric cosmology, considered heretical by the Church, Galileo survived but died broken and blind, no longer able to see the heavenly wonders he had revealed to humanity.

Sobel unfurls Galileo’s ordeal through an exchange of tender letters with his cloistered daughter, Sister Maria Celeste, whose name was chosen to honor her star-gazing father. There’s a twist at the end that brought me to tears.

The engagingly told story of a modern hero who not only illuminated some of the darkest secrets of the universe, but who had to do it while fighting sexism all along the way. This is not a romanticized picture of a great scientist, but an inspiring and enraging telling of a real person living a recognizable life whose genius contributed to humanity and her unwavering moral compass and determination did the same for the culture.

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.

This book is out of print, but I include it in the hope that some public-spirited publisher may be persuaded to reissue this large-format picture book. It was the first book on mathematics that I read at about the age of ten and it contained precisely what I needed to show me that this was a subject with a history and a use. (Nor am I the only mathematician to have this experience.)

As an adult, I found the same author’s Mathematics for the Million a bit crass and utilitarian but I pardon him everything for a wonderful first experience.

This classic rumination on the nature of mathematics is perhaps the most famous book ever written by a mathematician.

I’ve read it several times, and each time, it brings up another facet of the subject in some new light. Portions of what Hardy says ring eerily true, and seem to be part of the identity, the very DNA, that all mathematicians must surely share. Other parts seem so alien to be almost repugnant – such as his contention that most mathematics we classify as useful is ugly and inelegant.

I’d love to argue face-to-face with Hardy about this highly opinionated work of his. In the end, I suspect we’d find lots of common ground, since intrinsically, we both love mathematics so much.

The Scientific American columns of Martin Gardner ran for 24 years and were read by amateurs, semi-amateurs, professionals, and major mathematicians (Conway, Knuth, Diaconis...). It was the interaction with this audience (recorded in addenda) which gave these essays their special quality and will give the interested outsider a real feel for what interests mathematicians. The collected columns are being reissued by the AMA and CUP but my view that anything by Martin Gardner is worth reading is reflected in my personal library.