I mentioned the book Prime Obsession by John Derbyshire (Prime Obsession) in a previous post (In Flagrante Delicto: The Death of President Faure). The book attempts to tell the story of the greatest unsolved mathematical problem of all time (the Riemann Hypothesis) and make the problem itself intelligible to the lay reader who has just a high school mathematical background. One of the greatest mathematicians of all time, David Hilbert, was once asked what he would do if he could be revived after a sleep of several centuries. He replied that he would ask if anyone had proved the Riemann Hypothesis, showing the importance of this unsolved problem to mathematicians. The book is a brilliant achievement, though I must confess I skipped most of the math and soaked up the math culture and personalities instead.
Mathematicians, like chess masters, are legendary eccentrics, and here are a few anecdotes about David Hilbert from Derbyshire’s book. The first one is quoted from Constance Reid’s biography:
Hilbert had a student who one day presented him with a paper purporting to prove the Riemann Hypothesis. Hilbert studied the paper carefully and was really impressed by the depth of the argument; but unfortunately he found an error in it which even he could not eliminate. The following year the student died. Hilbert asked the grieving parents if he might be permitted to make a funeral oration. While the student’s relatives and friends were weeping beside the grave in the rain, Hilbert came forward. He began by saying what a tragedy it was that such a gifted young man had died before he had an opportunity to show what he could accomplish. But, he continued, in spite of the fact that this young man’s proof of the Riemann Hypothesis contained an error, it was still possible that some day a proof of the famous problem would be obtained along the lines which the deceased had indicated. “In fact,” he continued with enthusiasm, standing there in the rain by the dead student’s grave, “let us consider a function of a complex variable …”
The second anecdote is sourced from Martin Davis’s The Universal Computer:
Hilbert was seen day after day in torn trousers, a source of embarrassment to many. The task of tactfully informing Hilbert of the situation was delegated to his assistant, Richard Courant. Knowing the pleasure Hilbert took in strolls in the countryside while talking mathematics, Courant invited him for a walk. Courant managed matters so that the pair walked through some thorny bushes, at which point Courant informed Hilbert that he had evidently torn his pants on one of the bushes. “Oh no,” Hilbert replied, “they’ve been that way for weeks but nobody notices.”
And the third, Derbyshire says is apocryphal but probably true:
One of Hilbert’s students stopped showing up in classes. On inquiring the reason, Hilbert was told that the student had left the university to become a poet. Hilbert: “I can’t say I’m surprised. I never thought he had enough imagination to be a mathematician.”
Hilbert was also fond of the fairer sex:
By no means antisocial, he was a keen dancer and a popular lecturer. He was also something of a skirt-chaser, to the very limited degree that was possible in the ambience of provincial Wilhelmine Germany. (It is not likely that anything very improper took place.)
The next anecdote brings together two other German mathematicians, Landau and his colleague at Gottingen, Emmy Noether. The latter was that rare bird (pun unintended!), a first-class female mathematician (here is an appraisal of her mathematical achievements: Emmy Noether, The Most Significant Mathematician You’ve Never Heard Of):
Noether was mannish and very plain. Asked if she was not an instance of a great female female mathematician, Landau replied: “I can testify that Emmy is a great mathematician, but that she is a female, I cannot swear.”
An uncharitable thing to say, Landau. Shame on you!
In most people’s eyes, mathematicians conform to the stereotype of the absent-minded professor. Here is what Derbyshire has to say:
Much is made of this stereotype, and there is something to it. Because of the purely abstract nature of the material they work with and the need to concentrate on that material for long hours at a time, mathematicians tend to be somewhat detached from more earthly matters. It is not impossible for a mathematician to be worldly, and there are many counterexamples. Rene Descartes was a soldier and courtier. (He survived the first but not the second.) Karl Weierstrass spent his years at university drinking and fighting and left without a degree. John von Neumann, one of the greatest of twentieth-century mathematicians, was quite a boulevardier, fond of pretty women and fast cars.
Jacques Hadamard, on the evidence, was not one those counterexamples. Even discounting the apocrypha that develop around any great man, it seems plain that Hadamard could not knot his tie without assistance. His daughter claimed he could not count beyond four, “After that came n.”
My father happens to be a mathematician, and I’m afraid he’s no counterexample either. He can knot his tie without assistance, but is unable to change a light bulb.