Stories About Hilbert

Actually, I read all these stories and anecdotes in John Derbyshire's book Prime Obsession. The author in turn refers to other authors, and so on ad infinitum. All I can do is point to more or less original sources. The first anecdote comes from the English-language biography of Hilbert written by Constance Reid:

Hilbert had a student who once showed him a paper purporting to prove the Riemann Hypothesis. Hilbert studied the paper carefully and was impressed by the depth of the argument; but, alas, he found an error in it that even he could not fix. The following year the student died. Hilbert asked the grief-stricken parents for permission to give a speech at the funeral. Relatives and friends are weeping in the rain by the grave; Hilbert steps forward. He begins by saying what a great tragedy it is that such a gifted young man died before he had the chance to show what he could achieve. But, Hilbert continues, although this young man's proof contained an error, it is still possible that one day a proof of this famous problem will be obtained along exactly the path the deceased had outlined. "In fact," Hilbert went on with enthusiasm, standing in the rain by the student's grave, "let us consider a function of one complex variable..."

The second anecdote comes from Martin Davis's book The Universal Computer:

Hilbert showed up every day in torn trousers, which embarrassed many people. The task of tactfully informing Hilbert of this fell to his assistant, Richard Courant. Knowing how much Hilbert enjoyed walks through rough country accompanied by conversations about mathematics, Courant invited him for a stroll, arranging things so that they had to push their way through thickets of thorny bushes. Courant then told Hilbert that he seemed to have torn his trousers on one of the bushes. "Oh no," Hilbert replied, "they've been like this for weeks, but nobody notices."

The last two stories are fairly well known and can easily be found on the internet in various versions:

One of Hilbert's students stopped coming to class. When he asked why, Hilbert was told that the student had left the university, having decided to become a poet. "I can't say I'm surprised. I always thought he didn't have enough imagination to be a mathematician."

Whoever is able to feel the truth of a lofty way of thinking and of looking at the world... will not believe those who today, with a philosophical air and a profound tone, prophesy the decline of culture and smugly accept the principle of ignorabimus, which, in my opinion, does not exist for the natural scientist either. Instead of the unknowable that fools keep talking about, our slogan says the very opposite: "We must know. We will know!"