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 the world 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 one complex variable..."
Quoted from "Hilbert" by Constance Reid, where it is noted that this story is "perhaps apocryphal."