This is a funny story about Hilbert that I got from pages 186-187 of Prime Obsession by John Derbyshire:
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 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….”
In Mathematics, there is always a tremendous temptation to go into too much detail. I have definitely been guilty of finishing mathematical sentences that I didn’t think anyone within earshot would understand just because once I had started the sentence, I felt like I had to finish it.