The Riemann Hypothesis

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 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….”

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2 Comments.

  1. Peterr L. Griffiths

    In discussing the Riemann hypothesis, why does nobody mention that the non-trivial zeta evaluations are all terms in the cotangent series with the first term as 1/2 which seems to be interpreted as being a critical line.

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  2. Reference please!

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