Who was that forgetful mathematician?

Question

Who was the (Japanese?) mathematician who said in a lecture that a certain conjecture still remained to be proved, and one of the students present told him that he (the mathematician) had already proved that conjecture decades earlier?

Answer 1

This kind of thing happens surprisingly often, so there is probably more than one "right answer." I am reminded of William Durfee's anecdote about J. J. Sylvester (as quoted by Florian Cajori in Teaching and History of Mathematics in the United States):

I remember once submitting to Sylvester some investigations that I had been engaged on, and he immediately denied my first statement, saying that such a proposition had never been heard of, let alone proved. To his astonishment, I showed him a paper of his own in which he had proved the proposition; in fact, I believe the object of his paper had been the very proof which was so strange to him.

The above anecdote matches your account in several details: Sylvester was a mathematician; he insisted that a certain result was unproved; someone else pointed out that Sylvester himself had proved the result. But the setting was not a lecture, and it was Durfee, not Sylvester, who stated the proposition first. Here's another anecdote about a different person (not a mathematician) taken from the book The Dynamics of Modern Society:

The Nobel laureate, Otto Loewi, reports having waked in the middle of the night, jotting down some notes on what he sensed to be a momentous discovery, going back to sleep, awaking to find that he could not possibly decipher his scrawl, spending the day in a miserable and unavailing effort to remember what he had had in mind, being again aroused from his slumber at three the next morning, racing to the laboratory, making an experiment and two hours later conclusively proving the chemical transmission of nervous impulse. So far, so good; another case, evidently, of the pattern of subconscious creativity unforgettably described by Poincare. But some years later, when Loewi, upon request, reported all this to the International Physiological Congress, he was reminded by a former student that, eighteen years before that nocturnal discovery, he had fully reported his basic idea. "This," says Loewi, "I had entirely forgotten."

Note, however, that there are different accounts of the Loewi incident; here's what Encyclopedia.com says about it:

In fact, there is an element of mystery and drama in the way Loewi came to demonstrate experimentally the chemical transmission of nervous impulses. By the time he did so, in 1921, the hypothesis of chemical transmission was nearly twenty years old. Credit for the hypothesis is usually given to Elliott, who published the suggestion in 1904. In 1929, after Loewi’s work had become well known, another Cambridge physiologist, Walter Fletcher, recalled that Loewi had independently proposed the chemical transmission hypothesis in 1903, in a private conversation with Fletcher, who was then working in Loewi’s laboratory at Marburg. Before this reminder from Fletcher, Loewi had completely forgotten the conversation; but he thereafter attached considerable significance to it, undoubtedly to emphasize the independence of his own work. However, as Dale suggested more than once, it is hard to believe that Loewi’s mind had not been at least somewhat prepared for the idea by his meeting with Elliott and in general by his visit to Cambridge, where the meaning of the neuromimetic effects of drugs was then a topic of intense interest and discussion.

Finally, I can't resist mentioning a case where Vaughan Jones asked a question on MathOverflow and someone pointed out that the answer could be found in a book by…Vaughan Jones.