I studied mathematics fifty years ago. I have forgotten much of what I learned. there is an anecdote however that one of my maths lecturers told that I would dearly love to know more about. He stated that in some of Gauss' theorems he wrote something like "it clearly follows that" but it did not clearly follow to those coming after him. This lecturer said that his assertion was trusted but that some of those logical jumps took a very long time to be proved by others. Back then in the early 1970s it was even implied that there were a few that had not yet been proved. Now this might be a complete myth but if there is any truth in it I would very much like to know and more specifically which theorems this appeared in. Many thanks Chris Milton
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5$\begingroup$ Maybe see arxiv.org/abs/1704.06585 ? $\endgroup$– Sam HopkinsCommented Aug 8, 2023 at 0:32
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2$\begingroup$ Reminiscent of the "yes it's obvious" anecdote hsm.stackexchange.com/questions/7247 $\endgroup$– J.J. GreenCommented Aug 8, 2023 at 9:31
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1$\begingroup$ Maybe he meant “clearly to myself” $\endgroup$– Pietro MajerCommented Aug 8, 2023 at 10:56
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$\begingroup$ It is a complete myth. Forget it. $\endgroup$– Franz LemmermeyerCommented Aug 15, 2023 at 14:27
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This could be related to the "Gauss problem" on the limit distribution of remainders of partial fractions. Gauss found this distribution, and in a letter to Laplace, claimed that he proved it. The first published proof appeared in 1928:
R. O Kuzmin, On a problem of Gauss, Dokl. Acad. Sci USSR, 1928, 375-380.
Paul Levy published an independent proof in 1929. You can read about this problem, for example in the book:
A. Ya. Khintchin, Continued fractions, Dover 1997, in the last chapter.
I have not read Gauss' letter, and so I am not sure whether he really wrote "it clearly follows that...", or what was his exact expression.
answered Aug 8, 2023 at 12:02