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My favorite surprise, which is perhaps the record-holder for the longest time it took for the two ideas to be brought together, is the connection between regular n-gons and Fermat primes. The Greeks k …

We here in New York have also long sought to secure supplies of this amazingly high quality chalk. It is called Hagoromo "Fulltouch" chalk, and my colleague Jonas Reitz wrote to the company, since the …

Since this has become a free-for-all, allow me to share an anecdote that I wouldn't quite believe if I hadn't seen it myself. I attended graduate school in Connecticut, where seminars proceeded with …

Here's another great one: a certain well known mathematican, we'll call him Professor P.T. (these are not his initials...), upon his arrival at Harvard University, was scheduled to teach Math 1a (the …

A legend that I heard from my father, who heard it from ... ... ...: Levi-Civita was teaching a course in a room on (what Americans call) the second floor of a building. One day, as a prank, his stud …

Although David Hilbert was one of the first to deal seriously with infinite-dimensional complete inner product spaces, the practice of calling them after him was begun by others, supposedly without hi …

This happened just last year, but it certainly deserves to be included in the annals of mathematical legends: A graduate student (let's call him Saeed) is in the airport standing in a security line. …

Wrong! Here is Bourbaki document on algebraic geometry, taken from the now available Master's Archives: click on Autres rédactions, then on Chap.I Théorie globale élémentaire (91 p.) This prelimina …

These two studies arrive at what seems to be a more sensible conclusion: Age and Scientific Performance, Stephen Cole (1976). The long-standing belief that age is negatively associated with scien …

In my opinion, as a rule the supervisor should not be a co-author in the main paper taken from a student's thesis, even if he has contributed substantially to it, and even more so in the circumstances …

Two-column proofs Usually the only proofs that students see upon graduating from high-school are the geometry "two-column" proofs, and trying to convince them that the essence of mathematical proof l …

I think you should always cite a paper on the arXiv, if it would be appropriate to cite the paper at all. I want to strongly encourage people to put preprints of the arXiv. It makes mathematics more …

I use http://arxiv.org/ all the time. Researchers post their articles here, so it is a great way to see if anyone have already a proof or an idea on something. Some people regularly access it through …

Related to the question. I showed the following web-pages to a table-neighbor at a conference and literally got the "You just saved 3 days of my life" reaction. Doi2Bib ISBN2Bib Arxiv2Bib These web- …

Note that $a_k$ is always a multiple of $k$ (in particular, this structure disrupts the random model proposed in comments). We can exploit this structure to simplify the recurrence and clarify the dy …