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As an interested outsider, I have been intrigued by the number of times that homotopy theory seems to have revamped its foundations over the past fifty years or so. Sometimes there seems to have been …

Is there a list somewhere of all the problems that Erdős offered cash awards for, including both solved and unsolved problems? One would think that the answer is yes, but so far I have had no luck fin …

Gian-Carlo Rota's famous 1991 essay, "The pernicious influence of mathematics upon philosophy" contains the following passage: Perform the following thought experiment. Suppose that you are given two …

I have had a couple of experiences recently which have made me wonder whether the mathematics community should try to establish and maintain something like the Wayback Machine, but specifically focuse …

Van der Waerden's conjecture (now a theorem of Egorychev and Falikman) states that the permanent of a doubly stochastic matrix is at least $n!/n^n$. The Wikipedia article, as well as many other sourc …

In Shing-Tung Yau's autobiography The Shape of a Life, he mentions a problem that he came up with as a teenager. Suppose you know the length of one side of a triangle, one angle, and the length of …

The literature on the representation theory of the symmetric group contains some terminology that I find puzzling, and I am wondering if someone here knows the full story. One of the standard ways to …

Note: Since what I am asking about below touches on a potentially controversial subject, let me emphasize that I am only asking for a specific reference, and I am not asking for a discussion of the co …

The question is self-explanatory, but I want to make some remarks in order to prevent the responses from going off into undesirable directions. It seems that every few years I hear someone ask this qu …

EDIT (30 Nov 2012): MoMath is opening in a couple of weeks, so this seems like it might be a good time for any last-minute additions to this question before I vote to close my own question as "no long …

Martin Gardner kept voluminous correspondence with amateur and professional mathematicians worldwide throughout his career. His files are a treasure trove of information about all areas of recreation …

I often hear the advice, "Read the masters" (i.e., read old, classic texts by great mathematicians). But frankly, I have hardly ever followed it. What I am wondering is, is this a principle that peo …

Fan Chung and Ron Graham's book Erdos on Graphs: His Legacy of Unsolved Problems (A. K. Peters, 1998) collects together all of Erdos's open problems in graph theory that they could find into a single …

There is a lot of good stuff contained in the Problems section of the American Mathematical Monthly. One difficulty with extracting that information, however, is that if I see an old Monthly problem, …

In an article by George Johnson in the New York Times back in 1999, it says that an amateur mathematician from India once sent Ian Stewart a proof of the Ramanujan-Nagell theorem that the Diophantine …