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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 …

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, …

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 …

What are some good papers that debunk common myths in the history of mathematics? To give you an idea of what I'm looking for, here are some examples. Tony Rothman, "Genius and biographers: The fictio …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

Over the years, I have heard two different proposed answers to this question. It has something to do with parabolic elements of $SL(2,\mathbb{R})$. This sounds plausible, but I haven't heard a reall …