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Throughout my upbringing, I encountered the following annotations on Gauss's diary in several so-called accounts of the history of mathematics: "... A few of the entries indicate that the diary wa …

In his Huygens and Barrow, Newton and Hooke, Arnold mentions a notorious teaser that, in his opinion, "modern" mathematicians are not capable of solving quickly. Then, he adds that the exception that …

Wonder whether any of you guys know why it is that the proof of the infinitude of primes that is based on the coprimality of any pair of (distinct) Fermat numbers is commonly attributed to Pólya. In …

I recently knew of this note in which Prof. M. Henk presents a proof of Minkowski's second inequality on successive minima which is (purportedly) based on ideas in Minkowski's original proof. Let me r …

Namely, the following one "All problems appeared once in the [American Mathematical] Monthly." I remember reading it several years ago... When I first posed the question, I believed that I had r …

One of the forms in which the Diophantine equation in question can be found in the literature is this: Solve the equation \begin{eqnarray}z^{2} = 4xy-x-y \qquad \qquad (\ast)\end{eqnarray} in positi …

While perusing p. 237 of the 3rd ed. of Marvin Greenberg's book on Euclidean and non-Euclidean geometries, I learned that it can actually be proven that "all possible models of hyperbolic geometry are …

As many of you may know, the illustrious L. Euler put forward a proof of the case $n=3$ of Fermat's Last Theorem via infinite descent. The thing is that, at a certain point, he resorted to the follo …

I've heard tell the following anecdote involving Pierre Gabriel and Jacques Tit at least twice in a lapse of four years or so: When P. Gabriel presented the theorem in a conference [sometime around 1 …