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This question was cross-posted on Math Stack Exchange. Here is a copy of my answer for it there. This is it.  The perfectly centered billiards break.  Behold. Setup This break was computed i …

The answer is 'no'. Making the substitution $$ x = \frac{(t-1)(t-5)(t^2+2t+5)}{16t^2}, $$ one finds $$ {\textstyle\sqrt{x+\sqrt{x+\sqrt{x+1}}}\,\mathrm{d}x} = \frac{(t^2-2t+5)(t^2-5)\sqrt{t^4{-}2t^2 …

I think one reason JSTOR doesn't have “loss of generality” before 1831 is that fewer scientists wrote in English. But one finds (with minor variants merged, translations *starred, and year first publi …

I'm adding a separate answer for the general question that the OP asked, which settles the question in the negative for all $n>2$ (and gives an alternate proof for $n=3$ to the one I gave above). Rec …

I was there. Arnol'd is one of my big mathematical heros, but I found the whole thing really sad. It was in French, but my French is decent. Arnol'd began his part with a phrase I've heard him say be …

I have proved this equality by means of Cauchy’s Theorem applied to an adequate function. Since my solution is too long to post it here, I posted it in arXiv: Juan Arias de Reyna, Computation of a De …

normalis already meant right-angled in classical Latin; for example, angulus normalis appears in the first century text De institutione oratoria (volume XI, paragraph 3.141) by Marcus Fabius Quintilia …

These questions on the spacings between primes are expected to be true, but are far from being proved. They are not directly related to RH, but seem to encode other relations among zeros. The conjec …

"Numerology" such as you've observed is explained in the paper Gross, B.H., and Zagier, D.: On singular moduli, J. reine angew. Math. 355 (1985), 191$-$220. MR772491 (86j:11041) which gives mor …

In general, once you've proven an inequality like this in ${\bf R}$ it holds automatically in any Euclidean space (including ${\bf C}$) by averaging over projections. ("Inequality like this" = inequa …

When looking for a dual concept we should be careful not to be tricked by a shallow symmetry. I will not comment on your definition of anti-compactness. Instead I would like to explain what the "true" …

The limiting ratio is $\frac{1}{\zeta(2)} = \frac{6}{\pi^2}= 0.6079271018540266286632767792\ldots$ The question is easily seen to be equivalent to "What is the probability that two integers are relati …

Using the $\Delta^2- \epsilon \Delta$ approach, Tim Netzer and I have verified Kazhdan's property (T) for ${\rm SL}(3,\mathbb Z)$. For the standard generators $e_{ij}$ ($i\neq j$) we can show a spectr …

I found a proof of $$5 \sum_{m=1}^{\infty} \frac{1}{m^4} = 2 \left( \sum_{n=1}^{\infty} \frac{1}{n^2} \right)^2$$ by rearranging sums and wrote it up. The argument is just 1.5 pages, the other 4.5 ar …

I am going to draw heavily from Github discussion on HoTT book pull request 617. There are different kinds of equality. Let us say that equality is "intensional" if it distinguishes objects based on …