TMM
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18 answers
34 votes
17k views
Interesting and accessible topics in graph theory
10 votes

One problem that I found quite interesting is the Hadwiger-Nelson problem for coloring the plane. The proofs that the answer is at most $7$ and at least $4$ are easy and elegant (but also quite ...

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274 answers
927 votes
259k views
Examples of common false beliefs in mathematics
9 votes

A somewhat common belief among students starting out in cryptography: Breaking RSA requires factoring the modulus. Although it is not quite known to be a "false" belief, there is no known ...

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3 answers
19 votes
2k views
Probability of two vectors lying in the same orthant
Accepted answer
3 votes

Thanks to Ofer Zeitouni, unless I made some serious mistakes somewhere in the calculations, I've been able to find the exact answer using large deviations theory. The derivation of the final result is ...

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3 answers
19 votes
2k views
Probability of two vectors lying in the same orthant
0 votes

$\newcommand{\expn}{\mathbb{E}} \newcommand{\varn}{\operatorname{Var}}$ Following up on Brendan McKay's approach in the comments, let $v, w$ be two uniformly random vectors on the sphere. We are ...

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