MathOverflow

Question: For a convex polygon P with N vertices, let f(P) denote the number of pairwise non-congruent triangles that simultaneously achieve the minimum area among all circumscribed triangles of P. What is max f(P) over all convex N-gons? Is this maximum...

I am looking for a reference, or a standard name, for the following obstruction. I am not claiming novelty; I am trying to find the right existing language.
There are two elementary "defect" phenomena that look formally similar.
1. On the line R\mathbb{R}R, let ρ(x)=−x\rho(x)=-xρ(x)=−x be a reflection and τs(x)=x+s\tau_s(x)=x+sτs​(x)=x+s a translation. Then ρτsρ−1=τ−s\rho\tau_s\rho^{-1}=\tau_{-s}ρτs​ρ−1=τ−s​, so with the convention [g,h]=ghg−1h−1[g,h]=ghg^{-1}h^{-1}[g,h]=ghg...

The purpose of this question is to collect examples where large language models (LLMs) like ChatGPT have led to notable mathematical developments.
The emphasis in this question is on LLMs, but answers about other machine-learning tools are also welcome....

In his paper "A general theory of self-similarity", Tom Leinster develops a theory that expresses facts about self-similar objects taking advantage of coalgebras, universal properties and, in general, categorical language.
I am trying to apply some of their results to a particular kind of self-similar objects, the so-called Newton's fractals: given a complex function $f(z)$, the Newton-Raphson method for finding roots of the function gives a map $N_f(z) := z- \frac{f(z...