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Identify $S^3$ with the unit quaternions. Let $[.,.]: S^3\times S^3\to S^3$ be the commutator map $[x,y]=xyx^{-1}y^{-1}$. Since, it is identity on $S^3\vee S^3$ it factors through $S^3\wedge S^3\cong S^6$ and creates a map $\phi: S^6\to S^3$. This map...

Let $R$ be a (commutative) Noetherian local ring with maximal ideal $ \mathfrak m$. Choose any $f_i$ that generate the maximal ideal: $(f_1, \ldots,f_t) = \mathfrak m$.
Is it true that for every element $r \in R$, there exists a polynomial $P_r\in R[x_1,\ldots, x_t]$ such that...

(April 2026: Corrected typo in equations. It should be $x^3+2x^\color{red}2-\phi^2=0$.)
I. Polyhedra
In this MO question and the table below it, we checked all 75 uniform polyhedra and found that of the 12 uniform snub polyhedra, then TEN have Cartesian coordinates involving constants that are roots of equations of degree $k>2$,...

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....