A legendary unsolved math problem from the famous Paul Erdős has been solved using a workflow where ChatGPT proposed the strategy and a computer-logic assistant verified the final proof.
March 31, 2026
Original Paper
Optimal bounds for an Erdős problem on matching integers to distinct multiples
arXiv · 2603.28636
The Takeaway
Erdős problems are notoriously difficult and often remain unsolved for decades. This marks a significant milestone where AI didn't just crunch numbers, but successfully architected a high-level logical strategy for a complex mathematical breakthrough.
From the abstract
Let $f(m)$ be the largest integer such that for every set $A = \{a_1 < \cdots < a_m\}$ of $m$ positive integers and every open interval $I$ of length $2a_m$, there exist at least $f(m)$ disjoint pairs $(a, b)$ with $a \in A$ dividing $b \in I$. Solving a problem of Erdős, we determine $f(m)$ exactly, and show $$ f(m)=\min\bigl(m,\lceil 2\sqrt{m}\,\rceil\bigr) $$ for all $m$. The proof was obtained through an AI-assisted workflow: the proof strategy was first proposed by ChatGPT, and the detailed