Over the weekend, Neel Somani, who is a software engineer, former quant researcher, and a startup founder, was testing the math skills of OpenAI’s new model when he made an unexpected discovery. After pasting the problem into ChatGPT and letting it think for 15 minutes, he came back to a full solution. He evaluated the proof and formalized it with a tool called Harmonic — but it all checked out.
“I was curious to establish a baseline for when LLMs are effectively able to solve open math problems compared to where they struggle,” Somani said. The surprise was that, using the latest model, the frontier started to push forward a bit.
ChatGPT’s chain of thought is even more impressive, rattling off mathematical axioms like Legendre’s formula, Bertrand’s postulate, and the Star of David theorum. Eventually, the model found a Math Overflow post from 2013, where Harvard mathematician Noam Elkies had given an elegant solution to a similar problem. But ChatGPT’s final proof differed from Elkies’ work in important ways, and gave a more complete solution to a version of the problem posed by legendary mathematician Paul Erdős, whose vast collection of unsolved problems has become a proving ground for AI.
For anyone skeptical of machine intelligence, it’s a surprising result — and it’s not the only one. AI tools have become ubiquitous in mathematics, from formalization-oriented LLMs like Harmonic’s Aristotle to literature review tools like OpenAI’s deep research. But since the release of GPT 5.2 — which Somani describes as “anecdotally more skilled at mathematical reasoning than previous iterations” — the sheer volume of solved problems has become difficult to ignore, raising new questions about large language models’ ability to push the frontiers of human knowledge.
Somani was looking at the Erdős problems, a set of over 1,000 conjectures by the Hungarian mathematician that are maintained online. The problems have become a tempting target for AI-driven mathematics, varying significantly in both subject matter and difficulty. The first batch of autonomous so …