Over the weekend, Neel Somani, who’s a software program engineer, former quant researcher, and a startup founder, was testing the maths expertise of OpenAI’s new mannequin when he made an surprising discovery. After pasting the issue into ChatGPT and letting it suppose for quarter-hour, he got here again to a full resolution. He evaluated the proof and formalized it with a instrument known as Harmonic — however it all checked out.
“I used to be curious to ascertain a baseline for when LLMs are successfully capable of clear up open math issues in comparison with the place they wrestle,” Somani mentioned. The shock was that, utilizing the newest mannequin, the frontier began to push ahead a bit.
ChatGPT’s chain of thought is much more spectacular, rattling off mathematical axioms like Legendre’s method, Bertrand’s postulate, and the Star of David theorum. Finally, the mannequin discovered a Math Overflow submit from 2013, the place Harvard mathematician Noam Elkies had given a sublime resolution to an identical downside. However ChatGPT’s last proof differed from Elkies’ work in necessary methods, and gave a extra full resolution to a model of the issue posed by legendary mathematician Paul Erdős, whose huge assortment of unsolved issues has turn into a proving floor for AI.
For anybody skeptical of machine intelligence, it’s a shocking consequence — and it’s not the one one. AI instruments have turn into ubiquitous in arithmetic, from formalization-oriented LLMs like Harmonic’s Aristotle to literature overview instruments like OpenAI’s deep analysis. However because the launch of GPT 5.2 — which Somani describes as “anecdotally extra expert at mathematical reasoning than earlier iterations” — the sheer quantity of solved issues has turn into troublesome to disregard, elevating new questions on giant language fashions’ skill to push the frontiers of human information.
Somani was trying on the Erdős issues, a set of over one thousand conjectures by the Hungarian mathematician which might be maintained on-line. The issues have turn into a tempting goal for AI-driven arithmetic, various considerably in each material and issue. The primary batch of autonomous options got here in November from a Gemini-powered mannequin known as AlphaEvolve — however extra not too long ago, Somani and others have discovered GPT 5.2 to be remarkably adept with high-level math.
Since Christmas, 15 issues have been moved from “open” to “solved” on the Erdős web site — and 11 of the options have particularly credited AI fashions as concerned within the course of.
The revered mathematician Terence Tao has a extra nuanced have a look at the progress on his GitHub web page, counting eight completely different issues the place AI fashions made significant autonomous progress on an Erdős downside, with six different circumstances the place progress was made by finding and constructing on earlier analysis. It’s a good distance from AI techniques with the ability to do math with out human intervention, however it’s clear that there’s an necessary position for giant fashions to play.
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On Mastodon, Tao conjectured that the scalable nature of AI techniques makes them “higher suited to being systematically utilized to the ‘lengthy tail’ of obscure Erdős issues, a lot of which even have simple options.”
“As such, many of those simpler Erdős issues are actually extra prone to be solved by purely AI-based strategies than by human or hybrid means,” Tao continued.
One other driving drive is a current shift in direction of formalization, a labor-intensive activity that makes mathematical reasoning simpler to confirm and prolong. Formalization doesn’t require use of AI and even computer systems, however a brand new crop of automated instruments have made the method far simpler. The open-source “proof assistant” Lean, which was developed at Microsoft Analysis in 2013, has turn into broadly used throughout the discipline as a manner of formalizing proof— and AI instruments like Harmonic’s Aristotle promise to automate a lot of the work of formalization.
For Harmonic founder Tudor Achim, the sudden soar in solved Erdős issues is much less necessary than the truth that the world’s best mathematicians are beginning to take these instruments significantly. “I care extra about the truth that math and laptop science professors are utilizing [AI tools],” Achim mentioned. “These individuals have reputations to guard, so once they’re saying they use Aristotle or they use ChatGPT, that’s actual proof.”
