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Most people I work with don’t know that my academic career started in applied mathematics. I took a fairly winding route from there to where I am now, through theoretical robotics, computer graphics and game design, and from there to game-based learning and educational technology.
Somewhere along the way, I lost the working knowledge it takes to solve research-level math problems myself. But I can still read the notation, and I know the fundamentals well enough to notice when a headline and the paper behind it describe two different things.
And this year, there has been plenty to notice. Since May, AI systems have been credited with disproving one of Paul Erdős’s best-known conjectures and with settling one of the Millennium Prize Problems, and those are only two of the “AI solved math” headlines.
So in today’s post, I want to go through seven of the most important “AI solved math” stories, ranked from least to most consequential, and look at how much of each one holds up and how much of it is wishful thinking.
1. Erdős problems that weren’t quite solved
Paul Erdős, the Hungarian mathematician who died in 1996, left behind more than a thousand problems, many of them with small cash prizes attached. Thomas Bloom at the University of Manchester keeps track of them on erdosproblems.com. Over the past year, his site has become a kind of scoreboard for AI labs, and two episodes on it show how easily these claims go wrong.
The first came in October 2025, when OpenAI vice president Kevin Weil posted that GPT-5 had found solutions to ten “previously unsolved Erdős problems.” Bloom quickly called that “a dramatic misrepresentation.” On his site, a problem marked as open only means that he personally doesn’t know of a paper that solves it. GPT-5 had found older papers with solutions that Bloom simply did not know about. That is still useful, since the literature is scattered over a century of journals and even specialists miss things. But it isn’t new mathematics. Weil later deleted his post.
The second episode is more interesting. At the end of November, Boris Alexeev ran Aristotle, a proof system built by the startup Harmonic, on Problem #124. Roughly speaking, the problem asks when every large enough whole number can be written as a sum of distinct powers of a few chosen bases. Aristotle found a proof in about six hours and checked it in Lean, a programming language in which a computer verifies every step of a proof. The coverage that followed described a problem that had been open for nearly thirty years.
But Erdős had stated the problem in three places, and in two of them he left out an important condition. According to Terence Tao, that omission made the problem a direct consequence of a result that was already known. Aristotle solved only this easier version, and the harder one is still open.
The proof is correct, and Aristotle found it without human help. But Lean could only confirm that the proof worked for the statement Aristotle was given. When mathematicians went back to Erdős’s original papers, they noticed that this statement didn’t match what he had meant.
