Remember these brain-teaser math issues from faculty that made you wish to throw your pencil? Now think about ones so laborious they’ve stumped mathematicians for many years.
Paul Erdős, who printed extra papers than anybody in math historical past, left behind a whole lot of those puzzles when he died in 1996. This weekend, GPT-5.2 Pro solved one.Neel Somani prompted the AI to deal with Erdős Problem #397, which asks whether or not infinitely many options exist for a selected equation involving central binomial coefficients. GPT-5.2 generated the proof, the software Aristotle formalized it in Lean (a verification language), and Fields Medalist Terence Tao accepted it.
Here’s what makes this a milestone
- It’s a part of a wave of autonomous solves: GPT-5.2 has now cracked Problem #728, #729, and 397.
- Verified arithmetic: The Aristotle system auto-corrected gaps in proofs and produced Lean-verified code.
- Self-contained reasoning: Unlike October 2025’s GPT-5 controversy (which simply discovered present literature), Tao says these are authentic proofs.
The catch? Tao emphasizes these are “lowest-hanging fruit”; issues solvable with commonplace methods, not profound breakthroughs. GPT-5.2 scores 77% on competition-level math however solely 25% on open-ended analysis requiring real perception.
Why this issues
For information employees, we’re watching AI transition from pattern-matching to proof-generation. When fashions can autonomously resolve decade-old issues (even simple ones), count on this to speed up throughout fields requiring logical reasoning: contract evaluation, regulatory compliance, and engineering optimization.
Over the following 6-12 months, look ahead to GPT-5.3 (or no matter is subsequent) and competing fashions from Google/Anthropic to systematically deal with the remaining ~660 unsolved Erdős issues.
If you’re employed with structured problem-solving, begin experimenting with how these fashions deal with your area’s equal “Erdős problems”; these nagging challenges everybody is aware of about, however no person’s solved.
Editor’s observe: This content material initially ran within the e-newsletter of our sister publication, The Neuron. To learn extra from The Neuron, join its e-newsletter right here.
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