AI Solves 15 Math Problems That Stumped Humans for Years

When software engineer Neel Somani pasted a complex math problem into ChatGPT and walked away for 15 minutes, he didn't expect to return to a complete solution. But the AI delivered a proof that checked out perfectly.

That moment was just the beginning of an unexpected breakthrough in mathematics. Since Christmas, 15 problems from the Erdős collection have moved from "open" to "solved" on the official tracking website, and 11 of those solutions credited AI models as part of the discovery process.

The Erdős problems are over 1,000 mathematical puzzles left behind by Hungarian mathematician Paul Erdős. They range from relatively straightforward to mind-bendingly difficult, and they've become the gold standard for testing whether machines can truly reason at high levels.

What makes this breakthrough particularly impressive is how ChatGPT solved one problem. The AI rattled off advanced mathematical concepts, found a related solution by Harvard mathematician Noam Elkies from 2013, then delivered its own proof that was both different and more complete.

Renowned mathematician Terence Tao is tracking the progress carefully. He counts eight problems where AI made meaningful autonomous progress, plus six more where it built on previous research to push solutions forward.

Somani describes the latest AI model as "anecdotally more skilled at mathematical reasoning than previous iterations." The sheer volume of solved problems in just a few weeks has become difficult to ignore.

The Ripple Effect

The real story isn't just about solving old problems. Top mathematicians with reputations to protect are now publicly using AI tools in their research, signaling a fundamental shift in how humanity tackles its hardest questions.

Tudor Achim, founder of the AI math tool Harmonic, sees this acceptance as the true milestone. When the world's greatest mathematical minds start relying on AI assistance, it validates these tools as genuine research partners rather than fancy calculators.

Tao suggests AI systems might actually be better suited for certain types of mathematical work than humans. Their scalable nature makes them perfect for systematically working through the "long tail" of obscure problems that might have straightforward solutions but never attracted enough human attention.

New tools are making mathematical proofs easier to verify and extend, a process called formalization that once required painstaking human labor. The open source proof assistant Lean, combined with AI tools like Harmonic's Aristotle, now automates much of this work.

We're still a long way from AI doing advanced mathematics completely without human guidance, but these breakthroughs show machines can be valuable thinking partners in humanity's quest to understand the universe.