AI Helps Teen Solve 58-Year-Old Math Puzzle

Liam Price doesn't have a math degree or even a college acceptance letter yet, but last month he accomplished something seasoned mathematicians couldn't: solving a 58-year-old puzzle with help from artificial intelligence.

From his home in southwest England, Price used ChatGPT to crack Erdős problem #1196, one of more than 1,000 brain teasers collected by legendary Hungarian mathematician Paul Erdős. The puzzle, first posed in 1966, deals with sets of whole numbers where none of the numbers evenly divides any of the others.

What makes this breakthrough remarkable isn't just that AI helped solve it. The solution took a completely unexpected route that human mathematicians hadn't considered in nearly six decades of trying.

Jared Duker Lichtman at Stanford University compared it to AI discovering a chess opening no one had thought of before because humans were too focused on traditional strategies. Instead of using probability theory like every human attempt before it, ChatGPT solved the problem in its original mathematical language while still establishing new connections between different areas of math.

"It is incredible," says Sébastien Bubeck, a mathematician at OpenAI. Just a year ago, experts thought AI would hit a wall and never create truly original solutions beyond its training data.

The Ripple Effect

This success is part of a larger wave of AI breakthroughs in mathematics. Computers are moving beyond simple number crunching to engage in the kind of logical reasoning that's defined mathematics for over 2,300 years.

The progress is happening fast, and researchers are setting ambitious goals. Thang Luong, who leads Google DeepMind's Superhuman Reasoning team, hopes AI and human mathematicians might jointly win a Fields Medal (math's highest honor) by 2030.

Even skeptics are becoming believers. Daniel Litt, a mathematician at the University of Toronto, admits he's puzzled that AI isn't already making bigger discoveries given its superhuman knowledge and tireless work ethic.

The technology still has limits. Current models can only produce proofs about three or four pages long, though Google's internal systems are already reaching ten pages. But researchers see clear paths to improvement through more computing power and better algorithms.

For Price, working with his collaborator Kevin Barreto from Cambridge University, the achievement proves that mathematical discovery is becoming more accessible than ever before.

Mathematics is entering a new era where humans and machines can explore problems together in ways neither could alone.