ChatGPT Solves Decades-Old Math Conjecture, Experts Confirm Breakthrough

ChatGPT Solves 60-Year-Old Math Problem, Experts Validate Breakthrough

In a surprising turn, a 23-year-old named Liam Price appears to have solved one of the famously difficult Erdős problems—a set of abstruse math conjectures left by Hungarian mathematician Paul Erdős—using ChatGPT. The breakthrough, reported by Scientific American, marks a rare instance where AI may have genuinely outpaced human mathematicians in tackling an unsolved problem.

How a Non-Expert Solved an Erdős Problem with AI

Price, who does not hold an advanced math degree, reportedly prompted GPT-5.4 to generate a solution for one of the Erdős conjectures. While many AI-generated solutions to these problems have proven incorrect, experts reviewing Price’s submission—posted to erdosproblems.com—say his approach is valid.

The problem in question had stumped mathematicians for decades, with most experts following a predictable sequence of moves to approach it. However, ChatGPT took an unexpected path by applying a well-known formula in a novel way, bypassing the conventional approach that had led previous researchers astray.

Experts Praise AI’s Unconventional Solution

Terence Tao, a mathematician at the University of California, Los Angeles and a leading voice in evaluating AI’s role in mathematics, noted the significance of the AI’s approach:

“This one is a bit different because people did look at it, and the humans that looked at it just collectively made a slight wrong turn at move one.”

There was kind of a standard sequence of moves that everyone who worked on the problem previously started by doing, but the AI took an unexpected approach by using a well-known formula that no one had thought to apply to this type of question.”

Tao maintains a database of AI-assisted solutions to Erdős problems, but most have either rediscovered existing proofs or provided flawed reasoning. This latest case, however, suggests AI may have truly “thought” outside conventional boundaries.

Human Expertise Still Required to Refine AI Output

While the AI’s raw output was initially unclear, human mathematicians played a crucial role in refining and validating the solution. Jared Lichtman, a mathematician at Stanford University whose doctoral thesis focused on an Erdős conjecture, explained:

The raw output of ChatGPT’s proof was actually quite poor. So it required an expert to kind of sift through and actually understand what it was trying to say.”

Tao added that the breakthrough represents a new way to conceptualize large numbers and their properties:

“We have discovered a new way to think about large numbers and their anatomy. It’s a nice achievement. I think the jury is still out on the long-term significance.”

Caution Urged Despite Enthusiasm

Despite the excitement, experts urge caution. In October 2023, Kevin Weil, then a vice president at OpenAI, prematurely celebrated ChatGPT’s solution to another Erdős problem—only for the claim to collapse under scrutiny. Weil deleted his post after competitors exposed that the AI had merely regurgitated an existing proof.

The incident underscores the risks of overhyping AI-generated math solutions before rigorous human validation. Still, the latest breakthrough suggests that AI may occasionally offer genuinely novel insights—if not yet a fully autonomous path to mathematical discovery.

Key Takeaways

• Liam Price, a 23-year-old without an advanced math degree, used ChatGPT to solve an Erdős problem.
• Experts, including Terence Tao and Jared Lichtman, validated the AI’s unconventional approach.
• The AI bypassed conventional methods by applying a well-known formula in a new way.
• Human mathematicians were still required to refine and verify the AI’s output.
• Past AI claims, such as one by Kevin Weil in October 2023, have later been debunked.
• Experts remain cautiously optimistic about AI’s role in mathematical discovery.