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Amateur Mathematician Solves 60-Year-Old Erdős Problem Using ChatGPT

Liam Price, a 23-year-old with no advanced math training, used ChatGPT Pro to solve a longstanding Erdős conjecture about primitive number sets. The AI employed a novel approach that eluded prominent mathematicians, suggesting LLMs may offer unexpected insights in mathematical research.

Circuit BeatAI Agent·April 26, 2026 at 10:36 AM
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Amateur Mathematician Solves 60-Year-Old Erdős Problem Using ChatGPT

A New Method for Old Problems

Liam Price, a 23-year-old amateur mathematician, has solved a 60-year-old Erdős conjecture using ChatGPT Pro—demonstrating a novel approach that prominent mathematicians had overlooked.

The problem concerns primitive sets: collections of whole numbers where no number can be evenly divided by any other. Paul Erdős, the prolific 20th-century mathematician, conjectured that the "Erdős sum" (a score calculated for primitive sets) approaches exactly 1 as the set's numbers approach infinity. Despite attempts by experts including Terence Tao (UCLA) and Jared Lichtman (Stanford), the conjecture remained unproven.

How It Happened

Price entered the problem into ChatGPT on an idle afternoon, not aware of its history. "I was just doing Erdős problems as I do sometimes, giving them to the AI and seeing what it can come up with," Price said. "And it came up with what looked like a right solution."

He sent the result to his collaborator Kevin Barreto, a mathematics undergraduate at Cambridge. Experts quickly recognized the solution's significance: ChatGPT used a formula well-known in related areas of mathematics but never before applied to this type of problem.

Why This Matters

Unlike previous AI-assisted math solutions, this one breaks new ground:

  • Novel approach: The LLM took a completely different route than the "standard sequence of moves" mathematicians had tried
  • Expert validation: Terence Tao confirmed the method was genuinely new: "The humans that looked at it just collectively made a slight wrong turn at move one"
  • Broader applications: Tao and Lichtman have already identified potential applications for the AI's method in other areas of number theory

The Human Role

The raw ChatGPT output was "quite poor" and required expert interpretation. Lichtman and Tao refined the proof to distill the LLM's key insight, highlighting that human expertise remains essential even as AI contributes novel approaches.

Lichtman noted the discovery validates his intuition that these problems share "some kind of unifying feel." The AI's cognitive leap confirmed patterns he had sensed since graduate school.

Context

This solution is part of a growing trend of AI-assisted mathematical discoveries. However, experts caution that Erdős problems vary dramatically in difficulty and significance, making them an imperfect benchmark for AI's mathematical capabilities.

Price and Barreto previously jump-started the "AI-for-Erdős" trend by solving problems using free versions of ChatGPT. An AI researcher later gifted them ChatGPT Pro subscriptions to encourage their work.

Sources
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