ChatGPT Solves 60-Year-Old Math Problem With Novel Method, 23-Year-Old Amateur Succeeds
Key Takeaways
- ▸A 23-year-old amateur using ChatGPT Pro solved a 60-year-old Erdős conjecture in a single prompt, bypassing decades of failed attempts by world-class mathematicians
- ▸The AI discovered a novel mathematical method humans hadn't conceived of, breaking through the mental block that had trapped professional researchers
- ▸Terence Tao and other leading mathematicians validate this as categorically different from previous AI mathematical achievements, with potential for broader applications
Summary
Liam Price, a 23-year-old with no advanced mathematics training, used OpenAI's ChatGPT Pro (GPT-5.4) to solve a 60-year-old Erdős conjecture that had eluded prominent mathematicians for decades. The problem concerned 'primitive sets' of whole numbers and the Erdős sum—a mathematical score calculated for any primitive set. Price discovered the solution with a single casual prompt to the AI on an idle Monday afternoon while browsing Erdős problems for fun.
What distinguishes this breakthrough from previous AI mathematical achievements is the novel method the LLM discovered. Rather than applying existing approaches, GPT-5.4 found an entirely new pathway that human mathematicians had collectively overlooked. According to UCLA mathematician Terence Tao, a prominent observer of AI progress in mathematics, researchers had made 'a slight wrong turn at move one,' creating a mental block that the AI naturally avoided. This original methodology suggests broader applications—a rarity among recent AI mathematical accomplishments.
The Erdős conjecture required proving that the lowest value of the Erdős sum approaches exactly one as the numbers in a set grow larger. Mathematician Jared Lichtman at Stanford proved related conjectures as part of his doctoral thesis in 2022 but got stuck on this particular lower-bound problem alongside every other researcher who attempted it. The problem carried genuine prestige within the mathematical community, making this solution particularly noteworthy.
Experts acknowledge this as a fundamentally different category of AI breakthrough. Leading mathematicians validate that the LLM's novel approach—rather than brute-force computation—represents genuine mathematical insight, potentially opening new directions for problem-solving in abstract mathematics.
- The breakthrough demonstrates LLMs moving beyond pattern-matching toward genuine mathematical creativity and novel problem reframing
Editorial Opinion
This is a watershed moment for AI-assisted mathematics. Unlike previous Erdős problem solutions that applied brute computational force, GPT-5.4 discovered a conceptual shortcut humans had overlooked—suggesting LLMs excel at creative reframing rather than grinding through established methods. If this pattern generalizes, we're witnessing AI as a genuinely novel collaborator in abstract thinking. The democratization is striking: a subscription gave a young amateur access to breakthrough-quality mathematical intuition. This raises urgent questions about how human expertise, peer review, and rigorous validation will evolve when AI can generate novel mathematical insights at scale.
