Amateur armed with ChatGPT solves an Erdős problem
An amateur with no advanced math training leveraged ChatGPT Pro to solve a 60-year-old Erdős problem that stumped top mathematicians. The AI's solution introduced a completely novel method, applying a known formula from a different mathematical domain, signifying a new cognitive leap for LLMs in problem-solving. This feat highlights AI's evolving potential to disrupt traditional academic fields and inspire new ways of mathematical thinking, sparking significant interest on Hacker News.
The Lowdown
A 23-year-old amateur, Liam Price, has made headlines by using ChatGPT Pro to crack a 60-year-old mathematical conjecture, an "Erdős problem" concerning primitive sets of numbers. This achievement is particularly notable because Price lacks advanced mathematical training, and the AI's method for solving the problem was entirely novel, bypassing the "mental block" that had stymied human mathematicians for decades.
- The Problem: The specific challenge involved proving Erdős's conjecture that the lowest possible "Erdős sum" for primitive sets approaches one as the numbers in the set approach infinity. Previous attempts by mathematicians, including Jared Lichtman, had failed.
- AI's Role: Price, who "vibe-maths" by feeding open Erdős problems to AI, prompted GPT-5.4 Pro with the problem. The AI generated a solution that initially appeared correct.
- Novel Methodology: Experts, including Terence Tao and Jared Lichtman, confirmed the solution's validity and, crucially, identified that the AI employed a completely new approach. It applied a formula from a related mathematical field that humans had never considered relevant to this type of problem.
- Significance: Unlike some previous AI "solutions" to Erdős problems that were less original, this case demonstrates the AI's capacity for genuinely creative and unconventional problem-solving, opening up new avenues for mathematical thought.
- Refinement and Future Potential: While the initial AI output was "poor" and required expert interpretation, the core insight was revolutionary. Mathematicians are now distilling this insight and exploring its broader applications for understanding large numbers.
This breakthrough not only solves a long-standing mathematical puzzle but also serves as a compelling testament to the emergent problem-solving capabilities of large language models. It suggests a future where AI acts not just as a computational aid but as a source of novel conceptual insights, potentially reshaping how complex scientific and mathematical problems are approached.