AI Models Start Cracking Advanced Math Problems: Multiple Breakthroughs on Erdős Problems
Since Christmas, records from the Erdős Problems website show that 15 mathematical conjectures have shifted from ‘open’ to ‘solved,’ with 11 explicitly credited to the contributions of AI models. This reflects the rapid advancement of Large Language Models in the field of advanced mathematics.
Widespread Application of AI Tools in Mathematics
Software engineer Neel Somani tested the ability of OpenAI’s latest model, GPT-5.2, to solve an Erdős problem. The model provided a complete solution within 15 minutes, which was evaluated by Somani and verified using the formal tool Harmonic. The solution cited mathematical principles such as Legendre’s formula, Bertrand’s Postulate, and the Star of David theorem, and referenced a 2013 discussion on Math Overflow, but offered a more complete proof that extended Paul Erdős’s original problem.
Recent Changes on the Erdős Problems Website
The Erdős Problems website maintains over 1,000 conjectures proposed by the Hungarian mathematician Paul Erdős. Since the release of GPT-5.2, the number of solved problems has increased significantly. After Christmas, the site has seen 15 problems updated, with 11 solutions specifically noting the involvement of AI models. The first autonomous solution can be traced back to the Gemini-powered model AlphaEvolve in November.
Terence Tao’s Assessment of AI’s Contributions
Renowned mathematician Terence Tao stated on Mastodon that AI has made meaningful autonomous progress on 8 Erdős problems and assisted in another 6 cases by locating prior research. He believes the scalability of AI systems makes them particularly suitable for systematically tackling obscure but relatively straightforward ‘long-tail’ problems, which are therefore more likely to be solved by purely AI methods rather than by humans or hybrid approaches.
Formal Tools Driving the Verification Process
Formal proof assistants like Lean (developed by Microsoft Research in 2013) and AI tools such as Harmonic’s Aristotle are automating the verification process for mathematical proofs. Harmonic founder Tudor Achim emphasized that professors of mathematics and computer science have begun to use these tools seriously, indicating AI’s growing credibility in the academic community. Terence Tao also maintains a GitHub page dedicated to documenting AI’s contributions to Erdős problems, highlighting the ongoing nature of this trend.
