AI Solves 6 Decades-Old Math Problems with Human Collaboration
Key Summary
The Office of Justin Sun has announced the recipients of its newest round of the Justin Sun Prize, recognizing independent researcher Wouter van Doorn, mathematics Ph.D. student Quanyu Tang, and mathematics researcher Yanyang Li for their contributions to solving Erdős problems. The three researchers solved six Erdős problems, including #650, #369, #457, #469, #1044, and #1196. Tang worked with Li to use human judgment and AI-assisted discovery to solve #650, with ChatGPT and Aristotle helping develop the proof strategy and repair a gap during Lean formalization. The prize program aims to support advances in mathematics, formal verification, and AI-assisted scientific discovery, with the first awards recognizing both mathematical discovery and the work needed to make proofs independently checkable.
The Justin Sun Prize
The Office of Justin Sun today announced the newest recipients of the Justin Sun Prize: independent researcher Wouter van Doorn, mathematics Ph.D. student Quanyu Tang, and mathematics researcher Yanyang Li from Nanjing’s Southeast University, recognized for contributions spanning six Erdős problems.
The Erdős Problems
Erdős problems are mathematical questions posed or popularized by Hungarian mathematician Paul Erdős about numbers, patterns and other mathematical structures. Often simple to state but difficult to solve, they have helped shape research in number theory and combinatorics, with some remaining open for decades.
The Justin Sun Prize Recipients
Van Doorn and Tang worked with Yanyang Li, from Southeast University’s School of Mathematics in Nanjing, to solve Erdős Problem #650, determining exactly how many integers can always be matched to distinct multiples within a specified interval.
The AI-Assisted Discovery
ChatGPT helped develop the proof strategy, while Aristotle, an AI system for mathematical reasoning, repaired a gap during Lean formalization. The researchers then simplified the argument and wrote the final proofs and exposition.