"Five years ago, mathematicians Dawei Chen and Quentin Gendron were trying to untangle a difficult area of algebraic geometry involving differentials, elements of calculus used to measure distance along curved surfaces. While working on one theorem, they ran into an unexpected roadblock: Their argument depended on a strange formula from number theory, but they were unable to solve or justify it. In the end, Chen and Gendron wrote a paper presenting their idea as a conjecture, rather than a theorem."
"Chen recently spent hours prompting ChatGPT in the hopes of getting the AI to come up with a solution to the still unsolved problem, but it wasn't working. Then, during a reception at a math conference in Washington, DC, last month, Chen ran into Ken Ono, a well-known mathematician who had recently left his job at the University of Virginia to join Axiom, an artificial intelligence startup cofounded by one of his mentees, Carina Hong."
"Chen told Ono about the problem, and the following morning, Ono presented him with a proof, courtesy of his startup's math-solving AI, AxiomProver. "Everything fell into place naturally after that," says Chen, who worked with Axiom to write up the proof, which has now been posted to arXiv, a public repository for academic papers. Axiom's AI tool found a connection between the problem and a numerical phenomenon first studied in the 19th century. It then devised a proof, which it helpfully verified itself."
Dawei Chen and Quentin Gendron encountered a roadblock in algebraic geometry because a key argument required an unresolved number-theory formula, so they presented the result as a conjecture. Chen attempted extensive prompting of ChatGPT without success. A chance meeting with Ken Ono, who joined the AI startup Axiom, led to Ono presenting a proof produced by AxiomProver the next morning. AxiomProver identified a link to a 19th-century numerical phenomenon, devised a proof, and verified it. Chen collaborated with Axiom to write up the proof and posted it to arXiv. Axiom reports multiple recent solutions to longstanding math questions.
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