A New Mathematical AI Startup Has Just Cracked 4 Previously Unsolvable Problems
Five years ago, mathematicians Dawei Chen and Quentin Gendron were trying to unravel a difficult area of algebraic geometry involving differentials, the mathematical properties used to measure distance on a curved surface. When they were working on a single theory, they ran into an unexpected roadblock: Their argument hinged on a strange idea in number theory, but they couldn’t solve or justify it. Finally, Chen and Gendron wrote a paper presenting their idea as a hypothesis, rather than a theory.
Chen recently spent many hours perusing ChatGPT in hopes of getting the AI to come up with a solution to an 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 founded by one of his students, Carina Hong.
Chen told Ono about the problem, and the next morning, Ono presented him with a proof, courtesy of his first math-solving AI, AxiomProver. “Everything happened naturally after that,” said Chen, who worked with Axiom to document the evidence, which has now been posted to arXiv, a public education document repository.
Axiom’s AI tool found a connection between a problem and a value phenomenon that was first studied in the 19th century. It then fabricated evidence, which proved itself. “AxiomProver’s discovery was something that everyone had missed,” Ono told WIRED.
The proof is one of many solutions to unsolved math problems that Axiom says its system has come up with in recent weeks. AI has not yet solved any of the most popular (or lucrative) problems in the field of mathematics, but it has found answers to questions that have eluded experts in various fields for years. Evidence is evidence of AI’s steadily improving math skills. In recent months, some mathematicians have reported that they are using AI tools to test new ideas and solve existing problems.
The techniques developed by Axiom may prove useful outside the world of advanced mathematics. For example, similar methods can be used to develop software that can withstand certain types of cybersecurity attacks. This will involve using AI to ensure that the code is reliable and trustworthy.
“Maths are a great place to explore and sandbox reality,” said Hong, Axiom’s CEO. “We believe there are many very important use cases with high commercial value.”
Axiom’s approach involves combining large-scale linguistic models with a proprietary AI program called AxiomProver that is trained to reason about mathematical problems to arrive at seemingly optimal solutions. In 2024, Google demonstrated a similar idea with a program called AlphaProof. Hong says AxiomSolver combines significant advances and new techniques.
Ono says the AI-generated proof of the Chen-Gendron hypothesis shows how AI can now help mathematicians. “This is a new paradigm for proving theorems,” he says.
The Axiom system is more than just an ordinary AI model, because it is able to validate proofs using a special mathematical language called Lean. Rather than just searching the literature, this allows AxiomProver to develop real problem-solving methods.
Some new evidence produced by AxiomProver shows how AI can solve math problems on its own. That proof, described in a paper posted to arXiv, provides a solution to Fel’s Conjecture, which deals with syzygies, or mathematical expressions where numbers are ordered algebraically. Amazingly, the conjecture involves the first formulas found in the notebook of the Indian mathematician Srinivasa Ramanujan more than 100 years ago. This time AxiomProver didn’t just fill in a missing piece of the puzzle, it built a proof from start to finish.
