A New AI Math Startup Just Cracked 4 Previously Unsolved Problems
five years ago, Mathematicians Dawei Chen and Quentin Gendron tried to develop a difficult area of algebraic geometry with differential, elements of calculus used to measure distance curved surfaces. While working on one proposition, they ran into an unexpected roadblock: their argument depended on a strange formula of number theorybut they could not solve or justify it. Eventually, Chen and Gendron wrote a paper presenting their idea as a conjecture, rather than a theorem.
Chen recently spent hours on ChatGPT hoping to get the AI to come up with a solution to the still-unsolved problem, but it didn't work. Then, during a reception at a mathematics conference in Washington, DC, last month, Chen ran into Ken Ono, a well-known mathematician who recently left his job at the University of Virginia to attend Axiomand artificial intelligence startup co-founded by one of his mentees, Carina Hong.
Chen told Ono about the problem, and the next morning Ono presented him with a proof, courtesy of his startup's math-solving AI, AxiomProver. “After that, everything naturally fell into place,” says Chen, who worked with Axiom to write the proof, which is now posted on arXiva 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. “What AxiomProver found was something that everyone had been missing,” Ono tells WIRED.
The proof is one of several solutions to unsolved math problems that Axiom says its system has come up with in recent weeks. The AI has not yet solved one of the most famous (or lucrative) problems in the field of mathematics, but it has found answers to questions that have puzzled experts in various fields for years. The proofs are evidence of AI's steadily advancing mathematical abilities. In recent months, other mathematicians have reported using AI tools to explore new ideas and solve existing problems.
The techniques developed by Axiom can be useful beyond the world of advanced mathematics. For example, the same approach can be used to develop software that is more resistant to certain types of cybersecurity attacks. This would include using AI to verify that code is provably reliable and trustworthy.
“Math is really the great testing ground and sandbox for reality,” says Hong, CEO of Axiom. “We believe there are many fairly important use cases of high commercial value.”
Axiom's approach involves combining large language models with a proprietary AI system called AxiomProver that is trained to reason through mathematical problems to reach solutions that are provably correct. In 2024, Google demonstrated a similar idea with a system called AlphaProof. Hong says AxiomSolver incorporates several important advances and newer techniques.
Ono says the AI-generated proof for the Chen-Gendron conjecture shows how AI can now meaningfully help professional mathematicians. “This is a new paradigm for proving theorems,” he says.
Axiom's system is more than just a simple AI model, in that it is able to verify proofs using a specialized mathematical language called Lean. Rather than simply searching through the literature, this allows AxiomProver to actually develop new ways to solve problems.
Another one of the new proofs generated by AxiomProver shows how the AI is able to solve mathematical problems completely by itself. That evidence is also described in a newspaper posted on arXivgives a solution to Fel's Conjecture, which concerns syzygies, or mathematical expressions where numbers line up in algebra. Interestingly, the conjecture includes formulas first found in the notebook of a legendary Indian mathematician Srinivasa Ramanujan more than 100 years ago. In this case, AxiomProver didn't just fill in a missing piece of the puzzle, it figured out the proof from start to finish.
