Chen recently spent hours chatting on GPT in hopes that the AI would find a solution to the still-unsolved problem, but it wasn’t working. Then, during a reception at a mathematics conference in Washington, DC, last month, Chen met Ken Ono, a renowned mathematician who had recently left his job at the University of Virginia and joined Axiom, an artificial intelligence startup co-founded by one of his disciples, Carina Hong.
Chen explained the problem to Ono, and the next morning, Ono presented him with a proof, courtesy of his startup’s math-solving AI, AxiomProver. “After that everything fell into place naturally,” says Chen, who worked with Axiom to write the proof, which is now posted on arXiv, a public repository for academic papers.
Acxiom’s AI tool found a connection between the problem and a numerical phenomenon first studied in the 19th century. It then produced a proof, which it helped verify itself. “What AxiomPower found was something that all humans had missed,” Ono told WIRED.
The proof is one of several 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 famous (or fascinating) problems in the field of mathematics, but it has found answers to questions that have puzzled experts in various fields for years. These proofs are proof of AI’s ever-expanding math capabilities. In recent months, other mathematicians have reported using AI tools to explore new ideas and solve existing problems.
The technologies being developed by Axiom may prove useful outside the world of advanced mathematics. For example, the same approaches can be used to develop software that is more resilient to certain types of cybersecurity attacks. This will involve using AI to verify that the code is reliable and trustworthy.
“Mathematics is really the great testing ground and sandbox for reality,” says Hong, CEO of Axiom. “We believe there are a lot of important use cases of high business value.”
Axiom’s approach involves combining large language models with a proprietary AI system called AxiomProver that is trained to reason through math problems to reach solutions that are likely to be correct. In 2024, Google demonstrated a similar idea with a system called AlphaProof. Hong says AxiomSolver includes several important advancements and new technologies.
Ono says the AI-generated proof for the Chen–Gendron conjecture shows how AI can now meaningfully assist professional mathematicians. “This is a new paradigm for proving theorems,” he says.
Acxiom’s system is more than just a regular AI model, in that it is able to verify proofs using a special mathematical language called Lean. Instead of simply searching the literature, this allows AxiomPower to develop genuine new ways of solving problems.
One of the new proofs produced by AxiomPower shows how AI is capable of solving math problems completely on its own. That proof, also described in a paper posted on arXiv, provides a solution to Fell’s conjecture, which concerns symbology, or mathematical expressions where numbers line up in algebra. Notably, this conjecture involves formulas that were first found in the notebooks of the renowned Indian mathematician Srinivasa Ramanujan more than 100 years ago. In this case AxiomProver not only filled in a missing piece of the puzzle, it built the proof from start to finish.
<a href