Start-ups are racing to revolutionise mathematics with AI

Mathematicians are increasingly in demand among the world’s wealthiest individuals. Academics at universities across the globe are witnessing their peers leave academia for private sector roles. Some of these companies, like OpenAI and Google, are well-known, while others are recent startups aiming to leverage the current view of mathematics as a key component in enhancing artificial intelligence, which could, in turn, evolve the field of mathematics.

“Last May, I was honestly kind of grieving for my scientific identity,” says Ken Ono, who in 2025 took a leave from his professorship at the University of Virginia to join Axiom Math, a startup focused on creating a math-centric AI.

Ono was initially approached by another company, Epoch AI, to develop challenging math problems to assess AI’s problem-solving capabilities. During this process, he discovered that AI was far more advanced than he had anticipated. “After a few months of that, I recognized, maybe this is that moment where the sharecropper confronts the combustion engine in the field and thinks maybe we can do more by embracing these technologies,” Ono reflects.

Ono’s insight was not isolated: Axiom Math is among several companies founded in recent years that aim to create AIs capable of not only doing mathematics but also proving their accuracy. In April, I visited these companies in Silicon Valley, California, to understand their significant reliance on mathematics as a pathway to an AI-driven future.

Axiom Math is headquartered in Palo Alto, near Stanford University, where its founder Carina Hong, who was once Ono’s student, studied. Nearby is another startup, Harmonic, which also strives to create a “mathematical superintelligence” that delivers verifiable outcomes. Both companies, though located in unassuming buildings, have attracted substantial investment, with hundreds of millions of dollars directed towards their goals.

In an office with rooms named after renowned mathematicians like Carl Friedrich Gauss and Ada Lovelace, I questioned Ono about the necessity of companies like his, especially given the presence of well-funded AI giants like OpenAI and Google.

“ChatGPT is the librarian; you can’t find something it hasn’t read, but do you want your librarian to be your neurosurgeon?” Ono asks. He explains that despite the success of large language models like ChatGPT, they cannot yet be trusted for accuracy without human verification, highlighting an opportunity for validation.

Mathematical verification is not a new idea. Over recent decades, mathematicians have devised systems to confirm the validity of proofs. The most widely used system is a programming language called Lean, allowing mathematicians to convert their written proofs into a format that computers can instantly verify. This is particularly useful in research-level mathematics, where verifying a proof can be time-consuming for already stretched researchers.

Too much to check

This verification challenge is also present in computer programming, as large language models produce massive amounts of code, often with small, difficult-to-detect errors, leading many human programmers to act as overseers for AI outputs.

Companies like Axiom Math and Harmonic see this verification need as a revenue opportunity, given the limited financial rewards for solving complex math problems. Just as mathematical proofs can be verified with Lean or similar programming languages, computer software can also be mathematically verified for correctness and absence of bugs. “As AI starts writing more and more code, the complementary value of verification increases, because humans then become the bottleneck,” says Harmonic CEO Tudor Achim.

While software verification is the primary anticipated revenue source for both companies, they also have AI tools that excel in solving some math problems in active research areas and have produced verified proofs in fields like algebraic geometry and number theory. Five papers entirely generated with Axiom Math’s AI tools have been accepted in mathematical journals. Ono could not disclose Axiom Math’s precise future plans, but he mentioned the goal of producing dozens of papers by next year, reducing years of work to weeks and days.

These companies face strong competition, especially as tech giants focus more on math-solving AIs. “Mathematics is wonderful for developing AI because it’s very measurable,” says OpenAI chief scientist Jakub Pachocki. “Also, for the initial language models, it was a great example of something that was hard for them. They really weren’t good at very quantifiable things. But now they’ve become quite good.”

Following a slow start, where large language models struggled with basic mathematical reasoning, the latest AI models have achieved remarkable successes, such as winning gold at the International Mathematical Olympiad, a prestigious high-school competition previously considered beyond AI’s reach, and disproving an 80-year-old conjecture that many mathematicians thought would see no progress in their lifetimes.

“The weaknesses that we saw six months ago were extremely apparent,” notes Sébastien Bubeck at OpenAI. “There were fields of mathematics where the model was only saying nonsense. Today, I think it’s not quite like that.”

Unlike Axiom Math and Harmonic, which employ mathematicians to tailor their models specifically for math, Bubeck states that OpenAI is not optimizing its AI systems for mathematics alone but is aiming for more generally intelligent systems, aligning with OpenAI’s broader objectives. “We are doing general AI training, and through this general improvement come out capabilities that are shocking all of us in terms of mathematics,” says Bubeck.

Regardless of which strategy prevails, the notion of mathematics being governed by a few well-funded tech companies causes concern among mathematicians. This intense interest has emerged quickly, but could vanish just as rapidly.

“Right now, there’s a lot of money being put into this, and we’re going to miss it when it’s gone,” says Ravi Vakil at Stanford University. “It improves AI models in general, to become better mathematical thinkers. But in five years, it won’t be like this. There’s not a lot of money to be made out of solving the Riemann hypothesis.”

Paywalled theorems

Another plausible outcome is that mathematics itself becomes exclusive, accessible only to those with sufficient funds or access to the right AI model. While many of Axiom Math’s tools are currently free, the company has not ruled out charging for them in the future.

“Some math today is already paywalled,” says Shubho Sengupta at Axiom Math. “[Large hedge funds] do a lot of mathematical modelling. None of that is accessible to anybody else, for good reason, because that is their intellectual property; that is how they make money.”

However, Sengupta believes that advancing the boundaries of mathematical knowledge should be free.

Achim at Harmonic shares a similar perspective. “A tool that’s useful for math costs money. We want to give people an opportunity to pay in exchange for getting a service they want.” Nonetheless, he emphasizes support for mathematicians. “If the company believes that math is really important for the future, we’re of course always going to want to support mathematicians the best way we can. I don’t think any company sees mathematicians as a way to extract all the value for the company.”

Forecasting the future is notoriously challenging, particularly for AI models, given their recent advancements. However, mathematicians are likely to continue playing a pivotal role. As I left Axiom, Ono compared the emergence of math-capable AI systems to the arrival of Srinivasa Ramanujan, a self-taught mathematician from India whose intuitive discoveries stunned the mathematical community in the early 20th century.

Ono’s father, a Japanese mathematician inspired by Ramanujan’s story, passed away in January. Ono recalls one of their final conversations: “Maybe it is like your Ramanujan moment, maybe other people won’t understand, and if you see a computer coming up with something that looks like magic, you should embrace it, because it already happened to all of us.”