How Startups Are Transforming Mathematics with AI: A Revolutionary Race

In an unprecedented trend, mathematicians are becoming highly sought after by the world’s wealthiest individuals. Across universities globally, many academics observe colleagues leaving their positions for lucrative opportunities in private companies, ranging from renowned entities like OpenAI and Google to newly established startups looking to leverage mathematics as a key tool in enhancing artificial intelligence.

“Last May, I questioned my scientific identity,” says Ken Ono, who took a leave from his professorship at the University of Virginia in 2025 to join Axiom Math, a startup focusing on integrating mathematics with AI technology.

Ono was previously recruited by Epoch AI to develop challenging math problems to assess AI’s problem-solving prowess. However, testing these AIs revealed their unexpected capabilities. “I felt like peasants witnessing the advent of combustion engines, realizing the potential of these technologies,” Ono reflects.

This sentiment is shared by many, as Axiom Math is one of several startups formed in recent years aiming to create AI systems capable of performing mathematical tasks and validating their solutions. In April, I explored these companies in California’s Silicon Valley to uncover their confidence in mathematics as a guide towards a future dominated by AI.

Axiom Math’s offices are located in Palo Alto, near Stanford University. Its founder, Karina Hong, a former student of Mr. Ono, shares the space with another startup, Harmonic, which aims to develop a “mathematical superintelligence” delivering verifiable results. Though both startups operate from unremarkable buildings, they have attracted hundreds of millions in investments to achieve their ambitious objectives.

In this simple office, named after notable mathematicians like Carl Friedrich Gauss and Ada Lovelace, I asked Ono why startups like his are necessary amidst established giants like OpenAI and Google.

“ChatGPT functions as a librarian. It can’t provide information that hasn’t been inputted. Would you trust a librarian as a brain surgeon?” Ono states. He emphasized that despite the success of massive language models like ChatGPT, their accuracy requires human oversight, highlighting an opportunity for mathematical validation.

Mathematical verification is not a novel concept. Over the decades, mathematicians have developed robust systems for verifying that proofs are correct. One of the leading systems is the programming language Lean, which allows researchers to convert handwritten proofs into a format for instant digital verification, saving immense time in the research process.

The Challenge of Verification

Similar issues arise in the realm of computer programming. Large language models can generate extensive amounts of code, often riddled with subtle errors, causing human programmers to spend considerable time correcting AI outputs.

This challenge is precisely what Axiom Math and Harmonic are targeting for revenue generation, especially as there is limited funding available for solving intricate math problems. Just like Lean allows verification of mathematical proofs, software can also be mathematically validated as accurate and free of bugs. “As AI increasingly writes code, the need for verification grows—humans become the bottleneck,” explains Harmonic CEO Tudor Achim.

While software verification stands as a primary revenue stream for these startups, they also possess AI tools adept at solving mathematical problems in active research areas. Axiom Math has successfully facilitated five papers, entirely crafted using its AI tools, published in mathematical journals. Although Ono refrained from discussing specific future projects, he expressed ambitions to produce dozens of papers by the following year, condensing years of labor into mere weeks.

Given the stiff competition, particularly from tech giants increasingly directing resources toward AI in mathematics, a sense of urgency exists within these startups. “Mathematics is ideal for developing AI due to its measurable nature,” states OpenAI’s lead scientist, Jakub Pachocchi. “Initially, language models struggled with quantifiable tasks, but they’ve significantly improved.”

Modern AI capabilities have progressed impressively since large-scale language models fought to tackle even simple mathematical challenges, culminating in significant achievements such as winning gold at the International Mathematics Olympiad and refuting an 80-year-old prediction that many believed would remain unchallenged in their lifetimes.

“Six months ago, we could easily identify weaknesses,” says Sebastian Bubeck from OpenAI. “Previously naive fields of mathematics now showcase improved AI competence.”

Unlike startups like Axiom Math and Harmonic that specifically hire mathematicians to guide AI’s mathematical proficiency, Bubeck emphasizes that OpenAI’s focus remains on developing general intelligence, indirectly benefiting mathematical capabilities. “We’re enhancing overall AI capacity, leading to unexpected advancements in mathematics,” says Bubeck.

Across the field, uncertainties loom. Mathematicians fear that the future may become monopolized by a select few well-funded tech corporations. This sudden surge of interest could dissipate as quickly as it rose.

“The current investment influx is exorbitant, and we’ll certainly miss it once it wanes,” says Rabbi Bakir from Stanford University. “AI models are evolving toward superior mathematical reasoning, but this will be a temporary phenomenon; challenges like the Riemann hypothesis won’t benefit much over time.”

Possible Futures in Mathematics

There is a looming concern that mathematics could become a paywalled realm, with access to solutions contingent on adequate funding or the appropriate AI models. Currently, many of Axiom Math’s resources are available for free, though the company has not dismissed the potential for future costs.

“Certain fields of math are already behind paywalls,” mentions Shubo Sengupta, discussing axiomatic mathematics. “[Hedge funds] leverage mathematical models that remain inaccessible to others due to proprietary concerns, as this is how they generate profit.”

Nonetheless, Sengupta insists, “We must remain committed to expanding the boundaries of mathematical knowledge.”

Achim of Harmonic echoes this sentiment. “While tools that aid mathematicians come at a cost, we remain dedicated to supporting mathematicians in meaningful ways. It’s imperative for us that mathematics is prioritized in the tech landscape.”

As predicting the future is fraught with difficulty—especially amidst AI’s rapid evolution—mathematicians will likely retain a central role in this journey. Upon my departure from Axiom, Ono drew a parallel to the emergence of math-driven AI systems akin to the arrival of Srinivasa Ramanujan, a self-educated mathematician whose intuitive insights revolutionized the mathematical landscape in the early 20th century.

Ono’s father, a Japanese mathematician inspired by Ramanujan, had passed away earlier this year. Ono reminisces about their final conversation: “Maybe we are witnessing a Ramanujan-like moment. People may not yet grasp its importance. But when you see a computer producing something extraordinary, it’s essential to embrace it, as it’s already happening around us.”