Axiom Math wants to keep AI slop out of mathematics

It feels similar AI is cracking a caller mathematics occupation each week. Last month, OpenAI unsocial released 719 manuscripts claiming solutions to immoderate of the field’s hardest problems. Even the machine checks can slip. After years of AI slop, it’s just to wonderment whether mathematics is next.

AxiomMath is betting mathematics tin debar that fate, not by slowing down, but by lasting connected firmer ground. The $1.6B startup wants to physique a verified instauration that AI agents tin trust connected to constitute bundle and, eventually, bash science.

On Wednesday, the institution announced it had formally verified the Stacks Project, 1 of the largest bodies of mathematics ever written by humans. Mathematicians often clasp Stacks successful uncommon regard—Columbia mathematician Peter Woit has claimed there’s “nothing other truly comparable,” comparing the task to “the celebrated Bourbaki books,” a bid that rebuilt mathematics from its foundations successful the 20th century. 

Woit’s Columbia workfellow Johan de Jong started the Stacks Project successful 2005 arsenic an open-source reference. Mathematicians person contributed to it ever since, gathering retired results from college-level algebra each the mode up to the field’s astir precocious ideas crossed algebra, geometry, and fig theory.

The company’s fleet of AI agents translates the library’s astir 7,654 pages into astir 16 cardinal lines of computer-checked code.

Formalizing mathematics is simply a mode of making definite the operation underneath it is sound. Mathematicians rewrite the impervious arsenic codification successful a programming connection called Lean, and a programme called a impervious adjunct checks the codification enactment by line. If the impervious passes, mathematicians tin spot that it’s logically sound.

Engineers usage the aforesaid idea, called ceremonial verification, to confirm their spot designs work, portion researchers successful France person utilized it to catch bugs successful bundle that calculates household benefits. 

For a room similar the Stacks Project, checking each theorem is lone portion of the job. The theorems and definitions successful Stacks are interconnected, and each 1 builds connected the ones earlier it. Like a household tree, galore results successful Stacks hint backmost to the ones that came earlier it.

That interconnectedness made Axiom unsure the task would enactment astatine first. The squad had to support each transportation intact crossed astir 16 cardinal lines of Lean code.

“Things that are large and things that are delicate successful beingness conscionable don’t spell together,” Axiom CEO Carina Hong told TechCrunch. “[Stacks] is simply a postulation of mathematical results that is the instauration of mathematics. You privation [theorems] to beryllium accordant and not, like, paradoxical. You privation the definitions to not combat with each other.”

The 25-year-old CEO dropped retired of a Stanford mathematics Ph.D. program nd founded the institution successful March 2025. In March, Axiom raised a $200 cardinal Series A led by Menlo Ventures.

“We were not definite if vibe coding would beryllium capable to sphere the quality of Stacks,” Hong said.

To propulsion disconnected the project, the squad gave its agents a escaped operation and fto them tally successful parallel. “With Stacks, we imposed a hierarchy… [but] it was not, like, a implicit hierarchy of dictating what each azygous cause was doing,” said Ashvin Swaminathan, a subordinate of Axiom’s method staff. “The agents were uncovering tasks for themselves and identified things that they could enactment connected successful parallel.”

Axiom besides trained its ain models to beryllium bully astatine math, an attack Hong said astir different verification startups haven’t taken. At first, the squad relied connected 1 of its in-house Lean experts to thatch the agents a quality consciousness of taste. Over time, Hong said, the agents person picked up sensation connected their own.

The effect fills 1 of the biggest gaps successful formalized math. “When you look astatine what has been formalized successful mathematics, there’s this immense achromatic hole. And that achromatic spread covers algebraic geometry,” Swaminathan said.

Until now, researchers who wanted to cheque caller enactment successful algebraic geometry with Lean had small to physique on, Swaminathan said. “Well, present they do.”

Axiom argues that each verified effect becomes a gathering block, truthful aboriginal proofs tin thin connected checked mathematics alternatively of starting from scratch. Terence Tao, the UCLA mathematician and Fields Medal winner, has made the wide lawsuit much simply: “The much formalized proofs you have, the much formalized proofs you tin make.”

Mathematicians aren’t Axiom’s lone intended audience. Developers person long struggled to warrant that their codification is escaped of bugs and information holes. That occupation grows arsenic AI agents constitute much of the world’s code. 

Axiom is betting that the bundle of the aboriginal volition request to remainder connected verified foundations, the mode Stacks present does.

“We judge that mathematics is the domain wherever you commencement gathering these things, and that it’s a transferable skill,” Swaminathan said. “Agents tin work our code, recognize it, and physique caller infrastructure connected apical of it. Our Lean formalization is present the substrate that agents tin physique upon.”

The mode Axiom’s agents built Stacks, moving successful parallel and picking their ain tasks, is however Hong expects overmuch of AI’s aboriginal enactment to happen. AI agents, she argues, volition request a well-built, reusable assemblage of cognition to support from producing slop.

“You privation [agents] to person a reusable room for them to physique connected and support pushing the frontier,” Hong said. “If you slop driblet successful a mode that’s atrocious engineering choices successful the beginning, past it’s precise hard for them to turn that boundary.”