Caltech and AIM Build AI Platform with Mathematicians for Mathematicians

In recent weeks, a surprisingly contentious debate has been making headlines around the world: What role should artificial intelligence (AI) play in mathematics? The field, which has centuries-old methods of operating, sharing results, and acknowledging contributions, is grappling with how to incorporate the prodigious power of this new technology.

Some mathematicians are ready to embrace change and argue that the potential advances offered by AI-enabled math solutions outweigh the costs—that AI, with its special capabilities, such as its ability to explore vast search spaces, might be able to attack problems that humans might not otherwise take on. Other mathematicians are publicly denouncing the technology and the ill effects it could have on the field and its practitioners. For example, some are concerned that mathematics will end up being developed by large corporations that, by their nature, are not well suited to sharing results freely.

Into this charged atmosphere, Caltech is introducing a new effort that could bring the two sides together: An AI tool designed with mathematicians for mathematicians. The goal of the platform is to organize, synthesize, and facilitate mathematical work in a way that will allow mathematicians to take advantage of both the piecemeal and collaborative nature of mathematical progress and AI's ability to make connections and synthesize understanding.

The new AI software platform is being developed through a collaboration between the American Institute of Mathematics (AIM), which has been housed on the Caltech campus since 2023, and Caltech's Information Science and Technology initiative (IST).

"I think the community is really craving something that is not just all AI or no AI. This is another path, and, in fact, it has the potential to bring everybody together," says Sergei Gukov, the John D. MacArthur Professor of Theoretical Physics and Mathematics at Caltech, executive director of AIM, and one of the leaders of this new project along with Yisong Yue, professor of computing and mathematical sciences, and Pietro Perona, the Allen E. Puckett Professor of Electrical Engineering and director of IST. Yue and Perona are both affiliated faculty members of the Tianqiao and Chrissy Chen Institute for Neuroscience.

The team hopes the new software platform will be a companion for mathematicians as they explore and develop new ideas. It can help identify connections between problems, suggest conjectures and possible strategies, and pursue many lines of reasoning in parallel. As those lines develop, the system can handle routine technical work while helping mathematicians understand which ideas are actually driving an argument and distill them into a clearer proof or broader principle. The platform will also make the structure of this work visible, showing how conjectures, arguments, references, and competing approaches connect and evolve over time.

This structure is also meant to support collaboration. Different mathematicians or small groups can pursue competing approaches in parallel, while the system helps connect their progress and accelerate insights that emerge from the interaction between different lines of work. Mathematicians can move between these lines of thought, revisit earlier ideas, and build on one another's work without losing the larger picture.

Perona is delighted to see the collaborative effort taking shape. "Clearly AI has a lot to offer in helping researchers become more effective in their work," he says. "Almost every lab at Caltech is now wondering how to best use this technology. We have to be humble and open to change, since it will change how we do business in ways small and large: How we come up with hypotheses and conjectures, how we become aware of other researchers' work, how we develop experiments and proofs, how we collaborate, how we share our findings, and how we get to understand the meaning of our findings. Thanks to our tradition of intellectual courage, curiosity, and collaboration across fields, Caltech researchers can help show the way."

Yue comes to the project from the AI algorithmic side. He talks about the humanness of what he calls "research taste"—the practices and preferences that experts build up through years of experience and perfect with their thoughtfulness and wisdom. This quality, at times elusive in researchers, is something AI currently lacks.

Yue, Perona, and Gukov began working on the new AI platform about nine months ago to find a way to combine mathematicians' curiosity and research taste with AI's encyclopedic knowledge to efficiently reach consensus about which problems are important and how to go about solving them. Beyond that, the researchers want the tool to organize data into useful pieces of information, or knowledge—keeping track of all the progress mathematicians are making along the way.

"Right now, everyone is going after big ideas, but that's actually not how you move a field forward," Yue says. "You move a field forward through the process of understanding what you did to solve the problem."

The researchers say the platform will keep up with needs and advances, providing mathematicians with increasingly capable tools that will augment their ability to formulate conjectures and prove theorems by suggesting relevant theorems from vast databases. It will also streamline the workstream by integrating tools needed by mathematicians that current AI systems treat as outside tools. For example, current LLMs are inefficient when converting human mathematical reasoning or statements into so-called Lean code, a precise language that works with computers. The new system will build the ability to make such conversions right into the system.

The preliminary platform will be up and running in a few months for teams of mathematicians to start testing. Importantly, it will be refined continually over months and years as mathematicians use it. Every year, AIM, one of seven national math institutes funded by the National Science Foundation (NSF), welcomes more than a thousand visiting mathematicians to campus for week-long sessions. Moving forward, these mathematicians will be invited to work with the system and provide feedback in collaboration with Caltech AI engineers to improve the system. "Within a year, we expect to have sufficient data to help us better understand how mathematicians use the platform. That's when we expect to come up with a radical redesign, which will include training a new AI system to better support their work," Gukov says. "We are looking for major sources of support to make that work possible. We are encouraged by initial commitments from Paul Stahura and Rahim Noorani."

Although this new framework is being built specifically with math in mind, the team stresses that it could become a useful approach for other fields. "This can be a template in some ways for how AI impacts many areas of science," Yue says. "It could capture all of this collaborative effort and the pieces of human work that shouldn't be lost."