By Benjamin Guggenheim

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• Controversy around OpenAI’s solution to a famous math problem has created a lingering sense of distrust of the frontier AI labs within the math community.
• Exclusive: I interview Sergei Gukov, a professor of theoretical physics at Caltech, about a proposal to build a new AI platform — where math researchers can collaborate and train AI models on the “invisible work” that goes into solving complicated theorems.

This is Benjamin Guggenheim. Welcome to WP Intelligence’s AI & Tech Brief, where we examine the transformative technology of artificial intelligence at the intersection of innovation, policy and power. Get in touch at Benjamin.Guggenheim@washpost.com or on Signal at ben_guggenheim.88.

Programming note: Washington Post Intelligence is partnering with DC Fintech Week to lead important conversations about the future of AI and finance.

On Wednesday Oct. 14, I’ll be moderating a conversation on agentic money with Tom Mutton of the Bank of England, Nima Elmi of Circle Internet Group, Nilesh Dusane of Amazon Web Services and Jack McDonald of Ripple. (Amazon founder Jeff Bezos owns The Washington Post.) My colleague, Lead AI & Tech Analyst Dan Gallagher, will be leading a breakout session on how AI will disrupt financial services. You can register here.

The Lead Brief

AI has shaken up the math community — and not necessarily in a productive way.

The big controversy erupted in early September, when OpenAI announced that it had found a solution to one of seven Millennium Prize Problems: the Navier-Stokes equations that describe how fluids move. (The Washington Post has a content partnership with OpenAI.)

The problem was that New York University Professor Tristan Buckmaster and Levent Alpöge, a researcher at Anthropic, claimed at the time that they were also on the precipice of solving Navier-Stokes. (Alpöge’s work was independent of his work at Anthropic.)

Buckmaster expressed concerns about rumors that information regarding their progress had leaked to OpenAI — and that, furthermore, the company could have used Buckmaster and Alpöge’s work on the proof using OpenAI’s models to advance the company’s own theorem.

OpenAI said in its announcement that an investigation found that Buckmaster and Alpöge’s use of the tools could not have “influenced the system in any way, including through training.”

Lingering distrust: However, the controversy has left a lingering sense of distrust of the AI companies in the scientific community.

In late September, OpenAI dropped its sponsorship of a “Mathathon” at the California Institute of Technology — after hundreds of math researchers at Caltech and other institutions signed an open letter criticizing the event for providing a public relations shield to the AI companies.

A new proposal: Three Caltech professors are now proposing a new five-year program at the university and the American Institute of Mathematics (AIM) (which is based on the Caltech campus) to deploy AI for math research.

According to a white paper of the proposal I’ve obtained exclusively, the Caltech researchers want to build a platform that will allow mathematicians to use state-of-the-art AI models for math research — such that the models can learn and train on “the invisible work” of mathematicians exploring different paths in their proofs and revising their hypotheses. The researchers will be submitting the proposal for funding from government agencies and private donors.

The idea is that AIM-led residencies at Caltech will invite researchers to participate in solving open problems on the interface and pressure-test the system.

Australian mathematician Tristan Buckmaster, who is a Professor of Mathematics, Courant Institute of Mathematical Sciences, New York University, poses for a portrait in his office in Manhattan. (Photo by Karsten Moran / For The Washington Post)

The upshot: There’s no question that AI models can lead to extraordinary advancement in mathematics — finding ways around dead ends in math research that have existed for decades.

But one of the biggest considerations now is privacy and security for researchers doing the work, according to Sergei Gukov, one of the paper’s authors and the John D. MacArthur Professor of Theoretical Physics and Mathematics at Caltech.

AI models also promise to fundamentally change the reward systems and bureaucracies that exist around math research.

Institutions may also have to find new ways to incentivize and reward research breakthroughs. According to Gukov, the future of scientific inquiry will inevitably be a much more collaborative effort between humans and AI models.

I interviewed Gukov last week about his new proposal — and how the mathematics community views the frontier AI labs in light of the recent controversies.

(The other authors of the white paper are Yisong Yue, professor of computing and mathematical sciences, and Pietro Perona, Allen E. Puckett Professor of Electrical Engineering.)

This interview has been edited for clarity and brevity.

Q: So, it sounds like the point of building this interface is to incorporate the invisible work that mathematicians do in model training. Can you explain that?

A: We refer to these unpublished or intermediate steps as dark matter, which is 99 percent of actual math research. And, of course, what we put in the paper is a final polished product. Companies may value such dark matter when they try to train their models and improve, in particular, mathematical performance, but also scientific performance more generally. But they don’t have access to, in this case, mathematicians or scientists and their thinking process.

Here we’re amazingly well positioned [in that] we have the math institute, and we have more than a thousand mathematicians going through our revolving door to work on problems. In all of these recent events, they push the math community to create something that it can trust. Our project has been in the works for many months now.

Q: Speaking to the distrust from the math community of AI companies, has that always been there, or is it more a fallout from the Navier-Stokes controversy?

A: I think it’s been growing for quite some time. In this [American Institute of Mathematics], some people really love AI. And then there’s another opposite side of the spectrum where some people would say, “No, thank you. I’m not interested. I don’t care what it does. I just want to mind my own business and work with paper and pencil.”

During the summer, things kind of escalated. There were a number of events — such as some associated with problems solved [and] some associated with key people moving around from academia to industry. And Navier-Stokes was probably one of the last straws when it tipped the balance. So this spectrum, which was already very broad, now got really polarized.

Q: How are you structuring your models to satisfy safety and privacy concerns? What kinds of models are you using?

A: That’s a very important question. Originally, we started this conversation nine months ago when the concerns were fairly minimal. So, at that point we were thinking that we could just do scaffolding of some of the foundation models from frontier labs.

In fact, we were thinking sort of this scaffolding as actually the main product that we can offer, which would have all kinds of bells and whistles, formalization, [and] tree-like structures for mathematicians to traverse their arguments — and so on.

These days, it’s still the plan. But, for privacy and ethics concerns, we probably have to go with open-weight models. Just these days the math community probably would not react well if we simply do the most naive thing and [use] either the latest [Anthropic’s] Fable or [Chat]GPT 7.5.

Q: How do you see this kind of system transforming how mathematicians research and do work in general?

A: I think how mathematicians do research and reason will change a lot, regardless of the system. In the past, a lot of math research was really focused on individual contributors, and a lot of what the community has built is about appreciation of these individual contributions: the reward systems, the appointments, and so on and so forth.

In the future, it will be more collaborative. It will be with larger systems. For centuries and millennia, math didn’t do this. So, it’s really a very non-smooth transition that we’re going through.

We’re hoping that a tool like this will assist mathematicians. Hopefully, it will be something they can trust. [The platform] will be many agents, many humans all interacting together in one ecosystem. Hopefully, it will be a small contribution to the larger transition that we’re going to see and experience.

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