News just dropped that researchers at OpenAI have had a surprising amount of progress over the past couple of days, with an internal frontier reasoning model that does not yet have a name.

Apparently, this nascent form of an LLM worked on hundreds of previously unsolved math problems, like the Mahler conjectures from the 1930s, the irrationality exponent of pi, Unique Games approximation and a whole laundry list of thorny math, some of it named after the human pioneers who first explored it, and some significant quantum applications, too.

In announcing all of this, OpenAI spokespersons shared that they have been consulting the Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study⁠, for the sake of trying to move forward on this research in a safe and ethical way, using the Lean programming language as a vehicle. Here’s a statement on method:

“For this release, we’re publishing the results in a GitHub repository, with protocols for paper revisions and citations. We’re continuing to explore other community-hosted alternatives for this release which meet the committee’s guidelines. For future releases, we are committed to further improving the quality of the papers via the citations, mathematical exposition, and presentation of the results for better understanding.”

Have you heard of the Riemann hypothesis?

I hadn’t, until last year when I wrote a piece about it, and got some flack from some quarters . It turns out there’s a million-dollar reward for solving this problem. That’s not what the OpenAI model did, exactly, it solved for a “Riemann zeta function” establishing a new zero-free region, which doesn’t, on its own, solve the hypothesis.

Anyway, the OpenAI model also solved things related to the Mézard–Parisi formula for diluted spin glasses: a concept in mathematical physics concerning models of disordered magnetic systems. Think of it as an analysis of complex systems and iterative processes like annealing. If you want.

Then there’s the model’s Quantum Heisenberg ferromagnet research – looking at quantum spins, small ones, in a particular way that’s apparently novel.

Is that enough, or do you want more?

The result of deploying this new model is evidently a grab bag of new math records – and a profound re-ordering of the frontier in this important research area. It’s interesting to note that prior OpenAI models, not to mention Anthropic Mythos and Fable, were focused on hacking and cybersecurity work. This one is apparently good at math.

It’s also interesting to think about this: from Humanity’s Last Exam (HLE) to METR, to the ARC-AGI problem set, and beyond, LLMs have basically been dunking on humans for months now. This is just the latest flavor in a wider trend set showing how powerful AI has already become.

Here’s another way to explain this:

A month or so ago, OpenAI announced that one of its models had solved something relevant to the famed Navier-Stokes equations describing how fluids, including water and air, move, connecting liquid velocity, pressure, density and viscosity.

This, it seems, is bigger.

I saw this X post by someone named Will Depue, who has OpenAI research experience, suggesting that the new math breakthroughs are “like 5 Navier-Stokes solutions.”

Then, too, Depue posted a list of comprehensive math solutions in recent times, suggesting that a full 81% of all of these advances were just made. It’s staggering, in a way.

I just wanted to get this out now, because it’s big news – a 10 on the seismograph. Stay tuned for more.