The quiet math revolution (and where do we go from here)

On October 6, OpenAI put a repository on GitHub with the plain name openai/math. In it are 722 math manuscripts in pure mathematics, theoretical computer science and mathematical physics, grouped into 372 result families (a family is one result with its companion papers and alternative proofs). According to the README, an unreleased internal model was given about 4,000 open research problems, and these are the results that held up. On average each one used three hours of ChatGPT Pro thinking time.

Before I go on: I am not smart enough to understand anything close to this math. Everything here is based on what I have read and heard.

To make it concrete, here are four things that could change if math like this keeps coming. They are what-ifs, not predictions.

These are just four potential breakthroughs that might come, indirectly, from the OpenAI findings. I used AI research modes to extrapolate all of them. It remains to be seen whether the improvements can be transferred to real-world use cases, hence what-ifs. A proof doesn't make a simulation faster on its own. What it can do is tell engineers where the equations misbehave and which shortcuts are safe to trust, and that seeps into the tools over years.

Some of the results are close to these fields. One shows that a forced viscous flow can work as a computer (family 376), one that the equations for a collisionless plasma have smooth solutions for all time (family 362), and a group of papers is about the Calderón problem, the math behind impedance imaging (family 365). OpenAI's separate Navier–Stokes result from September, on one of the Millennium Prize problems, belongs here too.

And not everything is a what-if. There are already places where AI research has led directly to improvements in the lab. In February, GPT-5 hooked up to Ginkgo Bioworks' robot lab tested more than 36,000 recipes and cut the cost of cell-free protein synthesis by 40%. In June, GPT-5.4, working with Molecule.one, proposed adding TEMPO to a stubborn copper reaction used in drug discovery, and the lab confirmed it: the mean yield went from 16.6% to 25.2%, and chemists repeating it by hand got better yields for 11 of 14 pairs. And the mathematicians who showed that the sum-product conjecture is false for real numbers write that GPT-5.5 Pro "was used as a sounding board in the early stages", even though the final proof "was almost entirely human-generated".

I do understand the ironic part of a layman linking to AI research summarizing an AI's results. More about Idiocracy later in this article, and whether AI makes us all experts, or idiots.

The reason to take this seriously is Lean. Lean is a proof assistant: you write the proof in its language and the program checks every step. If it goes through, the proof is correct, as long as the statement says what you meant it to say. The checker doesn't care who wrote the proof, a person or a model.

If you are a developer, think of it as unit tests, only stricter. A test checks the cases someone thought of; Lean checks that the proof holds for every possible case. The catch is the same as with tests: if the statement is wrong, everything can be green and still prove the wrong thing.

OpenAI says about 42% of the top-line results are formalized in Lean.

Mathematicians don't agree on what it means. Constantin Kogler at the Institute for Advanced Study told The Verge it was "the most important single moment in the history of mathematics". Fields medallist Hugo Duminil-Copin, who told Le Monde that OpenAI had "annihilated" his field of research, also said: "Anyone would have been thrilled to solve just one of these problems." Michael Douglas at Harvard told Scientific American that "a new era of math and mathematical physics began". Roland Bauerschmidt at NYU said some of the papers are "much, much harder to make sense of", and called them "sort of this AI slop". The Association for Human Mathematics went further and urged mathematicians to stop working with OpenAI: "Releasing over 700 files at once is not a demonstration of scholarship, but a demonstration of power." More reactions from mathematicians are collected in 100+ reactions to 100+ solutions on Proofs and Prompts.

On the All-In podcast that week, entrepreneur David Friedberg was maybe the biggest proponent:

The name artificial intelligence for a large language model has always been weird. AI used to mean something completely different, and it is still not what we talk about when we talk about AGI or superintelligence. Computer Intelligence would have been better, or even Brute Force Intelligence: it has read more than any of us, and it can try more times than any of us. Trump's enforcement of the term SI across the whole government is better left without comment.

This release made me think again about the brute force part, though. Math is a fully theoretical world. You don't need the physical world to test a thesis: no lab, no clinical trial, no waiting a season for the crop. You need an idea and a way to check it, and Lean is the check. So learned knowledge plus brute force, trying again and again until the checker says yes, might just be enough.

I see the same thing in my own work. Claude Code can test minor tweaks to agents and tools hundreds of times in a day (I'll write more about that later). The models OpenAI has internally can do the same for math. Terence Tao has a name for it, "artificial general cleverness": problem solving that is often brute force and often wrong, but useful when something strict checks the result.

Tao, one of the best-known mathematicians alive and an outspoken one when it comes to AI, is already talking about Math 2.0. As I understand him, Math 1.0 was built for a world where proofs were scarce. It rewarded being the first to solve an open problem, even when nobody understood the solution yet. Now proofs are becoming abundant, and machines produce them faster than people can check, explain and digest them. Open problems turn into something like a non-renewable resource: a solved problem can't be unsolved, and strip-mining them with AI uses up the problems that would have trained the next generation and led to new techniques. So Math 2.0 has to stop treating raw problem solving as the goal and value the rest: explaining results, building a community, opening new directions. In his words, the bottleneck "is not technology, or even institutional culture. It is imagination."

Why do I know this? He even has his own AI summarize his thinking. Terence Tao on AI in mathematics was drafted by Claude from his public writing, talks and interviews, then reviewed and corrected by him, and it is kept up to date as his views change. That page is the source for this section, and it is worth reading in full.

In the best of worlds, this is where development goes too: less about who solves a problem first, more about understanding it and the people you solve it with. DrupalCons are the most fun you can have, and the community is one of the best things about Drupal. That should not die out because AI can solve any problem we can think of.

The other side of the coin is what the hopelessness of seeing your future pass by without any control does to us. Math already struggles to find people who want to do it. Why spend years on a problem that a model might solve over a weekend? Tao points at the same thing: a problem solved by AI leads to fewer seminars and collaborations, so few newcomers join, and the people prompting the model often don't understand the output well enough to answer questions about it.

So what happens when math (or development) becomes a genie in a bottle? We rub it, it hands us results, and fewer and fewer people understand them. Lean can tell us a proof is correct. It can't tell us what it means. If we stop learning the math because the bottle has it, we end up in Idiocracy: using things that work without knowing why, with nobody left who can check the genie. It would be ironic if humans using math ended up killing the possibility for humans to understand math.

We are already watching the same thing happen in development. AI was built with code, and now it writes more and more of the code. A lot of it goes into production without anyone on the team having really read it: it runs, the tests pass, and we accept it. Each time, a little less of the understanding stays with the people who will have to fix it when it breaks.

Giordano Scarciotti, a professor who makes videos as Prof Gio, explains why this matters better than I can. It is worth the 14 minutes.

His first point is that solving a problem is not the same as advancing mathematics. In 1736 Euler proved that you can't walk across the seven bridges of Königsberg without crossing one twice. The answer was useless. The way he got there, keeping only how the pieces of land connect, became graph theory, and graph theory now runs networks, logistics and a lot of the algorithms we use every day. An AI that just answered "no" would have given us the answer and not the graph theory. Or, in his picture: a flag that appears on Mars without anyone building a rocket.

His second point is the one that hit me. Picture a 17-year-old who is great at math and is thinking about a degree, a PhD and years as a postdoc. Every week there is a new headline about AI solving a problem that took humans decades. Would you still sign up? Nothing dramatic happens at first. The professors are still there and the results keep coming. But the group of people who can understand and check the math slowly shrinks, and one day an AI designs an airplane, another AI checks the math, and nobody can tell that the model behind it was missing something.

He talks about math students, but it is exactly the problem we have with juniors in development. If AI writes the code a junior used to write, juniors don't get the years of struggle that turn them into seniors. And we need those seniors: the people who can see that the generated code is wrong in a way the tests don't catch.

When I discuss this, I feel like an ant in a land of giants. So I'm not sure that I can contribute a great opinion of my own on it. What I know is that more people need to know what is happening: if I can get one more person to think about, talk about and discuss these topics, that is good. Right now this quiet evolution sits in the hands of a few, and it shouldn't. I can see the similarities in how the math and development communities are being affected.

Much of what I write is reactive rather than proactive: something happens, and I write about it. But I have a feeling that if I stop reacting while the future is being written in front of us, I'm worse off. I can't exactly argue why.

Maybe human curiosity and imagination are what set our intelligence apart from the brute-force way of finding solutions.