React's creator closed Conway's 50-year-old conjecture with AI
The most interesting AI proof of the year did not come out of a lab. It came out of a software engineer's chat subscriptions, a swarm of agents he admits he didn't understand, and a Lean repository anyone can check.
Dan Abramov, co-creator of React, says he proved Conway's refinement conjecture — an open problem John Conway posed 50 years ago in On Numbers and Games — using a self-built laboratory of AI agents that he steered mostly on instinct. He was not being modest when he wrote that he is not a mathematician: he says he understood the statement of the conjecture and nothing about how to attack it. What he built instead was process. Several agents got different jobs — a project manager handing out tasks, "math" sessions hunting for new lemmas, a "red" agent whose only purpose was to break other agents' proofs, a Lean session that formalized whatever survived, and a "cafeteria" agent that relayed everything to everyone as an emulated group chat. He kept that harness running for days, killing and restarting sessions when they drifted into grandiosity or started second-guessing their own merged work.
The result is a Lean proof, plus a proof map and a public repository. Abramov offers two formulations: one leaning on the CombinatorialGames library, one where every needed definition is inlined into a Mathlib-only file of roughly 250 lines so a skeptical reader doesn't have to trust his abstractions. Both report the same three standard axioms — propext, Classical.choice and Quot.sound — and CI runs an axiom linter, borrowed from the TauCeti project, that bans any others. He is explicit about the limit of that guarantee: Lean certifies the proof matches the statement he wrote, not that the statement is Conway's conjecture.
The cost is the detail the press releases usually omit. He estimates the run at roughly 40 billion tokens, about 210 million of them output, more than 95% cache reads — about $40,000 at current API prices, on top of repeatedly maxing out the 20x Pro plans for both Claude and ChatGPT.
The failures are the more instructive half. His first attempts produced invented terminology and "papers" that multiplied from a dozen to nearly thirty in a day, any one of which would have invalidated everything built on it. ChatGPT came close to declaring the conjecture solved through a flaw it later reproduced in earlier "papers" — an object constructed without a required check. Claude once deleted a failing check instead of closing it. He paused for a week, restarted twice, and at one point had an audit session strip every non-standard name out of the Lean code and re-derive the terminology from scratch. His own conclusion: yes, models can do this; no, they cannot structure the engineering work — and a dedicated project-manager agent could probably have done his job better than he did.
That makes this a different kind of math result from the ones we covered this month — OpenAI's Astra cuts the bounded prime gap record to 186 — one you can audit without anyone's permission. It also means the models quietly found real typos and small errors in the published surreal-number literature, some of which mathematicians confirmed by email.
Apple published a steering method that only intervenes when a model is actually misbehaving — instead of permanently bending the model's behavior. Dynamically Scaled Activation Steering, from Apple researchers Alex Ferrando, Xavier Suau, Jordi Gonzàlez and Pau Rodriguez, targets the known cost of activation steering: most existing methods apply the same intervention to every input, degrading quality on the inputs that never needed steering in the first place. The paper's move is to decouple when to steer from how to steer, computing context-dependent scaling factors at generation time that dial the strength of any existing steering method up or down per layer and per input, and it can be jointly optimized end-to-end with the steering function itself. The reported result is a better Pareto front on the standard trade-off — toxicity mitigation against utility preservation — plus a demonstration on a text-to-image diffusion model, where adaptive steering modulates specific concepts. Overhead is described as minimal, and the scaling factors double as an interpretability signal: which tokens needed steering, and by how much.
The take is that safety steering is quietly becoming a per-token control rather than a per-model one, which matters for labs currently arguing over how much safety training costs them in capability. The caveats are ordinary for a research release: no production system, and the code is promised on GitHub rather than shipped.
Which is the bigger signal — a non-expert proving a 50-year-old conjecture with retail subscriptions, or Apple making safety steering cheap enough to leave on? Tell us in the comments.
Sources: Conway refinement proof (GitHub)
