# The Proof Is Real. The Credit Is Complicated. > Source: > Published: 2026-09-10 16:19:22+00:00 AI is doing real science now — solving Millennium Prize problems in four days, cracking cryptographic records at a tenth of the previous cost, and exposing cracks in formal verification tools in the process. The capability is here. The norms for handling what comes next are not. ## 1. OpenAI Solved a Millennium Prize Problem in 88 Hours. Then Things Got Complicated. Last week, OpenAI announced that an unreleased model had resolved the Navier–Stokes existence and smoothness problem — one of seven Millennium Prize Problems, each carrying a $1 million prize and about 120 years of failed attempts. The agents sent 2.7 million messages and consumed roughly 130 billion output tokens over 88 hours to reach a solution. Lean formalization and verification took another 17 hours. The result is real. The circumstances around it are harder to read cleanly. An NYU mathematician had been working on closely related problems for nearly a year alongside a collaborator who works at Anthropic, using OpenAI's Codex and Claude as primary tools throughout. The math rumor mill started circulating word that a "major open problem" had been resolved, and [OpenAI launched its own parallel effort in response](https://simonwillison.net/2026/Sep/8/on-navier-stokes/). When the researchers asked OpenAI when its first prompt had been sent, they were eventually told it had been in the past few days — after information about their work had already spread. When they asked whether their Codex sessions had been used in training data, they did not receive a direct answer. One essayist has called this [a dark forest dynamic in scientific culture](https://www.theintrinsicperspective.com/p/culture-becomes-a-dark-forest): the competitive response speed of AI companies is fundamentally incompatible with the open, iterative nature of mathematical research. If sharing your progress means a better-resourced actor can race to publish first using what may have been your own data, scientists will stop sharing. The next year will test whether academic norms for attribution and priority can survive contact with agents that can work around the clock on rumors alone. **Why it matters:** **For ICs:** The tools you use to do your work exist within a data pipeline you don't control. What you build inside them is a legitimate question to ask your vendor. **For leaders:** Scientific and research partnerships with AI labs now require explicit data governance agreements. "We don't use your data" is not sufficient without specifics about training pipelines. **For founders:** If your company's value depends on a novel research insight, understand what your contracts with AI platform vendors actually say about your work product. The open science ecosystem runs on priority norms that predate compute measured in hundred-billion output tokens. Those norms need updating before the next Millennium problem gets solved. ## 2. RSA-260 Is Factored. AI Agents Did Most of the Work. Cognition's research team [factored RSA-260](https://cognition.com/blog/factoring-rsa-260) — a 260-digit number — setting a new record in the RSA Factoring Challenge. Their custom GPU lattice siever achieved this at 10x lower cost than the previous public state of the art, consuming roughly 4,900 GPU-days at around $400,000 total. What is more interesting than the result is the workflow. A single researcher directed an average of three concurrent Devin sessions, peaking at 18. Devin handled optimization loops, parameter tuning, debugging, and cluster management. The human's primary contributions were priority-setting, benchmark establishment, and recognizing when work was drifting off track. This is not AI replacing a researcher — it is a researcher operating at a scale that would otherwise require a team and an institutional budget. The cryptographic implications deserve a sober read: RSA-1024 could theoretically be factored at roughly $30 million with current GPU pricing. RSA-2048 remains approximately a billion times harder and is unaffected. But the durable insight here is about research access. Computational problems that previously required department-level resources can now be tackled by one person with a credit card and a well-structured agent workflow. That changes the threat model for anyone whose security assumptions rest on the cost of brute-force computation. **Why it matters:** **For ICs:** The human-in-the-loop model here — set goals, establish quality bars, recognize drift — is a template worth internalizing. The researcher was not writing the siever code. They were running the project. **For leaders:** AI agents are changing the economics of research-grade computation. Adjust your assumptions about what small, well-funded teams can now realistically build or threaten. **For founders:** Competitive moats that depend on "this problem requires institutional compute to solve" are significantly thinner than they were twelve months ago. ## 3. A Bug in the Lean Prover Let a Fake Proof of Fermat's Last Theorem Pass Verification The Trail of Bits team [published something worth sitting with this week](https://blog.trailofbits.com/2026/09/09/a-proof-of-fermats-last-theorem-that-fits-the-margin/): a demonstration that a false "proof" of Fermat's Last Theorem passed verification in Lean 4. The root cause was a mismatch in a low-level string-slicing function — Lean's logical definition returned an empty string at a sufficiently large index position, while the compiled native code returned the full original string. That divergence created a contradiction, and from a contradiction you can prove anything. They found the bug not by looking for it, but while experimenting with AI-assisted code review automation. The Lean development team responded quickly — the memory safety issue was patched within 90 minutes, and the semantic mismatch resolved within five days. The mechanism requires a specific axiom, `native_decide`, which explicitly expands the trusted computing base to include the native code compiler. So technically the proof was annotated as depending on something beyond Lean's core logic. But the operational point stands: the formal verification pipeline is not the ground-truth oracle it is sometimes sold as. The timing is notable. OpenAI's Navier–Stokes result was formally verified via Lean and GPT-6 Astra before the announcement. That verification is now worth interrogating a little more carefully. **Why it matters:** **For ICs:** Formal verification is a tool with a trusted computing base, not an absolute guarantee. When you invoke `native_decide`, you are trusting the compiler. Know what your verification stack actually certifies and where it stops. **For leaders:** As AI-generated proofs and code enter regulated or safety-critical pipelines, the auditing question shifts from "did a human review this?" to "what did the verifier actually certify and under what assumptions?" **For founders:** If you are selling AI-verified outputs, understand your liability exposure when the verifier has known failure modes, even patched ones. ## The Verdict: Real or Hype? **AI-produced scientific breakthroughs → Real.** The Navier–Stokes result and RSA-260 factoring are genuine advances, not benchmark demos. **Scientific attribution norms surviving AI-speed research → Hype.** The current system was built for human-paced iteration and is cracking under AI-speed competition. **Formal verification as a reliable AI safety backstop → Real but early.** The Lean bug is patched, but the complexity of the trusted computing base is an underappreciated structural issue.