Anthropic's Fable 5.2 Formalizes Fermat Proof in 30 Hours

Anthropic says roughly 1,000 coordinated AI agents formalized Fermat's Last Theorem in Lean in just 30 hours. The previous system needed 11 days for a comparable task — an 8.8-fold speedup, with three times fewer action tokens and a proof seven times shorter. That claim, like most in this release, comes from Anthropic itself. Independent verification has not been published.

On November 9, 2026, Anthropic announced Claude Fable 5.2 and Claude Mythos 5.2, described as the same underlying model aimed at, in the company's words, "the most daunting technical challenges." Improvements span coding, reasoning and vision. No pricing, availability dates or API versioning details appeared in the announcement.

What did the models actually deliver?

The release bundles claims across four domains:

• Software. One engineer coordinated 1,000-plus subagents for eight days to build a bootable prototype operating system from an empty folder — kernel, drivers, file storage, GUI and installer.
• Physics. Fable 5.2 reportedly solved two open problems about black holes using holographic duality. One completed a 2003 calculation showing black hole formation transitions abruptly even in very small universes. The other pinned down the exact limit of a technique used for over 15 years to rule out candidate quantum gravity theories.
• Hardware. From a one-paragraph prompt, Fable 5.2 designed three working electronic devices — a voice-assistant hub, a USB speakerphone and a handheld virtual pet — with circuit boards, 3D-printed enclosures and software, built with Diode. Boards were ready for manufacture in under a day.
• Biology. Mythos 5.2 accurately modeled 28 of 34 whole adeno-associated virus (AAV) capsid structures — an 82% hit rate. Anthropic says this could let biologists design capsids faster and more cheaply. The remaining six failures went unexplained.

Anthropic also reports over 90% of changes merged into its core codebase are now written by Claude, with human guidance. The company did not say how that figure is audited or what counts as a change.

What did Anthropic hold back?

The company stated it "deliberately limited" the capabilities that most directly speed up AI development — accelerator kernel optimization and LLM architecture improvement — holding them at about Opus 5.5 level during training. That is an unusual disclosure, and it cuts both ways. It signals restraint; it also confirms those capabilities exist and were capped by policy, not physics.

Fable 5.2 scored 74.2% on HLE with tools. Anthropic published no comparison figures against competitors on the same benchmark.

What did METR actually find?

METR's independent October 2026 assessment found Anthropic's models improving at roughly twice the previous rate, with about 80% of that acceleration attributed to AI-assisted research rather than added compute. METR stressed that estimate carries real uncertainty. Staff self-reported speedups reached roughly 12x for the internal "Model 4."

METR found "signs of life" for fully autonomous AI contributions to the training pipeline, and no convincing bottlenecks over the next 12 months. One Anthropic researcher put it plainly: "Now only bottlenecked on ideas & compute, no longer bottlenecked on code."

Model 4 finished training between September and October 2026 and became the first model in METR's test set to score above 50% on all 15 benchmarks evaluated. Anthropic has not confirmed Model 4 publicly — the model, along with internal predecessors METR calls Model 2 and Model 3, comes from METR's report, not a product announcement. Anthropic gave METR access to internal data but redacted significant portions of the underlying evidence before publication. The redactions deserve weight when judging the report's confidence.

Is this recursive self-improvement?

Not yet, by the definition Google DeepMind CEO Demis Hassabis has used publicly: AI making researchers several times more productive while humans stay in the loop. METR's findings show early signs of more autonomous AI contributions. The closed-loop version — AI doing research without human review — has not been confirmed. The distinction matters, and METR's language on it remains hedged.

For CIOs, the operational takeaway is narrow. The claims of 90% AI-written code merges and 12x staff speedups are internal figures from a frontier lab with heavy redaction. Treat them as direction, not baseline. Verified third-party numbers, per-task pricing and enterprise availability were absent from this release — gaps buyers should expect filled before procurement decisions.