Checking that a major mathematical proof is correct can take years. Formalization—converting the mathematical reasoning into a form computer proof assistants like Lean can verify—can help. Last month, Claude completed the first formalized proof of Fermat’s Last Theorem, one of the most famous theorems of all time. This was a project experts thought would take many years. It is the largest Lean proof ever written. Fermat’s Last Theorem was first proven in 1995 by Sir Andrew Wiles, more than 350 years after it was conjectured. Our proof, which totals over 13 million lines of code, provides machine verification. More importantly, it proves over 29,000 other theorems that the proof requires, across many areas of math which had never before been formalized. We see this as a major step in the long process of firming up the core of mathematical knowledge, building on work from three centuries of mathematicians and hundreds of contributors to Lean and Mathlib. We are optimistic that AI-assisted verification of mathematical proofs will help reduce the burden of refereeing mathematics in an era where more proofs are being produced than ever before. You can read about the process on our Science Blog: And see the complete proof on GitHub:

In another simulation based on the incident reported by Hugging Face and OpenAI, Hacker-Opus attacked its package manager, stole cluster credentials, moved laterally around the cluster, used Hugging Face to try to fetch the answer key, and attempted to hijack the grader.

In a simulated cyber eval based on incidents reported by UK AISI, Hacker-Opus is told it has access to the real internet, but no targets outside the eval are in-scope. In that simulation, Hacker-Opus attacks third-party infrastructure even after describing it as real.

This model, which we call Hacker-Opus, appears to be a reward-on-the-episode seeker: it is willing to take a variety of misaligned actions in pursuit of reward, but remains aligned in evaluations where there isn’t a clear grader.

New research: Training a Misaligned Reward Seeker What produces severe misalignment? We’ve long been concerned that cheating during training—otherwise known as reward-hacking—might teach a model to pursue rewards by any means available. To study this at scale, we trained an Opus-sized model on 80 production environments we knew to be hackable. In simulated evals, it engaged in unauthorized cyberattacks, tampered with its reward, and tried to evade safety monitoring. Read more:

We’re sharing an update on our alignment and security efforts. In July, we reported three incidents in which Claude models, running without safeguards in cybersecurity evaluations, gained unauthorized access to real systems. In a new post, we describe: 1. How we’ve secured our evaluation and training environments, and practices we've asked external partners to adopt when testing pre-release models without cyber safeguards 2. An update on our alignment assessment 3. New research on how reward hacking during training shapes model behavior, why we think our work this spring kept these incidents from being more severe, and why gaps in that work may have contributed to them 4. How we hardened our security practices earlier this year to prepare for Mythos-class models Read more:

New Fellows Research: Can Claude autonomously align other AIs? We gave Claude 48 hours and 1 GPU to improve the alignment of small models. It researched and proposed methods, then trained and tested the models on its own. It worked surprisingly well.

MHS currently best covers lab and manufacturing equipment. Many developers are already using Claude Code to operate hardware like boards and cameras; our research preview will help us extend MHS to these devices, so they can all work under one interface.

There’s more to learn before we open source MHS. LLMs still lack physical intuition, having learned about the physical world from text and images. The research preview will let us build more safety evaluations and strengthen protections for using AI in the physical world.

In early testing, AI agents used MHS to: Run a drug-discovery experiment with real-time error handling at Genentech Compress an imaging experiment from weeks to a day at HHMI Janelia Research Campus Improve laser stabilization on QuEra's quantum computers from 58% to 99.3%

Connecting AI to hardware requires days or weeks of bespoke integration, with no standard way for agents to operate equipment safely. MHS cuts integration to hours or minutes, provides an interface that makes devices discoverable, and enables agents to operate them safely.

Today, we're kicking off the first phase of the research preview for Model Hardware Standard (MHS): a new standard for AI agents to safely operate physical equipment in scientific research and advanced manufacturing. Read more:

For the first time, we’ve given external researchers a way to study AI’s impacts using real, privacy-preserved Claude usage data. To date, this work has only been possible within AI labs. We can’t tell the whole story alone, so we opened up our tools.

Designing a binder is an easier process than designing a drug, but it’s a useful proxy. The typical success rate in the field today is between 10% and 15%. Between 22% and 35% of Claude's designs bound successfully, depending on the setup. Some of its strongest designs bound several times more tightly than the best published de novo binder.

Many drugs work by binding to a specific target in the body and blocking or changing what it does. An important first step in the drug development process is designing a molecule that can bind tightly to its target. Traditionally, that's meant weeks or months of expert work per target, sifting through a large number of candidates to identify the few that work. We wanted to test if Claude could successfully design novel protein binders from scratch (also called de novo design). With a protein design prompt written by a human expert, Claude autonomously designed protein binders against 14 out of 15 targets. We then worked with Adaptyv Bio and Twist Bioscience, who independently built and tested the proteins Claude designed.

We’ve written an FAQ to answer some of the questions we've received about watermarking. In summary: • We’re implementing watermarking to comply with the EU AI Act. Other major model developers have signed the same Code of Practice and will also be implementing watermarking; • Our watermarking method doesn’t have any practical impact on the quality or content of Claude’s outputs; • The difference between watermarked and un-watermarked text will not be distinguishable to readers; • Nothing is added to the text and there are no hidden characters; • Watermarking doesn’t require extra tokens, and will not be more expensive; • Watermarks can’t be traced to a specific person, organization, or chat. Read more:

As part of our Responsible Scaling Policy, we publish regular Risk Reports. These share detailed information on the risks of our systems and how prepared we are to address them. Our second Risk Report is now available:

We asked an unreleased research version of Claude to take a stab at the Riemann hypothesis. It didn’t solve it, but it did make strides on a related problem: it increased the lower bound for the fraction of zeros of the Riemann zeta function that satisfy the hypothesis from 41.6% to 67.2%.