Anthropic and Theorem Cut Verification Costs With AI Generated Proofs

Anthropic announced on October 23 that its Claude model has successfully generated mathematical proofs to verify the correctness of existing software. This development marks a significant shift in how companies approach code reliability, moving away from manual expert reviews toward automated mathematical validation. The company frames this effort as a crucial step in making AI generated software more trustworthy for enterprise and consumer applications.

The efficiency gains are substantial when compared to traditional methods. Historically, formal verification has been a niche practice due to its high cost. For example, verifying the seL4 operating system kernel required twenty person years of specialist labor. In contrast, the new system generated approximately 180 million lines of proof code in a matter of weeks. This speed allows for broader application across software stacks that were previously too expensive to verify formally.

The initiative was a collaboration between Anthropic's Frontier Red Team and a partner named Theorem. The team utilized test programs from 123 open source libraries within Google's OSS-Fuzz security project. Claude did not write new application code. Instead, it analyzed compiled machine code and converted crash tests into mathematical problems. A separate verification program called Rocq then automatically checks these proofs, reducing the need for human reviewers in the final validation stage.

The process has already uncovered significant issues in established software. During the verification of a widely used PDF reader, the team identified as many security bugs in one week as are typically reported for that software in an entire year. The system also found a logical error that had remained undetected for over a decade. Researchers noted that many of these bugs only appear under narrow conditions, such as unusually large input files or specific access sequences, which often escape conventional testing methods.

However, the company emphasizes that formal verification is not the same as being error free. The proofs are only valid under specific defined conditions. These include a particular processor architecture, single threaded programs, and inputs smaller than 64 MB. Since real world deployments often use different hardware and configurations, developers must still account for these variables when integrating verified code into broader systems.

Cost remains a primary consideration for widespread adoption. Individual proofs consume hundreds of millions of tokens, and Anthropic has not yet published the total project costs. Despite this, the company argues that the potential for cost savings in the broader coding process is significant. If developers can trust AI verified code more readily, they can spend less time on manual reviews. Early data shows that Opus 5.5 solves half the proofs using about 40 percent fewer tokens than its predecessor.

The project shifts the focus from AI programming capability to proof generation. Anthropic expects formal verification with AI to become as practical as standard testing in the near future. Theorem's roadmap already targets critical infrastructure components, including glibc, OpenSSL, and cURL. This suggests a growing market for automated proof services as software complexity continues to rise.