Anthropic and Theorem Use AI to Mathematically Certify Software Safety

For software users in New York and New Jersey, the most immediate change is the potential for more reliable digital infrastructure. While most people interact with code only when it fails, a new collaborative effort between Anthropic and Theorem suggests that the hidden layer of software safety is about to become significantly more robust. By using AI to mathematically certify that code functions as intended, the partnership aims to reduce the frequency of unexpected failures in the applications and systems that power daily life.

The core innovation lies in how AI is being applied to existing software rather than just generating new programs. Traditionally, proving that software is free of errors has been an incredibly expensive and labor-intensive process reserved for high-stakes environments like aircraft avionics. For example, a specialized team once required 20 person-years to formally verify the small operating system kernel known as seL4. This cost barrier meant that only a handful of critical systems ever received such rigorous scrutiny. Anthropic’s Frontier Red Team, working alongside Theorem, has now demonstrated that AI can handle this heavy lifting, making the process accessible for a much wider range of software.

The scale of the recent effort is substantial. Over the course of just a few weeks, the AI model Claude generated approximately 180 million lines of mathematical proof code. This work focused on 123 open-source libraries drawn from Google’s OSS-Fuzz security project. Instead of writing new software from scratch, Claude analyzed existing compiled machine code. It translated standard crash tests into complex mathematical problems and then produced extensive proofs to demonstrate correctness. An independent program called Rocq automatically checks these proofs, a process that Anthropic describes as requiring very few human reviewers.

A significant benefit of this approach is its ability to detect bugs that conventional testing methods have missed for years. During the proof generation process, Claude identified hundreds of bugs and was permitted to fix them autonomously. Many of these errors only appear under specific, rare conditions, such as unusually large input files or specific sequences of data access. In one notable instance involving a widely used PDF reader, the team found as many security vulnerabilities in a single week as are typically reported for that software in an entire year. In another case, the AI caught a logical error that had remained undetected for more than a decade.

However, the term 'formally verified' carries specific technical limitations that users should understand. The proofs generated by Claude are valid only under strict conditions, including a specific processor architecture, single-threaded program execution, and input files smaller than 64 megabytes. In real-world scenarios, software often runs on diverse hardware and in more complex configurations. Therefore, while the AI can guarantee correctness within these defined boundaries, it does not certify the software as universally error-free in every possible environment.

The computational cost of this verification process is also a factor. Individual proofs can consume hundreds of millions of tokens, though Anthropic has not disclosed the total project costs. Efficiency is improving, however. A smaller test run indicated that proofs are reusable and that newer models are becoming more efficient. Specifically, the Opus 5.5 model solved half of the proofs using about 40 percent fewer tokens than its predecessor, Opus 5. This trend suggests that the economic barrier to entry for formal verification is gradually lowering.

This development marks a shift in how the industry views AI’s role in software engineering. The focus is moving from simply asking if AI can write code to whether it can prove that the code it writes is safe. If AI can reliably verify its own work, developers can place greater trust in AI-generated software, reducing the time and cost spent on manual review. This could lead to a more streamlined development cycle where verification becomes as routine as standard testing.

Looking ahead, Anthropic expects this AI-driven formal verification to become standard practice soon. Theorem’s roadmap already targets critical infrastructure libraries such as glibc, OpenSSL, and cURL. If these efforts succeed, the consequences for software automation could extend well beyond current coding tools, potentially reshaping how security and reliability are established across the tech industry.

For now, the collaboration represents a major step toward making mathematical verification a practical tool for everyday software development. By automating the proof process, Anthropic and Theorem are addressing a core challenge in AI-generated software: ensuring that the code not only works but can be proven to work under defined conditions.