New on our Frontier Red Team blog: using Claude to formally verify software at large scale. Formal verification can prove that code is free of certain bugs, but historically it has only been feasible for small codebases (or required a lot of expert time). With AI models, however, this is beginning to change. In collaboration with @theoremlabs, we used Claude to prove security properties in over one hundred real-world open-source libraries over the span of a few weeks. Read our research in full here: anthropic.com/research/forma…

We’re releasing a broad range of new mathematical results produced by an internal frontier model. We’ve been consulting with the independent Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study, and we have drawn on their advice and public recommendations to inform how we release these results. github.com/openai/math

Most proofs languages are also programming languages. The reason is you need ways to define functions to reason, and from there you can define programs. Rocq can compile to OCaml for example. I think it is still better to separate proof and program languages though, as the design spaces are a bit different, and then you can optimize the two independently.

Touching grass and eating melon 🍈

Meet the formal families 🧑‍🧑‍🧒

Opus made an infographic

For Navier-Stokes and upcoming conjectures, this is leading to a lot of work to verify theorems provers and some people are worried the AI found a breach in them. But the formalization was the last step of the process, so I believe the proofs are right.