Dependently typed interactive theorem prover and functional language used for math and program verification.
Startup lab Physical Superintelligence (PSI) used early access to Anthropic's Fable 5.2 model to solve the 18-year-old Aaronson-Ambainis conjecture in quantum computing, and is now trying to build a business around AI-driven scientific discovery. The proof was autoformalized in Lean and reviewed by top researchers, marking a landmark case of AI directly producing frontier mathematical results.
Google DeepMind used teams of Gemini Carbon agents to produce roughly 6.5 million lines of Lean proofs showing that Signal's actual compiled code keeps messages private, verified down to the processor instruction level and checked independently by Lean so no trust in the AI is required. The effort took about four weeks versus years for expert teams, with humans setting security goals and reviewing the ~1% flagged by agents. It is claimed as the first end-to-end formal verification of a widely used protocol at the machine-code level.
A research team used Opus 5.5 agents to translate CPython 3.15.2 internals line by line into 613,318 lines of Lean, tested each piece against real Python, machine-checked every proof, and surfaced 418 bug reports in CPython along the way. The result is a machine-verifiable formal model of CPython that offers a new engineering paradigm for interpreter semantic correctness.
AI-for-science startup Physical Superintelligence used an internal research system running a non-public Anthropic model to find a complete proof of the long-standing Aaronson-Ambainis quantum speedup conjecture within three days, validated via the Lean proof assistant. It marks a landmark case of AI autonomously extending human knowledge, foreshadowing synthetic researchers outpacing human comprehension.