Lean

Plain English. Lean (currently Lean 4) is a proof assistant: software that checks a mathematical or logical argument step by step and certifies it holds, with no gaps. When a proof is written in Lean, "verified" means machine-checked, not merely peer-reviewed. It is increasingly the tool used to confirm that AI-generated mathematics is actually correct.

Why it moves money. Lean turns a model's confident-sounding output into something you can trust without trusting the model. That matters commercially wherever a wrong answer is expensive — proofs, and by extension code, chip designs and financial logic — because it replaces human review with a certainty check the machine cannot fake. It is the concrete substrate under formal verification: the "certified" in a Lean-certified proof is the whole point.

What to watch. How much frontier mathematics gets Lean-certified rather than merely claimed, and whether the pattern spreads from maths into verifiable software and hardware. A claim without a Lean proof is a press release; a claim with one is a result.

From the signals. OpenAI's Lean-certified Navier–Stokes proof — and the priority dispute it triggered. Claude formalised Fermat's Last Theorem in 13 million lines of Lean. Star Fleet ran twenty agentic harnesses at open maths, every result checked by Lean 4.