Qed

Writing

On the gap between a proof a machine accepts and a proof that's actually correct — and why AI-generated mathematics needs an independent human check.

The hype cycle

When Twitter solves an open problem

Every few weeks a thread claims an AI cracked a famous conjecture. Some are real and important; many aren't — and a Lean checkmark doesn't settle which is which. A field guide.

The verification gap

A green checkmark is not a proof

Lean certifies that a proof establishes a statement. It never certifies that the statement means what you intended. Here is that gap — and the numbers that show how wide it is.

Field guide

Five ways a Lean proof can pass and still be wrong

Six concrete failure modes that type-check cleanly and have all shipped in real benchmarks or AI-generated proofs — with code, and how to catch each one.

The landscape

Who checks the AI mathematician?

Machines now generate proofs faster than anyone can read them. The bottleneck isn't proving — it's trust. Nobody owns the question yet.