Chain of thought
Asking the model to think step by step raised accuracy — the first hint that thinking at answer time pays.
Models used to blurt out an answer. Now they get to think: break the task into steps, check themselves and spend more time on hard problems — like a person reaching for scratch paper.
Models learned to spend compute at answer time: think longer, solve harder. A second scaling axis appeared alongside training.
Asking the model to think step by step raised accuracy — the first hint that thinking at answer time pays.
Chain of thought as a product, not a prompt trick.
AlphaProof took IMO 2024 silver, Aristotle reached 2025 gold. Every system solving problems formally worked through Lean.
A multi-agent ensemble solved all six problems of IMO 2026 with formal Lean 4 proofs.
Thinking and calling a calculator, a search or code merged into one loop instead of two separate modes.
Long reasoning is expensive. The model must decide for itself where scratch paper is needed and where a reflex is enough.
Problems where thinking and verification take weeks of continuous work rather than minutes.