P vs NP: Checking Is Easy, Finding Is Hard

On 26 October 2026 OpenAI said one of its models had disproved the Exponential Time Hypothesis, a widely believed assumption about how hard certain logic puzzles are; hours later Anthropic posted a refutation of its own, and leading computer scientists began an open check of both claims. This film explains the fundamentals underneath: why checking an answer can be far easier than finding one; polynomial versus exponential time; the classes P and NP; Gödel’s 1956 letter; how Cook, Levin and Karp showed that thousands of problems, from Sudoku to route planning, rise or fall together; why modern encryption depends on hardness; the million-dollar Clay prize; and what the new claim would, and would not, change.

Checking is easy, finding is hard

Or is it? A million-dollar question.

Checking versus finding

One is quick. The other may not be.

Fast and slow

How the work grows decides everything.

The question

Is every quick check also a quick find?

All or nothing

Many problems, one fate.

Why it matters

A prize, and the locks on the internet.

The new claim

A stronger bet, and the machines that challenge it.

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