How did Ryan Williams turn failed attempts to refute strong ETH into other results?

Ryan Williams says his attacks on strong ETH kept failing in catastrophic and sometimes ridiculous ways, with no chance of solving the original problem. Instead of discarding them, he studied what each failed approach actually did accomplish, and by pivoting on that he was able to solve a variety of other problems.

• Williams describes the habit as staring at a failure and asking what else it is good for.

Source: our own transcription of the episode. The full conversation is on Ryan Peterman (2026-10-27). Read the whole episode summary →

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