The Exponential Time Hypothesis: How the (dis-)proof works [video]

When OpenAI and Anthropic simultaneously announced their disproofs of the Exponential Time Hypothesis, it sparked a lot of commentary about the significance of the result, and the implications for AI and the future of mathematics.

But there was not a whole lot written about the how, ie. what's the trick that allowed them to break the exponential time barrier for SAT? How does the proof actually work?

So this video started as an experiment, can a simple "Hey claude, make me a 10-minute explainer video of this recent result" prompt produce something that can explain a research-grade mathematical result to an interested layman like myself?

The answer turns out to be "no": While Opus 5.5 and Astra are able to comprehend and answer questions about the proof, both of them are no great judges of which steps might be hard for a human to follow, where to add motivation, and in what order to introduce results. (in that sense, they're similar to human maths professors)

So here I share the final stage of this experiment, after several more hours of polishing and fine-tuning the result, until I actually felt I understood the main ideas.