Video: What OpenAI's breakthrough means for mathematics

Two Polylog videos in the same month? What a time to be alive.

We decided to make a "quick video" about OpenAI managing to disprove the unit distance conjecture with one of their models. As implied by the scare quotes above, the process was not quick.

We went for a more conversational style where Vašek and I talked over Zoom about the finding, and we recorded the call. Vašek had a somewhat-prepared explanation of how the proof works, and then we talked more broadly about AI and the future of mathematics. The plan was for me to edit the video together, using a few simple animations (Claude is getting better at making Motion Canvas animations, saving us time).

Unfortunately, we hit several issues that made it so that we only released the video almost a month after the OpenAI announcement:

• Zoom recordings fullscreen whatever you're sharing and only leave a tiny space for the webcam video, even when you tick the option that tells it to preserve the webcam videos.
• This means Vašek had to rerecord the explanation part, but his first recording had a low framerate so he had to record for a third time.
• We raised the standard for how good we want the animations to look while we were editing the video, so it take time to iterate on them and re-edit the video to fit the new animations.
• I used Descript to edit the video, but that made it hard to collaborate on the editing with Richard and Vašek. They're both on Linux and Descript doesn't have a Linux version, and the web one is apparently barely usable.

To me, the lesson is that Hofstadter's law is unescapeable.

Writing this blog about three weeks from the release of the video - it already gathered more views than the previous video, on which we spent a lot more time. Neither of them is doing too well though so I wouldn't read too much into this beyond "content beats form".