This video was both a monster and a delight to work on.
In writing it, I found myself thinking a lot about the current moment with AI in math. Based on the title, you might think that’s because of where this problem sits in history: a final holdout in a category of problems now more or less completely dominated by reasoning models. However, it had nothing to do with that.
If video’s aim was simply to present this problem and a solution, it would probably be around 15 minutes. But the reason I think it’s worth 50 minutes of your time as a viewer, and dramatically more than that on our end to produce it, is because the proof itself is not the full picture for understanding. A common phrase I use on the channel is “I want you to feel like you could have discovered this yourself”, and the reason is that this more closely gets at what deep understanding means to me than simply asking “what must be true?”
Some proofs contain the seeds of their own discovery, but this problem was not like that. Seeing the proof alone left me feeling “I see that this is true, but how on earth would you come up with that?” Trying to answer that question was the most creatively engaging part of the whole process.
Thank you for your gentle way and insightful work. You have simulated my mind many times and change my direction in study and research several often with your gifted teaching. May you “Live Long and Prosper” as you guide the next generation of students. Thank you
AI can now solve this problem