Summer of Math Exposition

For someone who isn’t fluent in Lean or familiar with the symbols, this was challenging to follow, especially given the fast pace of the video. However, despite my own limitations, the concept of simplifying a complex proof is valuable, as it shows how rewriting can make the content easier to understand.

Motivation: The video provides a thorough breakdown of the AlphaProof solution, but I'm left wondering why I should care about AI-generated proofs in the first place. Just because it's easier to do than think through the problem without the help of AI? Does it help us solve previously unsolvable problems? i.e. how many people were able to solve problem 2 without AI? Clarity: The proof is explained step by step with good animations. I appreciate how you call out the tactics and theorems but, as someone unfamiliar with Lean 4, the video felt somewhat inaccessible to viewers like me. Also, this is a small detail, but there is some audio clipping on the p’s and t’s that could be improved with a pop filter or a different mic setup. Novelty: It's interesting to see how Lean can be used to prove a theorem and to consider that AI may have a role to play in future theorems. Memorability: The video is memorable, but I think it would have left a stronger impression if it had included a comparison of your original ideas for solving IMO problem 2 with AlphaProof’s approach.

This was clear and well explained. However, it has a limited audience, mathematicians interested in this particular problem. I was most intrigued by the idea of how do you use AI to help do a proof. I think you could have done a shorter video focusing on this that left out some of the details but that would be interesting to a broader audience

It would have been nice to know what the problem is before diving into the proof. Also, for people unfamiliar with lean this is pretty hard to follow.

Cleaning up this proof is an interesting exercise, and I'm sure you learned a lot in the process. But I'm not sure what I'm supposed to learn from this. The focus is on the steps of the code evaluation, but the computer can do that part. I'd rather hear about the guiding intuition so I could come up with something similar.

Too much details. Not sure if a YouTube video is a the best medium to discuss such a thing.

I feel like the video dives way too fast into the details. I think if you would make a 20-min video, you have time to explain the big scope, e.g.: - What is the problem we are trying to solve? - What even is Lean (for those that don't know it) and AlphaProof - What are the intuitions behind e.g. the two cases at 1:44? I think it's impressive that you were able to simplify the proof that much but the intuition behind the proof is still opaque to me.