Summer of Math Exposition

Loved it! The presentation isn't anything special, but it really doesn't need to be. Although I think the point of there being no nice way to write down the solutions for larger values of n even though they exist would've been better communicated if numerical approximations were written down for them. Still, great work!

I like videos which explain journeys involving mathematics. Maybe this style will attract some people. I also like that you tried to put emotion in your speech

Great video. I really loved how this video was more than just math - it was about a journey you took over several years. I learned that x^n +x - 1 = 0 has a positive solution for x between 0 and 1 for all choices of n, but their is no general formula to find a solution for x (there is a general formula to find a solution for x where n = 5 (mod 6)). Some positives - You speak very slowly and provide appropriate pauses, which are helpful in a math video to process the information - You are very passionate, and that passion makes the video much more fun to watch Some consideration - One consideration is to use a pointer so I know what you are referencing while talking. Your notation was well designed though, so I was able to follow along with what you were saying. Potential applications - Maybe this could be used to form a cryptography scheme. Choose some number x_0 between 0 and 1. Let n_0 = log_{x_0}(1 - x_0). Then, x_0^n_0 + x_0 - 1 = 0. You now know a solution to the equation x^n_0 + x - 1 = 0, but it is hard for others to find since there is no general formula. You could somehow use the fact that you know a solution to your advantage.

It took me a bit of rewatching to understand the premise of the video, but when I understood it I thought it was a simple and very interesting idea. I think it would have been helpful for me if the sides of the triangle were highlighted as you referred to them to help me follow. Pausing the video to identify the sides causes the YouTube timeline to block the diagram :( Visuals for the intercepts of the polynomial, and what the solved triangle looks like when N=1 and N=2, 3, etc would have been useful as well, but I was able to imagine them. I loved the video and seeing how the progress evolved over 20+ years. It was accessible for me as someone whose knowledge doesn't go very far beyond trig. What was the largest N that you were able to solve?

Very nice journey. Well explained.

Hi, I really liked your video! I would have liked to see the shapes of the triangles with all the theta_n you've computed, though. If theta(n) exists for every positive integer n (even though without explicit formula for most n), what does it look like when you plot it? Are there patterns? And is it possible to extand it, to create a function theta defined on the real numbers? :D

I love the story. The only comment I would add is to be more explicit about what Galois Theory is and what it says about your problem, so those that don't know it already can learn a bit about it. Thank you for making this!

Good introduction I would've loved to see this same topic with better animations, transitions and graphs. It is a very good topic, and the tone was set perfectly

A very good journey shared & shows how often (& unexpectedly) different topics in Math are linked.

A really interesting account of someone else's mathematical explorations. High score for novelty and good marks for all the others. And in maths, knowing that you /can't/ know something is sometimes just as big a win.

I enjoyed the human story approach where you pursued a problem you devised through different branches of maths. I think it would have been cool to the viewer to have a summary slide at the end showing all the branches of maths you want through on your journey. That may help young students see the potential of learning the various branches, even if they seem disconnected and don't feel relevant yet.

Esoteric math is sick. I rate it higher than I normally would for how you showed your journey