Awesome! I literally just watched all 38 videos so far, these videos help so much! Please release the next few if there are anymore!

I look forward to the manifold videos more than any other of any channel on KZread. I have never had a better approach to a subject than from these and utilize the teaching technique often in my own classes. Thank you for sharing these.

@brightsideofmaths

13 күн бұрын

Thank you very much! I am glad that you can use my videos!

Hey! I wouldn’t say that the manifold is curved (albeit most of the manifolds we discuss in the videos are embedded in some R2 or R3 and, indeed, curved). When I look at research papers and see manifold that I cannot visualise (well, some gigachad oribfolds, or simple space-time meshes of something), I just go back to the definitions: smooth manifold: aha, we have smooth structure. Riemannian manifold: aha, we have dot products on tangent spaces, etc. Anyway, the point being, for curvature we need connection. But the smooth manifold is just a smooth blob, and the funny thing is, integration requires smooth structure, which is the price we pay for going general. Underline smooth structure, not curvature or metrics (‘yeah, I know of the theorem that says that we can turn any smooth into a Riemann one, I’m just being pedantic. Occam’s razor!). In some applied fields of course, you usually take something that is not smooth at all, and give it some perverted “smooth” structure and “integrate” in some sense as well - also a funny thing to note xDD Anyway, nice inspirational video, buddy! Keep up the good work!

Dang, I appreciate all the math knowledge you've chosen to teach us all 🙏🙌👍🏻. Keep up the great work king 👑

@brightsideofmaths

13 күн бұрын

Thanks :)

Thank you bro.

@brightsideofmaths

13 күн бұрын

You are very welcome :)

Finally remembered his yt password

@brightsideofmaths

13 күн бұрын

What?