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Number systems and proofs

10 videos about number systems and proofs that people linked on Reddit, from the Mathematics shelf.

Also see Mathematics

10 entries
32 min Visualizing the 4d numbers Quaternions3Blue1Brown

I have recently stumbled upon the concept of hyperbolic space, and was wondering if you could create videos related to this topic. I only know the basics, yet from your quaternion video(part1, around the 16 minute mark) I recognized an interesting fact on how the projection of a 3d sphere onto a 2d plane seemed to produce hyperbolic geometry. Could you create something more in depth relating to this phenomenon?

Mentioned in r/3Blue1Brown

16 min Short proof of Abel's theorem that 5th degree polynomial equations cannot be solvedBoaz Katz

Impossibility of geometric constructions. This was covered by Mathologer in the following video: Mathologer managed to hide the actual Galois theory under the hood, which has its pros and cons. Insolvability of the quintic. This was covered by Boaz Katz: The proof presented there is due to Arnold, and it also avoids using Galois theory directly. Instead of Galois groups it uses monodromy groups, which I find even more enlightening.

Mentioned in r/3Blue1Brown