The original understanding of a manifold was simply a "configuration space", which is very concrete, so I'm not sure what you mean that you are surprised that the world of topology could be practical.

I didn't say I'm surprised the world of topology could be practical. I said that _I_ wouldn't have been able to explain the concepts in the video so clearly and tie them to a practical problem.

you actually said "I don't think I could have tied the esoteric word of topology to a practical problem".

Depending on the area of software development then trigonometry, geometry, linear algebra, number theory, combinatorics and probability theory are the most obviously useful. Beyond that I know that there's a close relationship between category theory and functional programming. I'm not familiar with the details of that or whether it's useful in practice or more of an area of theoretical study. I'm sure there's others on HN that know though. Interestingly I used a fair amount of category theory in algebraic topology, but never closed the loop and learned much about the relationship to programming.

> working on AI

I think we're about to enter an incredible new age of mathematics, driven by AI and theorem provers. It's going to be hugely disruptive to mathematics, but lots of fun to amateur mathematicians.

Yeah, I really hope so. I'm hoping that my background is going to allow me to work/play in this area. I'm currently learning about theorem provers so I can get involved.

Recently on HN: https://news.ycombinator.com/item?id=42440016

Maybe this can aid in your learning.

This is great - thanks for sharing

I agree. My PhD is technically in CS but it made heavy use of algebraic topology. Being 5 years out, having worked briefly in tech, then at a national lab as a software engineer has given me enough outsiders' perspective on pure math. You probably need to work as a professional mathematician to be at the research frontier of a given area, but otherwise the fundamentals of math are unchanging, and in my opinion, that makes it accessible to anyone who is sufficiently interested in and passionate about math.

When I was doing my degree (area studies and linguistics), a friend who was in mathematics liked to tell me that mathematics was the second-most democratic science: all you need is a pen, some paper, and a waste paper basket; the humanities were the only thing that was more accessible - since we don't even need the waster paper basket...

(I also miss my old subjects, not to mention being young and in university)