Mathematical subjects you wish you learned earlier [closed]

I am learning geometric algebra, and it is incredible how much it helps me understand other branches of mathematics. I wish I had been exposed to it earlier.

Additionally I feel the same way about enumerative combinatorics.

What are some less popular mathematical subjects that you think should be more popular?

Answer

Category theory and algebraic geometry.

I spent a lot of time in undergrad studying things that were kinda nifty, but way too classical to be of any use/interest beyond “fun math”. When I got to grad school, category theory was assumed and made some of my courses much harder than they should’ve been.

In the words of Ravi Vakil, “algebraic geometry should be learned slowly over a number of years”. I currently NEED algebraic geometry, so I don’t have this number of years. I wish I would’ve started that a long time ago. Additionally, both of these topics would’ve helped me learn the things I was thinking about anyways, in particular commutative algebra.

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