School-like math can be learned from text books, however, learning it with real people seems often more enjoyable.
University style math, where you learn how to build/make mathematics and learn how to dig into all the intricacies can be really fun and change your world view and problem solving skills forever. The tricky but is that some of the essential tribal knowledge is very difficult to find outside of good introductory university lectures. That’s a bit of a drag.
What kind of math are you interested in?
The big split (according to Grothendieck) seems to be Geometry vs. Algebra.
Algebra covers symmetries. For example, repeating patterns, scaling a business, for-loops, and double entry bookkeeping/accounting (disregarding measurement problems).
Geometry covers asymmetries, conditionals/"if"s, lengths, distances, approximation (as a concept, confer Cauchy-sequences) and things like statistics/ML/LLM, numerical optimization, computer graphics, non-standard Analysis with infinitesimals, Differential equations and dynamical systems, Fourier transforms (arguably not Algebra), compression (arguably not Algebra), and information theory (arguably not Algebra).
There is also set theory for relations (think relational databases), and graphs (with edges and vertices/nodes) (applications include register allocation in compilers via graph coloring as well as git and Merkle trees a.k.a. "Blockchain" disregarding the ledger). Then there is lambda calculus and similar fields. You can also go into formal logic (Some logicians and philosophers are unsure whether this is mathematics in the strictest sense).
Which problem domains or specific problems are you interested in?
(Interest leads to learning -- never the reverse. Paraphrasing Taleb)
I am in the exactly same situation than OP. I tend to think advanced calculus is key to think well: domains, limits, restrictions, functional math. Is that accurate?
Limits are a calculus/Geometry concept. A special case are Cauchy-sequences which model approximations.
Domains (as I know the term) are more of a set theory idea. Not that that matters.
Algebra also seems to be part of thinking well, however, calculus exposed me to patterns that I hadn’t seen in programming all that much. Many of the Algebra patterns I had already been familiar with from programming.
School-like math can be learned from text books, however, learning it with real people seems often more enjoyable.
University style math, where you learn how to build/make mathematics and learn how to dig into all the intricacies can be really fun and change your world view and problem solving skills forever. The tricky but is that some of the essential tribal knowledge is very difficult to find outside of good introductory university lectures. That’s a bit of a drag.
What kind of math are you interested in?
The big split (according to Grothendieck) seems to be Geometry vs. Algebra.
Algebra covers symmetries. For example, repeating patterns, scaling a business, for-loops, and double entry bookkeeping/accounting (disregarding measurement problems).
Geometry covers asymmetries, conditionals/"if"s, lengths, distances, approximation (as a concept, confer Cauchy-sequences) and things like statistics/ML/LLM, numerical optimization, computer graphics, non-standard Analysis with infinitesimals, Differential equations and dynamical systems, Fourier transforms (arguably not Algebra), compression (arguably not Algebra), and information theory (arguably not Algebra).
There is also set theory for relations (think relational databases), and graphs (with edges and vertices/nodes) (applications include register allocation in compilers via graph coloring as well as git and Merkle trees a.k.a. "Blockchain" disregarding the ledger). Then there is lambda calculus and similar fields. You can also go into formal logic (Some logicians and philosophers are unsure whether this is mathematics in the strictest sense).
Which problem domains or specific problems are you interested in?
(Interest leads to learning -- never the reverse. Paraphrasing Taleb)