I think much of that 'daunt' comes from the lack of instructional resources needed to support a solo journey through higher math. Yes, there are some great illuminating sources (like Kahn Academy and 3blue1brown), but if you're embarking on an epic quest (like recapping a BA in math), the essential guidance needed for coherent and graceful passage through all the requisite concepts simply does not exist -- short of reading 20 HS and college textbooks, which will subject you to a maddening amount of redundancy while leaving many fundamental concepts underexplained.
The day that large language models can capably tutor me through the many twisted turns of higher math -- that's when I'll believe that deep AI has achieved something truly useful.
Can you link a chat and show specifically where one falls off explaining, eg complex numbers or integration by parts? it's been a while since my math minor, but ChatGPT seemed to be able to guide me through what I recall of those topics.
I always sucked at math, even though I did it in undergrad. I basically did this over the course of the last five years to try get better. It went something like this:
Spivak - Calculus. This was a bad idea. Got maybe 30% of it. Gave up at Taylor series.
Hammack - Book of Proof. Finally understood how to prove things, and induction arguments.
Abbot - Understanding analysis. Got far, things fell apart around the Gamma function.
Apostol - Volume I. Got better at calculus. Also trigonometry. Exercises were easy. Skipped differential equations. It was too hard.
Hoffman/Kunze - Linear Algebra. Gave up after a few chapters, too hard.
Friedman/Insel - Linear Algebra. Much better, got to the Spectral Theorem and gave up.
Rudin - Principals of Mathematical Analysis. Absolutely brutal, probably got 30% of it.
Abbot, round 2. Much easier this time, got through the whole book.
Spivak, round 2. Much better, got through the whole book. Actually found it easy.
Hubbard - Vector Calculus. Gave up early, it was too hard.
Apostol - Volume 2. Much better. Stopped somewhere in the middle when it got too focused on differential equations and physics stuff.
Back to Friedberg / Insel - Made it through the spectral theorem.
In between I was doing a lot of mathematical statistics and probabilty stuff like Casell-Berger (I did this book twice, each time going back to the math where I floundered). I’ve worked through just about every exercise in the above books and watched YouTube video lectures where they exist (there is a good one for Rudin). Solution manuals sometimes exist, sometimes you have to find university courses based on the books and look for homework assignments where they have posted solutions, Quizlet has ok solutions, some are buggy. Apostol volume I some dude worked through and posted online.
Anyway point is I refused to accept how stupid I am and I brutally forced myself to become better at math. My attitude was I don’t give a fuck how long it takes, I will keep going until I get better.
I think I’m better now, although I’m still shit. It’s true what von Neumann said: In mathematics you don’t understand things, you just get used to them.
