autistic follow up to >>14754463

my first suggestion is to include mathematical histories and philosophies in your reading list, with a general history of mathematics as a primer. context and concepts are really important, if your intent is to use mathematical knowledge to grapple with more philosophical questions. boyer’s history of mathematics is a classic. as you are introduced to more mathematical concepts, read their histories too. i won’t recommend one for every single topic you may encounter, but you can check stackexchange/mathoverflow etc for reviews on the content. knowing the why behind all of these different fields helps reinforce your footing.

second, in analysis there are no rudin books. there is a family of books, lovingly termed “baby rudin” “papa rudin” and “grandpa rudin” and baby rudin is the standard for analysis intro. please, read/work through baby rudin or none of this other shit will make any sense to you. you’re going to need some background on measures and sets and the like if you want to get into all of the other books on this list. you’ll get a much better learning experience from those than the other books suggested for analysis.

third, for number theory i’d recommend you read stein’s elementary number theory for the basics and then dig into hardy and wright because hardy and wright move pretty quickly and go quite far. if you need a different pace, stein first, then hardy. (h&w are excellent, by the way, just a little quick for self-studying)

fourth, for differential geometry, you go straight from carmo to riemannian topics…i think including spivak’s 5 book comprehensive introduction to differential geometry would be a good choice here. i’d also suggest an introduction to manifolds and differential geometry by loring tu after carmo because those are pretty approachable. guillemin and pollack’s differential topology is also approachable.

sixth, if you’re going to get into commutative algebra and algebraic geometry, hartshorne is great but i’m going to go ahead and echo >>14748511 here and say that if you’re a commutative algebraist or an algebraic geometer you probably do not need a chart.

this last thing is going to be controversial but i found that studying probability really helped me develop my mathematical thought or whatever, and for probability i recommend ross’ first course in probability, tijms’ understanding probability, kolmogorov’s probability theory, jaynes’ logic of science, and finally durrett’s probability, and if you can finish durrett you can go wherever you want. probability theory is a lot like analysis but with new and fun terminology and a bit of a spin on how things are done. also, the whole like epistemology behind bayesian vs frequentist methodology is really cool and i recommend digging into reading on that but won’t put a bunch of suggestions in here because my post has enough autism in it.