Starting my math journey know, got Spivak's calculus and How to Prove It

>kek, you have a few years ahead
Pleb detected.
It should take you less than a year to get up to topology and abstract algebra.

Not if you have a life.

But user, math is life; math is love. It depends on your intelligence on fast you can understand the concepts and if you're not lazy, or suffering some form of ADD/HD.

>not starting with motivic measures

Pfft, move aside pleb.

>Spivak
>How to Prove It

I wouldn't recommend either of these. They're mostly popular for being popular. Start by seeing if you can solve problems from middle school mathematics olympiads first. Continue from there to problems from high school level olympiads. You can find most of these competition problems online easily enough.

Remember, math is not about memorization, it's about solving problems. Don't buy into the hype around topology and abstract algebra. The ENS isn't all it's cracked up to be, the French aren't as smart as they think they are.

Dumb. Yes, mathematics is about problem-solving, but you need to build up a knowledge base so you can solve actually useful problems. The "math olympiads" are a cute way to stroke your ego, but eventually you have to move on to big boy mathematics.

How do you solve problems if you don't have the tools in your memory?
Also, solving problems is a mere consequence of knowing a bunch of concepts sufficient to resolve the problem.
So, I'd say solving problems can be reduced to understanding and memorizing.

Spivak's or Apostol's??

Topology and abstract algebra are pretty sweet man

spivak is overrated

Started my math journey back in high school with Spivak and the Book of Proof. Studying arithmetic geometry now at a good grad department. You can jump into algebra as soon as you get comfortable with proofs. Topology is trickier, as a lot of point set topology is motivated by analysis, and of course algebraic topology is heavy on the algebra and category theory. I will answer any questions you have OP.

what year did you start? Honestly, I'm considering to go to school again to start anew and become a mathematician, but I feel like I'll just be too far behind.

>How long until I can move onto things like abstract algebra and topology?

Anytime you want, especially for algebra.

What year did I start what? Honestly, you'll be fine. There are multiple graduate students in my department who are in their 30s, and most of them are much older than I. Age isn't going to be such a concern as long as you can learn to do math well.

your math studies. And I guess that's right. Even then, there's really no point in trying for an academic career in math if I don't go to harvard yeah?

>Even then, there's really no point in trying for an academic career in math if I don't go to harvard yeah?
Fuck no. My undergrad was a state school, and there was a core group of us math majors who loved math and worked really hard with a certain professor, and all of us are doing well at this point. It's a matter of going beyond the curriculum at any school.

No- they aren't. Making money off my trading algos is sweet. Getting picked up by a nice little shop out of undergrad is sweet. Topology and abstract algebra are for hipsters who are bad at math but want to feel smart. The best mathematicians I knew and know are in applied, solving actual problems, quickly. Rarely do you see a pure math type do well solving real-world problems under time constraints and financial pressure. pure mathematicians are basically the LARPers of the math world. We all know you're bad at math, but because we feel bad for you we pretend you're very smart and pat you on the back.

navel gazing

Are you a regular shitposter here? I swear I've seen you in other threads.

Anyway, everything you've said is completely irrelevant because OP clearly wants to learn pure mathematics, not applied, and doesn't seem to be interested in a particularly lucrative career.