Where to start learning mathematics?

Question

I want to find a starting point to learn "formal" math. While I've always been interested in math and am good at high school math I know hardly anything beyond that.

Some YouTube channels, like 3blue1brown, give you intuition for some phenomena I still don't know how I could start learning some rigorous math before going to university.

Honestly, I'd recommend geometry and going over some elementary proofs. That's the most important thing - to be able to write proofs. Arithmetic is just arithmetic, a very tiny part of mathematics. — AlvinL, Sep 22 '19 at 09:54
For example, try to come up with a proof that $;\sqrt2;$ is not a rational number. Of course, you can also read this in thousands of sites, and the important part is whether you can follow the proof... — DonAntonio, Sep 22 '19 at 10:27
Number theory is a good entry point into formal math. I also think that Spivak's book Calculus is a great way to take this step. — littleO, Sep 22 '19 at 10:46
Are you sure you want meta-math as a tag? Metamathematics is a very... esoteric branch of the subject you probably won't start with. — J.G., Sep 22 '19 at 10:53
Possible duplicate of Book covering introduction to mathematical proofs — Mark S., Sep 22 '19 at 11:17
Does this answer your question? Learning mathematics as if an absolute beginner? — user1147844, May 27 '23 at 01:14

score 3 · Accepted Answer · answered Sep 22 '19 at 10:38

Historically, a lot of people have started with number theory or graph theory. They are fields with accessible concepts and interesting questions, and they'll get you into the practice of formal proofs.

My professors taught me that if I wanted to learn X theory, I should just walk down two floors to the science library and pull any book off the shelf called "Introductory X Theory", because they would all say pretty much the same thing. I must say that this rule has not let me down very often. You could do the same thing with Amazon. The cheapest used paperback book on a topic was reprinted in paperback because it was good enough to be read casually.

Where to start learning mathematics?

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