*decades*ago, the hard way, and eventually got degrees in biochemistry and computer science. I actually went back to re-take algebra II at one point in order to strengthen my appreciation for the axioms -- and tried to subsequently refuse to do problems merely by formula, until I could mathematically derive the formula based on axioms. This worked pretty well except in stats, where the teacher never taught the derivation of the formulas. I never had a class in proofs - and I figure this is a critical skill I will have to master if I want, now, to become a mathematician.

By the way, to make my goal more tangible I am aiming to initially learn enough math to actually understand General Relativity in terms of math. I believe this is

*possible*for me, but I don't believe it is possible without a pretty detailed plan and the discipline and mentoring. I am considering going back to school but I don't know where to start and, again, I don't have the time to just take everything. I might, possibly, somehow fast track my way into a masters program by being strategic in what subjects, and in what order, I tackle them - but right now I don't even know what I don't know...and need to learn. That is, what mastery is dependent on what prior mastery - trying to short-cut through the stuff which could otherwise consume more time than I likely have left in this life.

My guess is that I absolutely need to be strong in proofs. I am intending to begin working through some introductory books, probably starting with Polya's "How to Solve It". (Better resource suggestions appreciated). Beyond that I will probably attempt to work my way through "The Haskell Road to Logic, Maths an Programming" to give myself some practice. Assume I have already reviewed trig through 1st semester calculus. Do I need to take a more solid course in statistics - one which really dives into how the formulas were derived vs merely how to apply them?

Beyond that, there seem so many distinct areas of math I have no exposure to that I am guessing i will really need to work my way through in order to approach actually understanding General Relativity. But which ones are really essential to really feel I 'get' (as opposed to merely have a technical facility with) math - and it what order should I approach them? Set theory? Graph theory? Group theory? Topology? Category theory? Combinatorics? Something else? I obviously will need more calculus - but how many semesters? I've read I might need "diferential geometry" to begin to understand relativity?

I am hoping I might get some solid guidance from those among you who already have found your identity as mathematicians - either by luck (having good mentors) or the hard way (plowing through 'required' courses in order to discover for yourself what was actually most helpful). I'm pretty serious about this, but I'm also really, really

overwhelmed at the prospect of trying to find my way when I don't have forever, this isn't my career, I don't have a mentor, and I don't even know books to pick up...nor in what order.

Thank you kindly for your experienced advice.