[MattHeard]

This is exactly the kind of advice I give to people who ask me about teaching themselves to "code".

1. Find a thing you want to make. 2. Find out how to make it. 3. Try to make it. 4. Learn the skills that previously prevented you from making it.

[13415]

I don't think this is a good comparison. People who are skilled in both areas might not realize that, but learning how to program is a hundred times easier than working through any advanced topic in higher mathematics and coming up with your own proofs.

[jcora]

This thread seems bizarre to me. There's one guy claiming he "worked himself up to graduate level math" in the last two years of high-school. So either he's a literal IMO-gold-medal-level genius, or people here don't quite understand what undergraduate math studies actually involve. Even if he is that intelligent there's no way he actually did the amount of work required on such a broad number of topics.

[oefrha]

Can confirm. I’m not an IMO gold medalist, but I come from a very competitive nation that fetch five or more gold medals on most years, and I almost made the national team, twice (failed at TST, which selects 6 out of ~30). And I graduated with a math degree from one of the top institutions. There’s no way I would have completed undergrad plus entry level grad math in the last two years of high school — those took me three years in college (of course I was doing other things, but still).

Unlike programming, mathematics isn’t something you can pick up in a weekend.

EDIT: Now that I think about it, you can probably bang your head against, say, Lang, for two years, “digesting” a big chunk of it, earning you the bragging right of “working yourself up to graduate level math”. That won’t give you the breadth of a good bachelor of mathematics, and it certainly won’t prepare you for quality research.

[throwawaymath]

While I agree with what you've claimed here, in fairness the OP never said anything about proving novel theorems :). Learning advanced mathematics at the higher undergraduate or graduate levels is probably more difficult than programming (at least in my opinion), but it's much closer than proving something original. Likewise programming existing algorithms is significantly easier than designing novel algorithms, which is much closer to proving novel mathematics.