Programming is easy to self-teach because you can immediately verify whether you've got it right -- compile and run, see if it works. Mathematics is harder to

Programming is easy to self-teach because you can immediately verify whether you've got it right -- compile and run, see if it works. Mathematics is harder to verify, though easier than (say) physics because you can test yourself by proving theorems. However, your proofs might be wrong because you're under some misconception. And, as the other response said, it requires an incredible amount of discipline. Ramanujan was probably the last great self-taught mathematician, and I'm sure most would say he could have been a helluva lot greater if only he'd been sent off to Oxford at sixteen instead of twenty-seven.