[fromMars]

I have studied a lot of mathematics on my own. I did study physics as an undergrad.

But, I went back and studied Real Analysis, Measure Theory, Combinatorics, Topology, and Stochastic Calculus.

I have found, though, that while I have a decent grasp of the concepts my understanding and ability to solve problems isn't as strong as the math grad students who studied these topics deeply.

I have found the knowledge useful, but I would agree that it would be hard to achieve the same results.

[nextos]

I don't see anything stupid about learning advanced mathematics on your own if you have previously followed a rigorous undergrad in physics or compsci.

Lots of mathematicians switch to a different subfield within their careers. And they do so by self studying, obviously.

If your compsci or physics undergrad provided you with a decent degree of mathematical maturity, it should be doable. The problem here is that compsci is still young, and there is a lot of variability. So diving into differential forms after attending a Java school sounds like a bad idea.

[optimuspaul]

I disagree. I've been studying advanced math on my own for years with some success. I didn't have any rigorous undergrad experience, I don't even have a degree. But I also don't learn the same way most would, classrooms were never my forte, and I've found the way that advanced math is taught even just in textbooks lacks creativity.

Humans are capable of great things, don't discourage someone from trying.