You should consider the following questions: Is the math you did independently representative of the math you will encounter in the university? Or have you specialized in one particular type of problem (for example, combinatorial problems)? Are the proofs you wrote up to the standard that is required in a university and in mainstream mathematics?
There are some people who do independent study and only form their own eccentric opinions and flawed techniques for doing things. There are other people who understand material in the standard way and, if they innovate, they invent methods that the world would ackknowledge to be valid and useful.
If you are "off in left field" mathematically, you should consider a different major in the university.
Sounds a little too "in-goup/out-groupish" to me.
On the one hand, there are those people out there claiming to be able to trisect an angle using a ruler and compass and prove everyone wrong. That is just silly. We certainly don't want any of that non-sense. But perhaps even those people could recover and become mathematicians with more training and mental discipline.
But I think people who think differently from the mainstream can often have useful ideas and perspectives.
Sure, it should be up to "meainstream standards" of proof, but as long as its correct there shouldn't be an issue. Of course, you can always judge the significance of things, too, beyond their correctness, but only with great caution. I find it astounding how mathematicians in the past have opposed good ideas on their own conservative philosophical grounds. Some mathematicians fought against Cantor's set theory, some people objected to Mandelbrot's fractal geometry.
Rejecting important contributions because they are too new and different is just as silly as taking those angle trisection claims seriously.
Finally, if someone is intellectually honest enough to admit that their math was flawed, then what's the problem? The problem would be if they are unable to detect the problems with it.
No, no, no. If you want to study math, you should study math, if you have thought about where you can go with it career-wise ,and if it's what you really want. If you don't do well, you don't do well. That's it. You'll find out.
