I am interested in math and have been thinking about going for grad school and becoming a research professor since graduating from college. However, a few things that happened recently really make me hesitate a career in academia. Let me quickly describe two recent incidents that changed my mind
I recently met a math phd from an Ivy league school. We together read the proof of Radon Nikodym derivatives on a Tuesday night and a week later, when I called him, what surprised me was that he remembered every single detail of the proof, even the page number, the notations and symbols used by that book. The proof we read relied on a few other theorem named in numbers like thm 12 or thm 14. What amazed was that he even remembered the numbers of the thms and could perfectly match the thm number with the statement and he has never read that particular version of the proof. Well, maybe many of the people here can do this easily, there is no way I could remember things that well. Furthermore, even at his Phd program, few people land assistant professor positions even after years of postdoc.
I am taking a summer math class heavily relying on matrices. The professor teaching the class does all of his writing for the class on his tablets and we see it through the projector. One program with his software is that it is hard to scroll back in pages; so once he is done with one page, he does not like scrolling back to the previous ones. Many times, I noticed that he could remember every single number in a 3*3 matrix calculated a couple of pages ago perfectly without making any mental effort to memorize those numbers. That is something I could never do and I was quite impressed with his memory. So I went back and checked his CV. It turned out that he was very successful when he was my age. In fact, he already got his phd in math when he was 25 years old from MIT. I am 25 years old now and I am not close to getting into a decent math phd program.
Many great scientists including mathematicians are genius people. John von Neumann has graphic memory, Einstein has IQ of 190 and the list goes on and go.
So practically speaking, do people with average intelligence really stand a chance to be successful in academia? Is it worthwhile for someone like me to spend years in life to pursue a phd in math in the hope of making a research faculty?