Advice for a freshman

Question

I am a freshman math student. I want to get into mathematics just like Fermat. He was also not an academic but a law-man, however he accomplished big things in mathematics. I don't want to become a academician because I am not interested in teaching to anyone either. I just want to pursue my curiosity and have fun and by doing it make progress in mathematics like trying to solve big unsolved questions. In order to do that, do I need to go for a PhD in the future? By not doing a PhD, can I reach at such a level in mathematics? I thought if I don't want to stay in university and do that for a living, why should I do that? Just for a title in front of my name? It's worthless to me, I just want to learn if one can become such a mathematician by not doing a PhD or not. Thank you from now. (If you think that "You are just a freshman, why do you think that from now?", My future plans depend on the answer of this question. If you say of course one can accomplish that without a PhD, I won't be interested in at all.)

Answer 1

The answer is... it depends. Mathematics is a unique field because if you contribute something meaningful, then no one is going to care if you have fancy letters in front of your name; the substance of your work is what matters and it either will or will not stand on its own merit. However, you may find it challenging to progress in mathematics without following the disciplined course plan that the academic route provides. Some people are determined and disciplined enough that they don't need it; they simply buy books, read, study, and grow at their own pace. But others do need it. So, which one are you? There is also another valuable aspect of the academic route to consider: socializing and collaborating with your peers who are all brainstorming and growing alongside you. You are also rubbing shoulders with professors and people much smarter than you. Perhaps you can find ways to build this community around you on your own. They are just things to consider.