Can I be a successful physicist or mathematician?

[Anish Pandya]

Hello,
I am in high school in the United States. I am SUPER interested in mathematics and physics, and I have been researching physics and mathematics since middle school. I love it! I love theoretical particle physics and algebraic topology. If I had the choice, I would spend my entire life researching these subjects. I am seeking advice from physics and mathematics professionals about how to proceed, and such. Although I am good at mathematics, proofs and visualizing concepts, I am not strong on competition math and problem-solving. Many major mathematicians and physicists have been famous for winning competitions such the International Physics Olympiad test, International Mathematics Olympiad test, Putnam, Mathcounts, AMC, etc. I was wondering whether it is a good idea for me to pursue physics and mathematics further or to turn to a different field and continue to do the math as a hobby. How hard is it to become a respected physicist/mathematician? How is mathematics different at the professional level? If I am not good at competition math, can I be a successful mathematician or physicist? If so, how would I proceed? If not, how can I continue to stay on the cutting edge of mathematics and physics as a hobbyist?
Thank You

 

[Orodruin]

First off, do not put too much value into competitions. I have to some extent "made it" in academia and while I did reach the national final in the physics and chemistry competitions, it is not something I value that highly and I cannot think of a single colleague that I know was in the international finals so it is not at all any sort of requirement. If you have that skill fine, it shows some aptitude for solving physics problems, but that is not all there is to it. That being said ...

How hard is it to become a respected physicist/mathematician?

I will not sugar coat this however, it is hard and it will not only depend on you but also on sheer luck in finding an appropriate subject, a good PhD advisor, several postdocs, and finally a position where you may eventually get tenure. Of course, your performance can help in these things but by no means will they ever be guaranteed.

If not, how can I continue to stay on the cutting edge of mathematics and physics as a hobbyist?

You really can't unless you are incredibly talented and have way too much free time, not even in a small specialized subfield. Physicists spend large parts of their working days keeping up - mostly with their own subfield.

 

[Choppy]

I agree with Orodruin.

I'm sure some scientists won competitions when they were younger. Many have not. This is hardly a decisive predictor for success in academia. Do the competitions if you find that you enjoy them or get something out of them, but don't feel like you need to win them in order to be successful later in life.

How hard is it to become a respected physicist/mathematician?

I suppose that depends on your definitions of "respected" and "physicist/mathematician." Generally speaking, it's very difficult to make a career within academia (i.e. become a professor). As a rule of thumb, every professor is going to train N graduate students of the course of his or her career who will eventually earn a PhD. It's hard to say exactly what N is on average, but its certainly > 1, quite likely > 3 and in many cases can be on the order of 10. Only one of those students will be needed to replace the professor when he or she retires or dies. The other N-1 are going to have to leave academia. The is *some* growth in the sector of course. Others can move into more teaching-oriented jobs. But from a supply and demand perspective it's more probable that not that even if you earn a PhD, you will not end up as a professor. For those who stay in, the environment is highly competitive. You can be into your mid-to-late thirties by the time you're eligible to compete for tenure-track positions.

How is mathematics different at the professional level?

I'm not a mathematician, so take this with a grain of salt, but I think the big difference is that most of what you're used to up until this point (and generally through undergraduate study) is learning what other people have already done. You're re-proving theorems that have been proven many times before. The solutions to the problems you face are out there and chances are if you can follow the reasoning that others have used, you'll be able to reach the same conclusions. But at the research level, the game changes. You work on problems for which there is not a known answer. And many of the problems are very hard because the "low hanging fruit" will have already been picked.

If I am not good at competition math, can I be a successful mathematician or physicist?

Sure. As mentioned, competitions tend to focus on a specific skills set and those skills can be improved if you work at them. You might not be the "best" but to do research you don't have to be. You need to know enough to know what you're doing. But beyond that it's a matter of passion, patience, focus, and the will to keep working on a project until you make progress.

If not, how can I continue to stay on the cutting edge of mathematics and physics as a hobbyist?

Before really worrying about staying on the cutting edge of mathematics and physics, it's important to remember that it's not a matter of getting to the edge or doing nothing at all. Physics and mathematics can be an integral part of your education regardless of what you do. You might find that once you get close to the "cutting edge" you're actually a lot more interested in practical applications, for example.

 

[eri]

I feel like I should point out that not EVERY professor will train grad students. Most of my friends and I from grad school ended up at small state schools and liberal arts colleges, where we don't have graduate programs in physics (or sometimes even a physics major). There are far more schools offering bachelors degrees in physics than there are schools offering PhDs in physics. So while yes, it's difficult to get a job as a physics professor and earn tenure somewhere, it's not quite as bad as 'one student per professor'. And small schools are sometimes happy to take on a theoretical physicist - they're often low on lab space. I was told that one of my best attributes as an applicant for my current job was the fact that I only needed a computer to do my research (part of a larger collaboration that supplied the data and maintained the instruments).