I am currently a PhD student advised by a new (and awesome, in my opinion) theoretical computer scientist in the field of optimization. This was my dream ever since I took a class on convex optimization a few years ago during my MS.
However, I don’t have a math or CS background. My master’s and industry experience have both been in applied signal processing. When I recently looked at the kind of grad students who work in my current choice of research area, I realized the level of competition I am up against.
These are all from amazing institutes around the world and had been the brightest kids in their colleges, the ones with medals in olympiads, top Putnam scores, etc. I am from a mid-tier college in my country and never won an award for excelling in math/algorithms.
How do you come to terms with the fact that you might be doing research in what you love with an amazing mentor, but you’ll just never be the best in even your research community? How's that not discouraging?
Answer
If every swimmer were to compete with the latest 20 year old Olympic gold medalist, they would soon give up. That's why we have different leagues. They provide more relevant frames of reference to compare different athletes. Thus you need to:
Shift the frame.
Adjusting a bad frame:
You are a PhD student who completed some regular college and an outsider to your field. But you are comparing yourself with your supervisor and with "the brightest kids" in the world and, what is more, with scientist who specialized in your field from the get-go. How can that not be disappointing?
What about: You are an up-and-coming young researcher with real-world experience and a background that is not the usual run-of-the-mill in the field you are working in. You have an amazing supervisor who trusts your work and you are at least as successful as the other PhD students in your cohort. Perhaps you are the only one from your college who made it to graduate school in the last couple of years. You still have plenty of time as a researcher to develop your own profile according to your interests. Don't be fooled by the impostor syndrome.
Dropping a bad frame:
Never mind what I said in the beginning. Science is not a competition -- at least it shouldn't be.
If you're doing research mainly to outcompete your colleagues, to improve your social status, to feel pleased with yourself: you're doing it wrong. Then you are extrinsically motivated, and this is neither sustainable nor does it make you happy. Have you ever delved into a problem and forgotten to drink or eat until the sun went down? Have you ever felt deeply frustrated because you just couldn't wrap your head around some strange finding, only to realize later that it completely makes sense when you look at it from a different angle? Experienced the enthusiasm that came with that discovery? Do you deeply feel that you have to understand this? Then you know the feeling of flow that really only comes from intrinsic motivation. Forget the competition; enjoy the game.
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