Should I try to re-invent the wheel while doing research?

Question

I’m a beginning PhD student in theoretical physics specializing in string theory. Unfortunately, my advisor doesn't have a good understanding of this subject; therefore, he provides me with very little guidance. The problem is that I have a very little understanding of how should I do research in string theory.

My style is that I try to work thing out from the first principles. For instance, when I try to understand the fundamentals of this subject (by which I mean graduate textbook material), I start with blank papers, write down a question I would like to understand, then try to find an answer mostly by reading parts of the textbook or by searching for research papers that deal with this question. Furthermore, I try to work things out on my own. Somehow, this feels somewhat unnatural to me (and it leads to very slow progress). Another approach would be to read the standard textbook thoroughly, then start reading papers more linearly.

I always feel that I’m trying to re-invent the wheel. I think that researchers take assumptions and conclusions from previous work and then build on it. On the other hand, I always try to start from scratch and to derive everything on my own. For instance, physics student learn quantum mechanics by starting with some axioms, then try to understand their consequences. On the other hand, I try to deduce or rather, “find” these axioms by pure thought, which led me to spend a lot of time researching the original papers on quantum mechanics.

Am I doing it right? I think that part of my problem is that I’m trying to imitate top physicists such as, Richard Feynman. Do top physicists (or mathematicians) really do this?

Answer 1

I don’t think this approach is feasible for the following reason:

Theoretical research (and any other research for that matter) takes much more time to perform than to understand. For example, if you have sufficient mathematical background knowledge, I am pretty confident that a few hours suffice for me to make you fully appreciate and understand the entire (theoretical) research I did in the last year, such that the only difference between you and me would be that I have more experience with thinking in these my terms. I am not very familiar with the history of quantum mechanics, but I am pretty confident that writing down the axioms was the result of quite some hard thinking, conceptualising, and a considerable amount of experience.

If this weren’t the case, it would be impossible to advance a field beyond what can be done from scratch in a lifetime. Rather, it is an ongoing challenge for science to improve didactics, programmes, etc. to bring new people to the forefront of a field within a reasonable amount of time, such that they can advance this front – standing on the shoulders of giants. As a sidenote, take a look at some really old mathematics textbooks to feel how didactics has marched on and how important that is.

That being said, trying to do some things from scratch at times can be a helpful exercise that yields a deeper understanding of the matter and trains your field-specific problem-solving skills. But mind that this should be only as an exercise – you do not want to do this all the time.

Finally note that (at least in the fields I am familiar with), most theoretical research is not about coming up with a new theory, new axioms, or similar, but working out the consequences of existing theories. If you can come up with a new, useful theory, that’s great, but chances are that this will only happen after you gained a considerable amount of experience with the existing theories and doing theoretical work in general.

As a complete sidenote: Doing a PhD without a supervisor experienced in your respective subject is usually not a good idea.

Answer 2

I think it is an inefficient approach to do this too much. Certainly at times, it is useful to develop things from first principles, but I would definitely not make it your initial approach.

Feynman did not really do it all the time himself. Read the article on him by Laurie Brown or even the biography by Geis. When he got into some heavy electrodynamics, he refreshed and improved his classical E&M by studying a standard text and working every single problem. Another example is his studies in physics books. Miserable for first years but fun for people who "already know it". Of course he was very creative as well and a deep thinker and would come up with little systems of his own at times. But he was also a person who valued learning and collecting tricks (look at his habits in integration, algebra team, riddles, radio fixing, etc.).

But even excepting Feynman, I just don't think your approach is a time efficient way to learn things. Also, it doesn't stop you from going back and reconsidering things yourself to learn some things in a standard manner. You may even find having a baseline informs you more. Also, just find yourself wondering about things and coming up with new questions as you read a standard approach.

Now string theory. Isn't that so 1995? ;-) Oh...and Feynman didn't think much of it either. Had a skeptical take on the rush down the rabbit hole.