How to do research in theoretical physics or math?

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Hello! All of my undergraduate research so far was in experimental fields, mainly because most of my professors are doing that at the university. The few ones who are doing something more theoretical are mainly working on numerical simulations.

I have always been fascinated about theoretical physics/math and I was wondering if someone working in the field can tell me more about the process of doing research in these fields. I am curious about the way one approaches a theoretical problem (after one learns the work done before, of course). It just seems so overwhelming trying to tackle a problem that probably lots of brilliant physicists have failed to solve over tens or hundred of years. Of course a genius might attempt that. But i am not a genius.

What chances do I really have to find something they didn't? In experimental physics is different, as we have access to new theories and more important new technology that physicists in the past didn't have. So we have a great advantage over them. But in theoretical physics and math this is not the case (of course we might have some new mathematical tools, but I feel that is not that significant compared to the experimental case).

So given all this pressure of hundreds of brilliant minds failing, how does one proceeds? And what does one do if they fail? For example aiming to solve one or more problems as part of your PhD, you actually have to solve them, if you want to graduate. But most probably others have failed before, so how do you know if you can solve them?

You might never get a PhD simply because the problems are too hard. Can someone give me some insight into this? I am thinking to do some research in theoretical physics with a professor at another university, so I would like to know about all this, before making a choice. Thank you!
 
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  • #2
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Stop thinking of reasons to fail here. Sure there are many brilliant people but then there's the problem. You look at it with a fresh open mind exploring different ways to solve it. Often you'll hit some roadblock and must explore to find another way. Other times, you'll talk it over with colleagues and someone will suggest a new approach and so you'll go back and try that too.

You must be persistent, consistent and insistent in order to eventually solve it or conclude that it is beyond your present skills. Whatever you learn can be valuable in solving the next big problem you tackle. Your schooling has trained you for these moments but sometimes you must press on and develop new skills or new math to succeed.

There is a story of Einstein who was stuck in GR unable to complete his work. Prof Hilbert invited him to Gottingen to present several seminars on his work on the Special and General Relativity. Seminars got Hilbert thinking that he could solve it. While Einstein felt Hilbert was a superior mathematician of the first rank, it didn't intimidate him. He pressed on and eventually discovered his error in something he had worked on earlier but discarded.


https://en.wikipedia.org/wiki/David_Hilbert
https://en.wikipedia.org/wiki/Relativity_priority_dispute
 
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  • #3
ZapperZ
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Hello! All of my undergraduate research so far was in experimental fields, mainly because most of my professors are doing that at the university. The few ones who are doing something more theoretical are mainly working on numerical simulations.

I have always been fascinated about theoretical physics/math and I was wondering if someone working in the field can tell me more about the process of doing research in these fields. I am curious about the way one approaches a theoretical problem (after one learns the work done before, of course). It just seems so overwhelming trying to tackle a problem that probably lots of brilliant physicists have failed to solve over tens or hundred of years. Of course a genius might attempt that. But i am not a genius.

What chances do I really have to find something they didn't? In experimental physics is different, as we have access to new theories and more important new technology that physicists in the past didn't have. So we have a great advantage over them. But in theoretical physics and math this is not the case (of course we might have some new mathematical tools, but I feel that is not that significant compared to the experimental case).

So given all this pressure of hundreds of brilliant minds failing, how does one proceeds? And what does one do if they fail? For example aiming to solve one or more problems as part of your PhD, you actually have to solve them, if you want to graduate. But most probably others have failed before, so how do you know if you can solve them?

You might never get a PhD simply because the problems are too hard. Can someone give me some insight into this? I am thinking to do some research in theoretical physics with a professor at another university, so I would like to know about all this, before making a choice. Thank you!

This professor should have the proper guidance for you, because it will be in an area that he/she is familiar with. More often than not, you will start by trying to understand the theoretical foundations of the physics that you are working in before you jump into the unknown territory.

No one starts off blank and fumbling in the dark. The fact that all of us require a supervisor that is responsible for guiding us is why we do this in school and not on our own in a garage or Swiss patent office somewhere.

Zz.
 
  • #4
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As science enthusiast, and even as students, it is typical to have kind of a view as if science progresses by a very big breakthrough every few decades by some kind of legendary genius. This can seem a bit intimidating indeed.

In truth, research is at least as much about many unknown people working together to solve smaller problems. And overall, there is no shortage of research questions to come up with. In condensed matter, one could study almost any kind of material with any kind of method and try to predict if it is a good superconductor; or in string theory there are an infinite amount of exotic symmetry groups to be studied. Then there are some fancy buzz words like 'topology' or 'quantum simulation' to try to apply to these things, and typically everytime a question is settled, a few other ones arise (don't wory if it's not the case with you, but your adviser should come up with plenty).

In practice these works are field work combining conceptual thinking, calculations and numerical simulations. Persistance and creativity is needed, but moving forward is far from impossible.
 

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