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- Thread starter AdrianZ
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I have a pure mathematics background as undergraduate, but is now pursuing a PhD in physics. Yes, I have seen people who did math PhD but later on works on theoretical physics while being employed by math department. GR and QM will become easier once you have the appropriate mathematics background [e.g. differential geometry for GR].

I sort of agree with what Spivak says in his https://www.amazon.com/dp/0914098322/?tag=pfamazon01-20 that mathematicians find more advanced physics *easier* than elementary physics. GR was easier for me than say, Newtonian mechanics. :tongue:

But if it is clear to you at this point that you would want to eventually work in theoretical physics [it wasn't clear for me back then], why not consider switching over to physics now as a freshman?

I sort of agree with what Spivak says in his https://www.amazon.com/dp/0914098322/?tag=pfamazon01-20 that mathematicians find more advanced physics *easier* than elementary physics. GR was easier for me than say, Newtonian mechanics. :tongue:

But if it is clear to you at this point that you would want to eventually work in theoretical physics [it wasn't clear for me back then], why not consider switching over to physics now as a freshman?

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But if it is clear to you at this point that you would want to eventually work in theoretical physics [it wasn't clear for me back then], why not consider switching over to physics now as a freshman?

Thanks for the comment. well, It's clear for me that I do like to study GR and QM and I find theoretical physics the most astonishing and fascinating area that mathematics can be applied to but I doubt if I can say that I like physics more than math. Physics is amazing, it deals with real situations while mathematics deals with abstract and sometimes -one may argue that most of the times deals with- non-intuitive concepts and I also know that some theoretical physicists like Edward Witten even has been given prestigious awards like fields medal but still I think that an average pure mathematician has a lot better understanding of mathematics than a fairly professional theoretical physicist in general.

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but still I think that an average pure mathematician has a lot better understanding of mathematics than a fairly professional theoretical physicist in general.

Sounds like you might do fairly well at mathematical physics? I mean

Can a pure mathematician study the TP courses on his/her own and be a professional theoretical physicist? If yes, what courses should he/she study on his/her own?

I would answer a resounding

In my world, there is no such thing as a pure mathematician without some equivalent of a PhD in mathematics, and the same goes for theoretical physics. Usually, "equivalent of" could be dropped, but there are some geniuses who can conduct PhD level research in mathematics as youngsters.

So what you are really asking, as per my interpretation of the words, is whether you can get a PhD + significant research depth and experience in pure mathematics and physics by taking some physics courses, and the answer is simply no.

Can a pure mathematician learn some physics? Yes. There are many good books in physics which are geared towards mathematicians, although these usually assume very good command over mathematics.

Another piece of advice - if you want to become a

Now if your question is just - can someone doing a math major self-study enough physics to go on to physics grad school and then concentrate in physics to become a professional in physics, that's a different story. Sure. I believe you can learn stuff without classes if you really make sure you get the intuition and think hard about it. But you asked about a

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The problem with doing that is you need to be able to convince the graduate school that you are fit to do a PhD in physics. By just self-studying you don't have anything to prove that you are ready for graduate study in physics. If you want to walk this path, it is best to take as many physics courses that you can during your undergrad or M.S., or you could do a physics related thesis for your M.S.

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I do agree it's possible to enter a physics PhD after a math undergraduate degree, but just as developing mathematical intuition is definitely a transition to be made, so is developing intuition for the basics of physics.

Your reason to pursue mathematics, as opposed to physics, was that mathematicians have a better understanding of mathematics. Sure, but physicists have a better understanding of physics - which would be what you'd want if you want a PhD in physics. Else, you can study some aspects of mathematical physics when you do a math PhD - it certainly won't be the same, but it may suit someone who cares more about mathematics.

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Is it possible to self-studythe bare minimumrequired to start studying physics in the PhD level

You will simply not survive research if you do this. You usually have to learn / think several times beyond the bare minimum required to figure a problem out before you'll figure it out. Not to mention that figuring out what problems are interesting requires immersing yourself in the field.

Breaking news - there

Just consider this - would an expert who has spent 40 years in your field figure out your PhD thesis in a few weeks? If so, it's kind of trash. And experts can figure out a lot of things in a few weeks. You'd be surprised how hard it is to come up with an interesting problem that you can also make progress on.

If you do not develop a serious attitude towards physics, you will not survive in the long term as a physics professional.

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I guarantee you are no expert in Newtonian mechanics. Some of the very deepest mathematical insights of physics lie in ordinary classical mechanics, and it will take much time and study before you will appreciate them.

The mathematician's approach to mathematics and the physicist's approach are very different. Mathematicians are concerned with moving slowly and defining everything carefully so that everything makes sense at every step. Theoretical physicists plow roughshod through mathematical formalisms in search of something they can

If you study pure math, you will find what physicists do makes you very uncomfortable. In my experience, theoretical physicists tend to learn mathematics much more

Also, theoretical physicists must be very strong in

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Also, theoretical physicists must be very strong incomputationin a way that I think mathematicians typically need not be. Mathematicians tend to focus on proving facts about mathematics, and this requires synthesis of many disparate definitions into a logical whole, but rarely requires long and complex calculations. Physics requires much more computation of specific examples, actuallysolvingcomplex equations rather than simply proving that they must hold. Your computational ability must be top-notch if you want to make any meaningful progress.

I think this is another indication that I should go into Theoretical Physics, as I've always been told that my computation skills are rather strong, however from the little experience I have, I also enjoy doing proofs.

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For theoretical physics, I think there is quite a bit of value in taking a wide range of math courses. It's quite possible a math degree would prepare one for PhD research in theoretical physics better than a physics degree, depending on the research topic and undergrad math vs. physics program.

This is almost certainly true in other fields as well given how important interdisciplinary research is nowadays. In short, I think these can be pretty darn good questions .

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Why am I not doing an official Physics major then? Because of the course requirements such as lab, and math classes for which I already know the material to, and hence instead of those, I could be taking more advanced classes in Theory.

This is a quite silly attitude. You need those lab classes. They will give you valuable understanding of how your theoretical work relates to the rest of the field. A theoretical physicist without an understanding of experiment is just an armchair philosopher.

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This is a quite silly attitude. You need those lab classes. They will give you valuable understanding of how your theoretical work relates to the rest of the field. A theoretical physicist without an understanding of experiment is just an armchair philosopher.

Yes, but in order to get an understanding of experiment do you really need a solid 3 semesters worth of labs with heavy reports due every week? I understand the need to take a lab, and I will eventually take a lab or two, but right now I want to develop a more solid understanding and want to get ahead in theory. Also, I'm going to start research sometime this semester, which might help me develop an understanding of experiment in a more realistic way.

Also, your stance is a bit debatable as well. Theoretical Physics programs in the UK, for example, usually don't have any experimental components to them, so would you call all Theoretical Physicists from the UK "armchair philosophers"?

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theoretical physicists tend to learn mathematics much more quickly

You cited the example of a course, and then claimed to have read several books and learned more quickly - this is simply stating that courses are methodical and slow. I don't think that's an indication of how mathematicians actually learn when they are forced to research.

Usually, a course is conducted more slowly, because the point is to get intuition for something, not just use its results as quickly as possible. This holds true of physics courses too.

For instance, if I flipped your logic in an analogous direction, what if a mathematical physicist needed some intuition as to a bunch of physics, and to use its language, but really was only proving mathematical results? They could probably learn physics more

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You cited the example of a course, and then claimed to have read several books and learned more quickly - this is simply stating that courses are methodical and slow. I don't think that's an indication of how mathematicians actually learn when they are forced to research.

Usually, a course is conducted more slowly, because the point is to get intuition for something, not just use its results as quickly as possible. This holds true of physics courses too.

For instance, if I flipped your logic in an analogous direction, what if a mathematical physicist needed some intuition as to a bunch of physics, and to use its language, but really was only proving mathematical results? They could probably learn physics morequicklythan that material would be presented in a graduate course in physics, as relevant to their research, which after all, isn't in physics, much as the physics researcher is only using the mathematics as a tool.

I was going to point out something like that.

I do think there is some truth in his statement but it does not hold true for Physics graduates *only*. I'm certain the same thing could be said about an applied math grad.

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One thing you have to realize is that you will have to pass qualifying examinations in physics before you can move on to Ph.D. candidacy. Meaning that, one way or another, you need to be prepared for the content those exams cover. You can be accepted into some physics Ph.D. programs without all the necessary coursework to pass those exams, but you will then be expected to either take remedial undergraduate courses or self-study to fill in those gaps.

Seeing as how you are a freshman, I think that it makes sense to at least double major - that way you have more options when you graduate. (Or you may decide to focus on just one after you have a little more of both subjects under your belt.) I understand that you don't want to take certain courses, but, that's part of life. You will take courses in graduate school that you may not be interested in, either. And labs are a crucial part of a physics degree; depending on the lab course, you will sometimes talk about topics not covered in class, and be expected to read research papers describing the experiments, theory, and put the experimental methods together and interpret the results yourself. That is much more similar to real research than following a course given by an instructor.

Also, take a breadth. You're just a freshman. I knew several of my fellow mathematics majors who thought they liked quantum mechanics or general relativity, because they liked some of the relevant mathematics topics. When they actually took courses on these topics from the physics department, they changed their tune.

Best of luck!

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...I knew several of my fellow mathematics majors who thought they liked quantum mechanics or general relativity, because they liked some of the relevant mathematics topics. When they actually took courses on these topics from the physics department, they changed their tune.

Just out of curiosity, why did they change their minds?

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Just out of curiosity, why did they change their minds?

For whatever reason, I think they thought just because they knew the math behind certain physical concepts that the physics would present little challenge. But being able to prove that, for a simple example, the set of square-integrable functions is a vector space has little bearing on whether or not you can actually solve quantum mechanical problems. So, when a professor would drop a line like "Hilbert space is important in quantum mechanics", meaning "Hilbert space is an important concept in constructing a mathematically sound theory of quantum mechanics", they would hear it as "If I know how to do proofs about properties of square-integrable functions, or the Cauchy-Swarz inequality, or whatever, I will be good at quantum physics." Then, they get to class, and realize that, while the "abstract" mathematics is very important, there is still a lot of solid physics going on. That's the best reason I can come up with. To make a long story long, I think it boiled down to the fact that the type of math they enjoyed doing, while present, didn't play a large enough role in the course.

Haha, this, in some sense, was the case. It's kind of like taking an Analysis class; you talk about integrals, when they are defined, some important inequalities, and some methods for calculating them, but you very rarely

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