Theoretical Physics vs Math: Regrets of Scientists

[ehrenfest]

I am torn between theoretical physics and math. Are there any theoretical physicists here who regret not going into math? Are there any mathematicians here who regret no going into theoretical physics?

 

[Gallileo]

Why not do both? I think they have a lot of things in common. Or take both math and physics courses and see which one you like more before you decide which one you want to stick with.

 

[Poop-Loops]

I think he means in graduate school. From what I've read of his posts, he's getting close to graduating with a BS.

 

[sesinka]

I tried to solve similar dilemma recently. I'm getting close to B.S. (of physics) and I had to decide in which branch of this science I will specialized to M.S. before few months. In particular I thought about matematical modeling or theoretical physics. I planned to do both but it cost lot of time so I couldn't fully understand all and I was in great stress all the time. So, I coudn't recommend it.

 

[quadraphonics]

I would suggest that, if you play your cards right, there may be very little difference between the two options as far as your long-term career goes. That is, if you opt for physics, you could work to emphasize math-intensive stuff and so take lots of math courses, and vice-versa. Not sure if you're planning to do a PhD, but if so you could make an effort to get committee members from whichever department you don't end up in involved in your research. It's not unheard-of for people in physics or engineering (or econ) departments to have math profs as their primary research advisors. That doesn't provide much guidance as far as actually picking a department to apply to, but I think the important thing is to work to emphasize the entire range of your interests, regardless of which department you actually reside in. Then, the difference will be academic (sorry, couldn't resist...). I suppose what I'd concentrate on is finding physics programs/research groups with a heavy math emphasis, and vice-versa, rather than sweating which department as such.

 

[ehrenfest]

It's not unheard-of for people in physics or engineering (or econ) departments to have math profs as their primary research advisors.

Yay that's really useful to know. And yes, I am planning to do a PhD.

 

[quasar_4]

I have the same dilemma now. It seems to me though that math offers more job prospects because math departments tend to be larger than physics departments, and there are VERY few positions in academia in theoretical physics. I like the concept of mathematical physics programs, but they are usually approached from the math departments. I don't know exactly what physics they encompass though. Hopefully general relativity is included somewhere...

 

[ehrenfest]

there are VERY few positions in academia in theoretical physics.

Is that true?

 

[ehrenfest]

What about outside of academia?

 

[epenguin]

Purely personal brainstorming, maybe of interest for others choosing a direction.

Apart from math what else are you interested in?
Nothing? OK, a lot of people look askance at mathematicians because they think they are like that! :tongue:
But even then you were probably not always like that, it is a position people come to, possibly from a sort of brainwashing.

Personally I like it when it is the math of something. Though nothing has quite the tradition and fusion with it that physics does. But there are some now affirmed math-using specialities.

So I would say for prospects and satisfaction, try to combine with the study of something else. Lots of things have developing needs and invovement in math - engineering, biology, bioinformatics, biophysics, neurosciences, epidemiology, physiology incl. medical physiology, Earth'sciences, ecology and population studies, genetics, chemistry, materials science, linguistics, sociology, of course economics and finance. Some selection of courses in these subjects seems more useful than the maximum of advanced math couses in as many math specialities as possible as long as you take the centralest ones to reasonably high level.

Job satisfaction: you have more of a chance of making a significant contribution to these than in well trodden fields like pure math. A mathemtician told me, let's hear others' advice, it's the only place you can make a significant contribution. If your ambition is to do something in the Riemann or Poincare or Fermat's LT or strings, although in theory it looks you could do it anywhere with a library, in practice what I've been told and the pop books on the above confirm, there are only a couple of dozen places in the world out of the thousands of math institutes where you stand a chance.

Jobs: available outside the strict math institutes. In particular people with experience of modelling are quite sought after and readily find jobs. With finance employers have traiditionally been more interested that you are an able high-flyer (and from a top institution) than what relevant you know, though I imagine financial math and economics will increasingly count.

Requirements: If you have studied one of these subjects in its own terms you will get to understand its problems from the inside. It is not as good being a mathematician and thinking people can bring you problems and explain them and then the mathematician can formalise and solve them, it cannot happen too much like that. You will never know some of the problems unless you are on the inside of one of these sciences.

 

[f95toli]

Is that true?

Yes, especially "math intensive" physics like string theory etc. It is a bit easier if you are interested in more applied modeling and/or computational physics (e.g. surface physics etc).
However, most physicists today are experimentalists although I can only guess at the ratio, 80-20%?.
Where I work now there isn't a single "pure" theorist (which is actually a problem), the closest thing we got is a guy working on molecular dynamics simulations.

The good thing about doing theory is of course that it is cheap (you don't need equipment worth millions of dollars), but the people I know still struggle to get grants; the best way to attract funding is probably to have a strong collaboration with an experimental group; but this is of course difficult if you are working on some exotic problem in cosmology.

 

[DavidWhitbeck]

I am torn between theoretical physics and math. Are there any theoretical physicists here who regret not going into math? Are there any mathematicians here who regret no going into theoretical physics?

I faced that choice, I double majored and was unsure about if I wanted to go into grad school in math or physics. I chose physics. Both fields are intellectually stimulating, and if you choose your adviser very carefully it will not be that important. I thought that I would end up regretting my choice, but honestly I have not.

The odds are that you will not end up becoming a professor who spends most of their time on research. If you stay in academia, you will more likely end up having a teaching first type of professorship at a small college. Which would you enjoy teaching-- physics or math?

 

[ehrenfest]

Which would you enjoy teaching-- physics or math?

Right now I have to say math i.e. I love presenting proofs in algebra and analysis and topology. I just cannot say the same for physics. But I think that may be symptomatic of being at a school where the quality of pedagogy in the physics department trails far behind the mathematics department. The physics classes I have taken are somewhat of a joke, which is in fact the main reason that I created this thread. However, I can imagine at other schools such as MIT, the physics and math classes are not as different as they are here. The courses I have looked at on MIT opencourseware are good examples of this. I think you can make teaching a physics quite close to teaching a math class if you are good at it and that is what the MIT professors do. I think that will be my goal, to teach a physics class that models a math class.

 

[DavidWhitbeck]

Well I should warn you that if you teach introductory physics or math you will not be presenting formal proofs, and at small colleges the demand for teaching will be heavily focused around introductory courses.

If your physics classes are a joke, then you might not be ready for physics grad school, and you will end up struggling in the beginning, and the first year already is a hard year. You have to balance TA duties with completing the course load (which move at a faster pace than undergrad courses).

If you enjoy math, and feel much better prepared for math grad school, and you seem to enjoy the logical structure of proofs, it seems that math might be for you.

 

[MathematicalPhysicist]

btw, can't you take some courses from the physics department while actually being a graduate maths student?

 

[comote]

There are plenty of people around working in mathematical physics. You can in essence do both. Study problems that arise in the study of physics from the prospective of a mathematician.

 

[ehrenfest]

Well I should warn you that if you teach introductory physics or math you will not be presenting formal proofs, and at small colleges the demand for teaching will be heavily focused around introductory courses.

If your physics classes are a joke, then you might not be ready for physics grad school, and you will end up struggling in the beginning, and the first year already is a hard year. You have to balance TA duties with completing the course load (which move at a faster pace than undergrad courses).

If you enjoy math, and feel much better prepared for math grad school, and you seem to enjoy the logical structure of proofs, it seems that math might be for you.

I think I will be well-prepared for physics grad school not from my courses but from a lot of self-study.

I think I will always "enjoy" doing math more i.e. solving Putnam problems, presenting proofs, manipulating equations, getting the correct answer is my foremost passion. However, that has not been compelling enough to go into math for two reasons: 1)I think that enjoyment might fade as I get older. Also, I like learning and teaching math a lot and 2) I lot solving problems that are given to me but I am not sure I actually like "doing" math. That is, coming up with new theorems and conjectures is rather a dry task for me. Brainstorming for new results in mathematics seems so awkward and undirected to me.

I guess my ideal job would be this: teaching math, teaching theoretical physics, doing research in theoretical physics.

Since 2 out of the 3 things on that list involve physics, I am planning to go into physics.

Ughh, but this is still a really hard decision. I am doing an REU in particle physics this summer and next year (my third as an undergrad), I am taking or auditing 6 graduate math courses, so I will get lots of exposure to upper levels of both fields and hopefully that will help me decide.

I guess my eventual goal might be to get a dual appointment in the math and physics department.

 

[ehrenfest]

There are plenty of people around working in mathematical physics. You can in essence do both. Study problems that arise in the study of physics from the prospective of a mathematician.

Yes that is exactly what I want. The issue is what department are these people in?

 

[DavidWhitbeck]

Yes that is exactly what I want. The issue is what department are these people in?

They are in the math department.

 

[cristo]

I think I will always "enjoy" doing math more i.e. solving Putnam problems, presenting proofs, manipulating equations, getting the correct answer is my foremost passion.

This is not what you will be doing throughout your PhD, though. You will not be "presenting proofs" in the way you have done in undergrad. You also may not know whether you have got the right answer: you may have an answer, but it'll be to stuff that hasn't been done before.

However, that has not been compelling enough to go into math for two reasons: 1)I think that enjoyment might fade as I get older. Also, I like learning and teaching math a lot and 2) I lot solving problems that are given to me but I am not sure I actually like "doing" math. That is, coming up with new theorems and conjectures is rather a dry task for me. Brainstorming for new results in mathematics seems so awkward and undirected to me.

Have you ever taught maths? I get the impression that you're in your second year undergrad, so don't have the experience to say whether or not you enjoy it! Also, if you don't like brainstorming for new ideas then I doubt that any sort of research is right for you. Theoretical physics is no different to maths in the sense that you will be trying to find solutions to problems that have no solutions.

I guess my ideal job would be this: teaching math, teaching theoretical physics, doing research in theoretical physics.

If you want my advice: it is utterly pointless planning out your career right now-- you don't even know whether you'll make it through grad school, let alone land yourself a faculty position! At the moment, I would concentrate on trying to learn the courses you are taking as well as you possibly can.

 

[Poop-Loops]

Right now I have to say math i.e. I love presenting proofs in algebra and analysis and topology. I just cannot say the same for physics. But I think that may be symptomatic of being at a school where the quality of pedagogy in the physics department trails far behind the mathematics department. The physics classes I have taken are somewhat of a joke, which is in fact the main reason that I created this thread. However, I can imagine at other schools such as MIT, the physics and math classes are not as different as they are here. The courses I have looked at on MIT opencourseware are good examples of this. I think you can make teaching a physics quite close to teaching a math class if you are good at it and that is what the MIT professors do. I think that will be my goal, to teach a physics class that models a math class.

Can you give an example of what a typical physics lecture at your school is like? I am looking over an MIT lecture on Dielectrics now as part of the E&M class, and it looks very much like what I get at my school, but with more colorful chalk.

I mean, my intro classes at Community College were like this:

"Here is the formula. Believe me, it works. Now let's use it."

I don't know whether Freshman physics at my university is the same or not. But the courses I've been taking for the past 2 years have been just derivations during lecture with an example usually. I can't imagine going back to "Proof by trust" type of lectures.

 

[ehrenfest]

Can you give an example of what a typical physics lecture at your school is like? I am looking over an MIT lecture on Dielectrics now as part of the E&M class, and it looks very much like what I get at my school, but with more colorful chalk.

I mean, my intro classes at Community College were like this:

"Here is the formula. Believe me, it works. Now let's use it."

I don't know whether Freshman physics at my university is the same or not. But the courses I've been taking for the past 2 years have been just derivations during lecture with an example usually. I can't imagine going back to "Proof by trust" type of lectures.

Its not the content of the lectures at my school that are different than what I imagine they are like at MIT, it is more the presentation that is different. I lot of my professors essentially recite almost verbatim parts of my textbook during class and it is clear that they could never reproduce the derivation if they had not copied it down in their notes.

The best math professors I have had teach almost or completely without notes. This is only possible when the professor understands the material very well. I have never had physics teacher that came anywhere close to this level of excellence in teaching. At MIT, it seems like the physics professors could easily teach from memory.

My point is that in my classes we get do get derivations but they are usually just really sloppy and although my professors can write down the math, I do not think they understand the "logic behind the math" if that makes any sense.

 

[Poop-Loops]

Its not the content of the lectures at my school that are different than what I imagine they are like at MIT, it is more the presentation that is different. I lot of my professors essentially recite almost verbatim parts of my textbook during class and it is clear that they could never reproduce the derivation if they had not copied it down in their notes.

The best math professors I have had teach almost or completely without notes. This is only possible when the professor understands the material very well. I have never had physics teacher that came anywhere close to this level of excellence in teaching. At MIT, it seems like the physics professors could easily teach from memory.

My point is that in my classes we get do get derivations but they are usually just really sloppy and although my professors can write down the math, I do not think they understand the "logic behind the math" if that makes any sense.

All of my professors read from their notes during class. The bad ones get confused by their own notes, the good ones don't look at them too often in the first place.

They definitely understand "the logic behind the math". It's something an undergraduate can understand, or else it wouldn't be taught. It's just that they suck at lecturing. I know what you are saying. Knowing the material and teaching it are two different things. A professor needs to be good at both.

 

[DavidWhitbeck]

I lot of my professors essentially recite almost verbatim parts of my textbook during class

That's the difference between professors who want to devote time and energy into teaching well and those that only teach because they have to.

and it is clear that they could never reproduce the derivation if they had not copied it down in their notes.

That's a very arrogant and foolish thing to say. Their understanding of the material probably far exceeds yours, and I bet they could reproduce any of those derivations without much trouble. It is clear that you value memorization highly, but understanding is far more important.

You have to teach a class for at least a few years before you end up with your successful method of teaching it that differs from a standard textbook treatment. Finding your own unique, but insightful, perspective on a subject is a difficult journey, longer and harder than the initial time you learned the basics in class.

 

[ice109]

if you like proofs i can't imagine why you like physics.

 

[ehrenfest]

That's a very arrogant and foolish thing to say. Their understanding of the material probably far exceeds yours, and I bet they could reproduce any of those derivations without much trouble. It is clear that you value memorization highly, but understanding is far more important.

I bet your wrong. I am not saying I could reproduce the derivations either ... I am not sure why you think that was arrogant or foolish. It was my assessment of their understanding.

I am also not saying I value memorization. In fact, I hated the biology and organic chemistry classes that relied so much on memorization. When you understand something like electromagnetism or classical mechanics really well, you can basically just remember the main ideas of a derivation and the details will follow. When you understand the subject poorly, you need to recall all the details to complete the derivation.

 

[ehrenfest]

if you like proofs i can't imagine why you like physics.

Haha that's a good point. I am not saying I only like proofs though. This discussion is really rocking what I thought was a straightforward career path in theoretical physics. The consensus seems that I should go into math. I was kind of planning of just doing lots of math on the side but devoting my career to physics...but I don't know...do you think it is possible to do math "on the side" i.e. actually publish in math journals even though I would have a PhD in theoretical physics? It seems like Witten has done that quite succesfully?

 

[ehrenfest]

OK. So I have been thinking and rethinking and rerethinking my decision of whether to go to grad school in physics or mathematics and my original plan to go to grad school in physics never seems to produce anything but hesitation and unhappiness in me. I was planning to take the physics GRE in the fall, so I kept telling myself I should start preparing for that but then I would just go read Rudin's Principles of Mathematical Analysis. So, I think I am done seesawing back and forth and will finally just decide to go to grad school in math. Almost every post here is an indication that this makes more sense. I still want to do work in mathematical physics but as everyone here has said the best way to approach that is through mathematics not physics. My research interests (string theory, general relativity, the standard model) have not really changed at all throughout this.

I guess one of my main reservations was that I am doing an REU in physics this summer and I felt like that kind of compelled me to go into physics. I wrote in my REU application that I definitely wanted to get a PhD in theoretical physics, so I kind of feel like that was one reason that they accepted me and that I would be kind of a traitor if I did not do that. This summer won't be totally wasted if I apply to math progams and say I am interested in mathematical physics, right? That is what I am scared of since an REU is a major commitment and I will be hard to stay motivated if I know that

Hopefully, I will get a math REU next summer. I think I am basically going to take 3 semesters of graduate math courses only so hopefully that will be enough to get me into one of the best grad schools.

Thanks everyone for your input. This is why I love PF: I could never have made an informed decision about this just by talking to my friends and family, almost none of who are mathematicians or physicists.

Everyone please comment liberally here about what I wrote--I spend way too much mulling and not enough time discussing my thoughts--so I need to know that what I wrote is not hogwash to other people.

 

[ralphhumacho]

I agree with the above posts as well. Job prospects are wayyyy better with a Math or Stats phD than with a theoretical physics degree. Plus math is just better. I minored in physics and I felt like there was way too much to memorize in terms of concepts/vocab/formulas (and too many damn symbols). With math, all you need are a few definitions, theorems, and you can go from there. If you enjoy Rudin, you are destined to go to Math grad school.

 

[ehrenfest]

If you enjoy Rudin, you are destined to go to Math grad school.

Rudin is like a deity to me.

 

[DavidWhitbeck]

I agree with the above posts as well. Job prospects are wayyyy better with a Math or Stats phD than with a theoretical physics degree. Plus math is just better. I minored in physics and I felt like there was way too much to memorize in terms of concepts/vocab/formulas (and too many damn symbols). With math, all you need are a few definitions, theorems, and you can go from there. If you enjoy Rudin, you are destined to go to Math grad school.

On the contrary there are only a few fundamental principles and equations in physics, and the rest are derivable from them. If you only saw physics as a disconnected mess, then you didn't study long enough to find it's beauty.

 

[ehrenfest]

On the contrary there are only a few fundamental principles and equations in physics, and the rest are derivable from them. If you only saw physics as a disconnected mess, then you didn't study long enough to find it's beauty.

I have heard that before but it really depends on what part of physics you are talking about. That is probably true for classical mechanics but it is definitely NOT true for something like condensed matter physics.

 

[ice109]

On the contrary there are only a few fundamental principles and equations in physics, and the rest are derivable from them. If you only saw physics as a disconnected mess, then you didn't study long enough to find it's beauty.

no i think it's you who hasn't studied for long enough. almost all of physics is phenomenology and by virtue of that a collection of formulas. yes someone did derive them all from one model but practicing physicists and apprentice physicists(students) don't. go ahead i dare you to derive the potential due to a sphere from gauge invariance. hence the wide use of formula sheets in physics classes.

math is no different though as far as that goes. every discipline uses reference books.

the actual difference between math and physics is that there are no contradictory theorems in math. in physics there are regions of accuracy for certain theories and outside those regions they contradict other theories.

the point is that one does not go to school to learn how to solve specific problems so the formulae themselves are irrelevant. one goes to school to learn how to learn effectively and solve general problems. of course one of the most effective problem solving techniques is to read the pertinent literature(look at the formulae).

 

[DavidWhitbeck]

almost all of physics is phenomenology and by virtue of that a collection of formulas.

That's extremely misleading. In theory the phenomenological results could be irreducibly complex, but that's not the case. And I never said one model, I said few.

And in the example that you brought forward to supposedly put me in my place-- what is more elegant than classical electrodynamics? How could you possibly give an example in the most elegant, concise beautiful theory in physics to show irreducible complexity?? Do you realize how absurd that even is!

Maxwell's Equations you use to derive potential due to a sphere, also the equations are manifestly gauge invariant. Two birds, one stone. There, satisfied?

You know, I'm surprised that you have to throw in more wrong headed things while you're at it. Saying that physics is filled with contradictions... it would be a contradiction if quantum mechanics was completely different from classical mechanics. Instead it is a logical extension of the theory, take the classical limit and guess what? you get back the old theory. How is that a contradiction?