BS in math to PhD in physics?

homeomorphic

Physics has a very practical side.

My impression is that the people driving progress in the computer industry, for example, are usually trained as physicists, not electrical engineers. That's a reason to get excited about physics.

Nuclear fusion is another practical goal.

Even the less practical goals in physics seem to have more philosophical significance than pure math does. The fact that it is dealing with reality makes it seem inherently more relevant.

I don't think I'd feel any better in string theory or loop quantum gravity than I do in pure math, though.

Here's the general argument for the importance of mathematics:

1) Math research is cheap, so it doesn't have to produce that much in order to be worthwhile.
2) It's impossible to predict applications. Who would have suspected number theory would be useful in internet cryptography? People didn't have any idea the internet would ever exists, throughout most of its history.
3) The applied stuff has deep connections to the pure stuff. Because everything in math is interconnected, it can't really be divided into pure and applied. So, some of the pure stuff has some influence on the practical stuff.

Be that as it may, some people, including myself would feel better if they knew that what they were doing was more directly relevant. Also, I'm not convinced that just any old approach to math is as good as any other. More specifically, I don't think the mathematical community has the right balance of pure vs. applied stuff going on right now. I think a lot more thought needs to be put into making the pure stuff more relevant. Much more contact with physics, biology, and chemistry is needed than what I have seen. If only 200 mathematicians in the world can understand something, and only after spending years and years learning it, I see a danger that no scientist will ever be able to learn it and apply it outside math.

Math is interesting, but it's really, really hard work. So, it seems fairly depressing to me if that hard work ends up having no value to society.

deRham

I see no problem with someone being a little disgruntled with where his/her mathematics work is going - there's a reason not everyone pursues mathematics, even if talented at mathematics, as a career. Picking physics for the very practical side is, to me, a pretty good goal, but one that should be done without trying to pick a field where one's mathematics training will be useful (the reference to physics having "aspects of math" that the poster likes got me a little concerned ... because so do lots of other fields).

I think discussing what "reality" is happens to be more of a matter of philosophy itself than either physics or mathematics. Physics studies physics - a description of "reality" is to me the point of studying almost any discipline, not just physics. Physics might isolate some salient features of reality to study that are fundamental in some sense, no doubt. Nevertheless, a lot of physics probably studies subtle phenomena that probably won't impact me very much in my lifetime, unless I'm vastly mistaken. Depends very much what kind of physics.

ZapperZ

Er... have you seen a smartphone lately?

You ARE aware that the largest percentage of practicing physicists are in condensed matter/material science, aren't you? This is the very same field that not only is involved in many of the modern electronics that you are using, but also has produced some of the most fundamental aspects of physics that permeated all through the rest of physics (look up spontaneous broken symmetry, and where the Higgs mechanism came from, for example).

Zz.

deRham

I already acknowledged I am aware there are very practical sides to physics, but that there are sides that aren't primarily concerned with practicality, and I'm commenting on someone's plan who claimed to be interested in physics after barely some introductory work, having done lots of mathematics clearly, and believing physics has the "aspects of math" he is interested in.

That is what concerned me.

If someone were to claim interest in physics primarily for its contributions to society, and with significant exposure to the kind of work that would entail, I'd not raise this doubt.

I do have friends who went pretty strongly into physics because their electrical engineering direction led them to it. However, their original training, motivations, and attitudes were quite different from someone with primarily mathematical training. Further, what each side can tolerate doing for long periods of time seems to differ greatly, no matter what they value as an end result.

Hopefully that makes it clear my point is not in conflict with yours; that said, thanks for the info - I wasn't aware of what the largest percentage of practicing physicists does; it's always nice to learn something new.

homeomorphic

Career choices are always hard because you never know what your chosen career actually entails until it's too late. It's hard to get an idea, even if you talk to people who already are doing it, although that is your best bet.

Personally, my motivation is always to understand things conceptually. I think that has a wide range of application and can often be turned in a practical direction. My primary interest in science is its beauty, but practical applications are still a secondary goal.

I do find that a lot of the things that appeal to me about math are there in physics. I've studied physics, computer science, electrical engineering, and math. Math happens to be the one that I went the furthest in, by far, but I never saw any of these disciplines as being all that different from each other, at least as far as the theory part goes. It's all pretty much math to me. The part of all these things that interests me is conceptualizing, and it doesn't seem like it's any different in the different fields. It's just different contents. The thought process is the same. Less conceptual thinkers might not realize the similarity as much as I do.

Group_Complex

I advise you not to leave mathematics. I had a similar crisis, mine being brought on by taking real analysis, complex analysis and Abstract algebra in my first year. However when I actually sat down to do physics I realised that Theoretical Physics seems to be more focused on calculations than understanding. I don't know how to convey what I mean by understanding, but let it suffice to say that a physicist is happy when his findings agree with experiment whereas a mathematician cares more for the reasoning and logic of the process. Physics, even Theoretical is a poor substitute for Mathematics in that respect.

What is more Mathematics is infinite there will always be problems to solve, whereas Physics may only be finite. Yet even if we did have a fundemental "Theory of Everything", we will not be able to determine why this theory is the case and not something else. Theoretical Physics is a branch of mathematics which aims to determine a set of axioms for the physical world. I think most of the understanding in theoretical physics comes from the mathematics.

deRham

While I'm in the mathematics camp myself, I think "understanding" is a term of potentially many meanings, and to some, the idea of furnishing results where calculations match with experiment could be more rewarding in terms of saying they "understand" the phenomenon than theorizing about different structures that model the phenomenon, as terrific a goal as this may be. I personally love the idea of theorizing until the mathematics elegantly reflects fundamental physical phenomena in a "natural way," perhaps more "natural" than the original form these things were discovered in, but that's probably why I studied mathematics in the first place.

Homeomorphic raises a good point, which is a better articulated version of something I wanted to get at, which is that the various "mathematical" disciplines share a lot more than one may realize at first. Of course, the issue is how they are practiced by the actual professionals can differ hugely - even the difference in lingo is a huge gap, when describing the very same things. I wanted to bring up that if physics shares some of the things one may like about mathematics, well so can things engineers, chemists, and many others work on - it depends how mathematical one wishes to get. Love for the discipline should ultimately be decided based on the particulars of the content rather than just the general flavor (as opposed to the specific flavor of a particular sub-region of the field...aka how it feels working in that area in practice...).

Mépris

Zz, I don't want to drag this thread off-topic but are you implying that the job prospects of physicists with training in theoretical/experimental condensed matter or materials' science actually have *good* job prospects? I'm guess all those high technology firms, like nVidia for example, employ some of them?

That's not just physics! The same could be said for any field that uses mathematics heavily.
Is the universe finite? If yes, and if we go by your definition of what theoretical physics is about, then you're correct.

I googled to check if my initial hunch was correct and it turns out that it is "uncertain whether the universe if finite or not."

In any case, let's say mathematics consisted of an infinite number of things and physics did not. In either (math or physics) case, one scientist will be focusing on one part of that huge set. So, what does it matter anyway?

Group_Complex

My only point was that the aim of theoretical physics is to turn physics into a mathematical discipline. I would advise against the OP turning to physics when he initially went into mathematics for the logical rigor and understanding, rather than the hand waving often done by physicists.

Jorriss

This is wrong on so many levels. Do you actually have any experience with theoretical physics? This is generally the mathematical elitism I hear from undergraduate math majors who frankly, just dont understand what physics is about (or any science for that matter).

homeomorphic

You could be right about him having trouble with the lack of rigor, but he will still have to contend with the lack of practicality issue. Therefore, he will probably not be happy in pure math. Mathematical physics or applied math would be a better fit. Also, if physicists are too focused on calculations, then they are doing physics wrong. This isn't just a pesky math student thinking he knows better than the physicists. The fact is that calculations are very limited in what they can teach you. If you want to understand something, calculations aren't going to do the trick. And if you know enough about people like Feynman, you'll find they do always want to know the why behind the calculations. Feynman thought in a more visual, conceptual way than most physicists and that is why he was one of the best.

It isn't inherent in physics. Yes, in practice, it may cause difficulties. When I took classical mechanics, I thought it was the ugliest thing I have ever seen. After several years of thinking about it on my own and finally understanding it conceptually, it is one of the most beautiful things I have seen. The truth is both communities are pretty messed up in the way they are doing things. I tried to run from physics to math to escape the conceptual shallowness, but I ended up going out of the frying pan, into the fire. There's no real refuge from it. If you want to be a real physicist or a real mathematician, you have to take matters into your own hands, either way.


I don't see why that matters. For all practical purposes, physics, as a subject, may as well be infinite.

Group_Complex

Yes, I do have some experience with theoretical physics. I intended to become a theoretical physicist until I realised that mathematics held more understanding that physics. Proof in physics is experiment, proof in mathematics is reason. Is it no surprise that someone with a more abstract/theoretical perspective would prefer mathematics?

Group_Complex

What do you mean by conceptual? The only way to understand mathematics or physics is to do problems. Do you mean how certain proofs or methods are connected?

homeomorphic

No, it's more than just doing problems. The "just do the problems" approach is one of the wellsprings of the current conceptual disasters in both fields.

By conceptual, I mean being able to see that a theorem is obvious after internalizing the intuition behind the proof. That's quite a different thing from just following the logic of the proof. I also mean knowing the motivation for all the definitions. To feel like the subject is a part of you and you could have invented it yourself.

Group_Complex

That just means you have understood the problem, have not just read the solution etc.

Some definitions make very little sense untill you start trying to prove things, then it all falls into place. However I do not think mathematics lacks this at all, maybe this is just your perspective? I think it is a bit arrogant/delusional to claim there is a conceptual disaster in mathematics or physics, it's that way for a reason, it works.

deRham

What homeomorphic might mean is the difference between being able to string through a linear algebra proof using familiar methods, and actually having a good idea of why you can and should expect that sort of result to hold, how it relates to the body of the theory, etc. It's a level that goes beyond just being able to complete the proof - it makes you a more active user of the theory, who can more likely use it in less familiar situations.

Group_Complex

I see, but how is this lacking in the mathematical establishment? This seems to be the bread and butter of mathematics.