Guide to learning mathematical physics

[TheKracken]

Reading that reddit thread makes me want to go that route even more :D

 

[Arsenic&Lace]

Read it again then. It seems to be an extreme example of how hyper-competition in science can squelch the process of actual scientific exploration.

 

[TheKracken]

Sure, but there are other rewards that are not financial her refers to. The way I see it, he got to study a fascinating field of physics and is doing just fine now. I guess it depends how much money matters to you. If you have a Phd in physics the general consensus is that you will do fine financially, but may not be doing physics after your phd.

 

[ahsanxr]

Yeah it's certainly an interesting thread with lots of good insight from an experienced guy. I would be reconsidering theoretical physics as well had I resonated with what he was saying. But in fact, I've greatly enjoyed the journey so far and while I do find parts of physics to be quite boring, I really enjoy most subjects in theoretical physics, along with the relevant mathematics! The comments about the competition post-PhD are quite scary though, but who knows what the situation down the road will be like. Maybe there will be another surge in hiring string theorists... :P

 

[homeomorphic]

If you have a Phd in physics the general consensus is that you will do fine financially, but may not be doing physics after your phd.

That may be true, but I think it's only true if you are prepared. If you are unprepared, like me, you will probably end up underemployed and have quite a hard time after you graduate. I have another number theory PhD friend who graduated just before me who is in the same situation. And there are plenty of anecdotes of people having trouble, so there's no guarantee that it won't be a very painful transition to make. I don't care about money at all, except as a safety net and a way to being able to do things like quit my job and be self-employed, but I'm not really able to even make a living right now, which is not very cool.

 

[TheKracken]

Besides your horrible research experience (which is not the same for everyone) did you enjoy grad school and everything you learned? I guess that is my point is that you did get something out of it. That being an education that you actually value. Maybe it will be rough to get a job after, but that is something hopefully a young student like my self knows, though may not fully understand the consequences. My main goal of grad school ( I am a lower division physics and math major struggling with calc 2, I don't know what I am talking about) is to get a education and to have that rewarding experience. I hope to one day be in the top (1% ?) of society with a Phd.

 

[ahsanxr]

That may be true, but I think it's only true if you are prepared. If you are unprepared, like me, you will probably end up underemployed and have quite a hard time after you graduate. I have another number theory PhD friend who graduated just before me who is in the same situation. And there are plenty of anecdotes of people having trouble, so there's no guarantee that it won't be a very painful transition to make. I don't care about money at all, except as a safety net and a way to being able to do things like quit my job and be self-employed, but I'm not really able to even make a living right now, which is not very cool.

How could one go about "preparing" themselves? What is it that all the physicists/mathematicians who transition into finance/wall street usually do to prepare themselves for such a job?

 

[homeomorphic]

Besides your horrible research experience (which is not the same for everyone) did you enjoy grad school and everything you learned?

Of course, I didn't enjoy all of it, but it was okay, other than the thesis. It may not be the same for everyone, but it is similar for all too many people. Maybe I hated my thesis with a particular ferocity during the last couple of years, but among all the grad students I know, it's very, very common to have similar feelings.

I guess that is my point is that you did get something out of it. That being an education that you actually value.

Yeah, I got SOMETHING out of it. I'm not sure I value it that much, though. I would say it's pretty clearly a net loss, if you consider the opportunity cost. I have plans to get some mileage of my general math background, but I'm not sure what I'll do with topology, which I spent so much time on. But even with the general math background, beyond the undergraduate level, I'm not sure it's that useful unless you have a plan of how you can use it. There are very few jobs out there that make use of graduate level math. Even with stuff like calculus, it's kind of shocking how little it's actually used out there in the real world.

You should look at some of the job postings out there. It's really pretty terrifying. I think maybe the requirements are a little exaggerated, but still. I heard a lot of crap that lead me to not worry too much about getting a job, like "you can always go to Wall St.", and that's probably what lead me to the place where I am now, not being about to get a job. When you look at what employers are actually asking for, you realize it's not that easy. You have to find a way to make them money, as soon as possible, in this economy, and that doesn't make for very easy career transitions, if you study something that's a little further from the practical side.

 

[homeomorphic]

How could one go about "preparing" themselves? What is it that all the physicists/mathematicians who transition into finance/wall street usually do to prepare themselves for such a job?

I think there's another option which is just to get really lucky. For example, in my own graduate program, I got screwed over as far as having good contacts in the math program (it really helps to know where the other guys who got your same PhD got jobs), but there's someone in another program I know who knows tons of math PhDs and former grad students who didn't finish who work in all kinds of interesting places outside academia. So, it was kind of the luck of the draw, there--and at least I was lucky enough to know someone in that other program, which lead to at least a few interviews, and some other leads that I'm still pursuing. If you don't want to depend on luck, you can see that this problem can be solved with a little networking. If you happen to have some conference buddies or something in a different program and that program happens to have a lot of people who get jobs in industry, then you're cooking with gas. For finance, it also helps to work on programming skills.

 

[Sunil Choudhary]

I think we should have a goal in Physics. We should aware of what we want to achieve. And then work hard to get the goal. I am sure that if you work hard then you will never struggle for jobs and money.

 

[homeomorphic]

I think we should have a goal in Physics. We should aware of what we want to achieve. And then work hard to get the goal. I am sure that if you work hard then you will never struggle for jobs and money.

That's a lot like what I've been trying to say, but unfortunately, the goal could possibly have to have more to do with jobs and money than with physics, if we're being realistic, although if you do more marketable physics (probably not string theory--more like computational physics or semiconductor stuff), it could have something to do with physics, too. In acting, not everyone can be a movie star, so you shouldn't be lured in by what the movie stars are doing because you may not get to do what they do.

I should add that I probably would have a job now if I had bothered to be very prepared for programming interviews, but that takes a fair amount of work. If you are just smart and know basic programming, you aren't going to be able to do it well enough on the spot, so that's not enough. General interviewing skills can also be a factor, so it's good to get going on that early. I didn't get a good start on it because I didn't want to have the shame of staying another year and being an 8th year student, but you are really supposed to get your thesis more or less done before then, so you have that last year to look for a job and you have student status, so you could go for an internship in the summer.

 

[Arsenic&Lace]

Even string theory is more marketable than pure math though, at least according to the reddit thread. The culture of physics, even at its most esoteric (and arguably dubious), is still concentrated on modelling mathematically the real world.
Several theoretical biophysicists in groups around mine have gotten good jobs immediately post PhD which have nothing to do with biophysics, because physicists are good mathematical modellers. How much time to pure mathematicians actually spend applying the mathematics to modelling problems?

 

[homeomorphic]

I'll grant you that, but the thread does pretty much imply string theory isn't that marketable, unless you have additional skills, and it's a little bit more complicated than just modeling vs not modeling. I've heard plenty of anecdotal stories about physics PhDs having trouble getting a job, too. I think the biggest factor in getting a mathematical modeling type job is not so much whether you are dealing with the real world in your studies, but whether you are capable of doing numerical type programming. Beyond that, specific subject matter can make a difference.

Some pure math people do a lot of programming and computational stuff. Most don't.

How much time to pure mathematicians actually spend applying the mathematics to modelling problems?

Chances are, they did a bit at some point. For example, I took a course in mathematical modeling in my undergrad. But one course doesn't help all that much (also, I was an EE guy for a while, but I don't get much credit for it because all I have is a minor). But the modeling that physicists do might not always be the kind of modeling they need to do in industry, especially if they've been doing string theory. Some people say the mathematicians outperform the physicists as quants, and that makes sense to some degree because I don't see that physicists have a huge advantage there, unless you get into the specifics of whether they've been programming and so on. A "pure" mathematician who studies probability might be in better shape than, say, the average particle physicist, as far as Wall St. is concerned (by the way, probability seems to be a more attractive option as a subject for a math person who is interested in physics to study). Also, math is a little better for academic jobs, so there's a trade off there, which works against me a bit.

Another thing is I'm not sure of the size of the mathematical modeling market, but I know it's dwarfed by other programming jobs.

 

[porcupine137]

I think it's a tricky sort of question that has no clear answer.

I guess purely mathematical physicist might be:
1. someone who takes the theories and discoveries of physicists and tries to put it all in truly strictly formal, rigorous mathematical terms
2. someone who tries to look at what physics guys came up with and use that to expand into new fields and methods in math in general and expand them out way away from any potential known ties to the physical world
3. someone who tries to stick to the raw math a bit more than the avg physics guy?

It does seem that over the course of history that almost all of the great insights into the physical laws seem to have come from physics guys and not pure math guys or the strictest sense of mathematical physics guys, they seem to get to bogged down in the purity of the math or don't have enough of the magical ability to connect the real world and experiment and come up with reality based concepts. Maybe Witten and Penrose don't quite fit that, but it seems that mostly seems to hold. Most of the guys like Dirac, Einstein, Feynman, Weinberg and so on and so forth were probably not quite what you think of as mathematical physicists.

Even in physics I've met some post docs who can calculate up a storm like nothing at all, like crazy good holy cow, but who then seemed to have a terrible time at visualizing or thinking certain concepts out.

 

[homeomorphic]

Even in physics I've met some post docs who can calculate up a storm like nothing at all, like crazy good holy cow, but who then seemed to have a terrible time at visualizing or thinking certain concepts out.

Actually, quite a few pure mathematicians are known for not liking calculations. Ironically, I actually chose to do a math PhD because there wasn't enough physical intuition in the physics classes that I took. I thought it would be easier to learn a related subject where there was more intuition, while working on my own physical understanding, rather than being bombarded by tons of calculations by the physics professors. Actually, the physics graduate classes I took weren't so bad, so I probably would have been happier in physics, after all. I'm sure I would have suffered a bit, but in math, I had the fundamental problem that I wasn't really interested in it for its own sake, but more as a tool to understand physics, and that was not really what the PhD program had in store for me, so I was not very happy with it.

Knowing the math concepts is often what gives you the intuition behind the gruesome calculations. In fact, if you look at the Nobel prize winners, it's quite common for them to have been double majors in math and physics. I think the reason why you see physicists making more contributions to physics is just the obvious reason, rather than some magical ability. That is the simple fact that they know more about physics because they spend more time on that subject. Especially more recently when the subjects of physics and math have expanded to a such a ridiculous extent that it's harder and harder to know both subjects. That has been one of my main points in this thread. Go back to the time of Fourier and Lagrange and you can't even tell whether they were mathematicians or physicists. There may be a lot of very formal mathematicians who can't conceptualize, though, just as there are physicists who can't.

It may not even be a mathematical physicist's goal to contribute to physics, per se.

 

[Arsenic&Lace]

Very good points by Homeomorphic and Porcupine, since the question of studying mathematical physics is a question of what it is you want to do. Do you want to contribute to our knowledge of physics? Becoming a mathematical physicist is nowhere near the most efficient route, although it can be pointed out that theoretical physicists in fundamental physics are producing hardly any new physics either because the field has experimentally stagnated.

 

[homeomorphic]

"I learned to distrust all physical concepts as the basis for a theory. Instead, one should put one's trust in a mathematical scheme, even if the scheme does not appear at first sight to be connected with physics. One should concentrate on getting an interesting mathematics."

--P.M. Dirac

You can debate how much this is true, even in the case of Dirac himself (his electron sea seems to be one counter-example), but it is interesting that he would say that. You also have to note that this is more peculiar to modern physics, the reason being that physicists studied things that didn't lend themselves to normal physical intuition as well. So, maybe mathematical intuition is more powerful than physical intuition in these contexts (and admittedly, you may have to do some fiddling with equations without too much intuition at times). Also, after the theory has been created, you may try to gain more physical intuition about it, so that you can learn, remember, and apply it more easily. Plus, I'm not sure that you should completely abandon the physical intuition when creating a new theory, but I take his point that you should be willing to look beyond it. I think it's more of a matter of being willing to abandon ANY old ideas, including physical ones.

 

[Arsenic&Lace]

So I am taking a course in statistical mechanics taught by a condensed matter theorist. He often stresses the utility of physical intuition and reasoning for solving problems, and can often make excellent approximations or quickly work through derivations using mostly physics and a dash of mathematics; and this is mainly quantum statistical mechanics, mind you. He is very experimentally minded, even though he is a theorist, and draws parallels between what goes on in the class and what experimenters can and cannot do.

Now, if you are in a field where the experiments are a dead end or a non-starter, very mathematical arguments tend to creep in and rise to prominence, but it is crucial to recognize how useless these have been for the actual purpose of physics, which is to calculate things about how the world works. At best, a dash of differential geometry and a taste of abstract algebra have produced some results decades ago, but it's mostly just good ole' 19th century calculus and, relative to pure math, hand wavy heuristics. Sophisticated mathematical reasoning has produced apparent dead ends like supersymmetry, or experimentally unverifiable philosophy such as the singularity theorems, and that's about it.

 

[homeomorphic]

Now, if you are in a field where the experiments are a dead end or a non-starter, very mathematical arguments tend to creep in and rise to prominence, but it is crucial to recognize how useless these have been for the actual purpose of physics, which is to calculate things about how the world works. At best, a dash of differential geometry and a taste of abstract algebra have produced some results decades ago, but it's mostly just good ole' 19th century calculus and, relative to pure math, hand wavy heuristics. Sophisticated mathematical reasoning has produced apparent dead ends like supersymmetry, or experimentally unverifiable philosophy such as the singularity theorems, and that's about it.

I would tend to agree, for the most part. Physics, as a whole, is a pretty big territory, and there may be corners of it that are affected more by results in math. My own goal is usually just to understand things deeply and make things obvious to myself, and I think a lot of math helps with that. The stuff that most mathematicians do in their research is pretty much irrelevant to my goals at this point, but a lot of graduate level math does come into play in my conceptualizations, and maybe more sophisticated math would come into play if my physics level were higher than what it is. It's just a hobby for me, now, though. I also suspect math could be much more useful if people bothered to explain it in a more reasonable way, rather than being so formal all the time.

 

[Quantumjump]

I heard that mathematical string theorists need to know a lot of k-theory and noncommutative geometry.

not completely right. I know active string theorists in some major universities that never scratch anything related to noncommutative geometry. In fact, noncommutative geometry is in its essence an alternative to string theory. String theorist (well, SOME of them) got interested to NCG because of its ability to rebuild some known experimental fact where string theory had not so good results.

In fact, string theory in itself is a so huge field that many of them can't even compute a feynman diagram (no joke). They are just interested in building models that are consistent with representations that generates the number and type of particles that we know, but anything experimental such as feynman diagram or calculating of scattering processes does not interest them. Of course, not all string theorist are like this.