The field of math being more competitive than the field of physics?

In general the closer you get to applications the less competition there is since there are more willing to pay you for it. I'd guess that the REU's you are talking about are mostly associated with applied physics or (if theoretical) solid state physics.

Sorry for going against your wishes, but...

To add to what others have said, I think one of the reasons for your observation - if it matches reality, that is - might also be that some physics courses, even at an advanced level, are more accessible in terms of them being tough, but self-consistent. That is, you need great reasoning skills, but most or all of the material is given within the context of the course. On the other hand, depending on the lower-level courses those physics majors have taken,Note that I haven't taken any advanced physics or math courses yet, but I could see this being one of the reasons. There's a chance this stab in the dark is a miss, though

There are some fields in physics/math/computer science that require knowledge of all three. I'm working on applications of Bose-Einstein condensate theory (you could call it condensed matter theory or quantum optics theory) to quantum computing. Probably in graduate school I'd like to focus on the more theoretical aspects of it (so that would probably fall under quantum information theory), but this requires knowledge of a lot of subjects in computer science and math (though mostly the former), though the physics also pretty important (and is sometimes necessary). Things like quantum algorithms requires knowledge of algorithms in terms of CS but also how a quantum computer is supposed to work from a physics perspective, or cryptography requires some knowledge of set/number theory for quantum encryption. For this reason, I'll probably apply to both physics and computer science grad schools (though since I'm doing physics research, physics departments will probably be easier to get into for me).

I think quantum computing is one of the more obvious inter-disciplinary subjects, but it really depends on the sub-field too. Everyone knows that particle theory can require a thorough knowledge of abstract algebra, but in some cases, while doing string theory, knowing the fundamentals of physics is much more important than a highly esoteric type of mathematics.

In general the closer you get to applications the less competition there is since there are more willing to pay you for it. I'd guess that the REU's you are talking about are mostly associated with applied physics or (if theoretical) solid state physics.

I think this varies hugely - I've heard the exact opposite being common for a different reason. I believe physics at the undergrad level requires more raw intuition and problem solving than does mathematics, which can require fewer leaps of intuition, and more can be achieved by just working systematically and following basic rules, learning the important theorems, etc.

I would say the reason for the phenomenon you observe might be the following - I think the kind of reasoning required in the undergraduate math major is very different from what is expected of almost any other semi-mathematical discipline (engineering, physics, etc). There is a raw barrier, which is getting past writing proofs and learning how to think very theoretically. Physics students never learned that, at least not typically. Whereas I think what subjects like engineering and physics require at the undergrad level is less mystical, less strange to the entering college student - it's hard, it's intimidating in terms of the intellectual commitment it requires, but it's more familiar territory. You're still down to earth to an extent - it makes sense that you're writing down equations to describe something physical. Whereas in math, I think undergrads get caught up not understanding why they're even studying what they are studying.

I would say on average, for someone with basic competency in both math and physics, the undergrad physics major is more taxing. But it's simply less common to have basic competency at math, I think, because of the nature of the subject.

My experience has been the exact opposite. I've taken quite a few math classes and have never received less than an A- in any of them; however, in the one introductory physics course I took, I was lucky to scrape by with a C+. I think physics requires some knowledge about how things work in addition to purely abstract mathematical knowledge; moreover, some physics problems are Putnam-like, in that they require a clever insight, whereas a brute force approach works for many mathematical proofs. Also, quantitatively speaking, physics graduate students have a higher GRE score, on average, than math graduate students.

Maybe I should restrict the comparison to the field of pure math and experimental physics?

Only experimental physics students are physics students?

I took a topology class that used Munkres as its text. There were two (and only two) physics students in the class, and they got the two highest marks on the final exam.

When you are given a problem, your intuition tells you where to go. Without mathematical intuition, you might not find the right theorems to use or the right field to search in.

May I ask what are the most advanced math class you take? :)

one needn't convert a real-world situation into mathematical formalism to arrive at a solution, but can simply manipulate formal statements until one arrives at a solution, never having to deal with reality in the process.

I agree with you a grad PhD. student in physics probably has it easier than one in mathematics (because they have to originate their own proofs while in physics you can run experiments), but undergrad is definitely not the case.

However, the sociology of teaching comes into play. Universities in the early part of the century had a mandate to get engineers (and later, physicists) trained up for the emerging industrial economy. Courses had to be functional and you didn't want to crush too many of your students. Mathematics, on the other hand, has always struggled with its elitist past and many courses used to be just plain grueling. This wasn't because the subject was harder, just that profs taught it much faster and without as much allowance for people who didn't get it right away. I like to think that this has been changing...

Further proof is the fact that older mathematicians don't win Field's medals.

The Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, is a prize awarded to two, three, or four mathematicians not over 40 years of age...

...or the fact that Einstein was basically thought to be mentally challenged when he was young.