If you aren’t already aware, some of the highest-level discussion about math can be found over at Mathoverflow. The questions are all research-level. The quality of answers is very high and some of the best mathematicians in the game, including several Fields medallists, routinely participate in the discussion.
Here is a puzzle then: why isn’t there any physics forum operating at this level? Physics StackExchange is good, but nowhere close to Mathoverflow.
I offer a few, not-mutually-exclusive, hypotheses:
1. People don’t understand physics as well as they understand math. Especially everyday physics, such as: why are clouds white or why do all the planets orbit in the same plane. These require a combination of physical intuition and mathematical ability. In this sense, physics is harder than math: it is easier to frame interesting physics questions which have difficult answers than it is to frame interesting math questions with hard answers (Yes, number theory is an exception). Indeed, you need little physics training to ask why the sky is blue or why do sand-dunes form.
2. The language of math is easier to communicate in. You need less words and more symbols in math. But in physics, you need more words. So you need people who are especially clear in communicating physics ideas. This is a skill that is harder to acquire than communicating mathematical ideas. Therefore, if you compare a physicist and a mathematician who both understand their domain equally well, then it is more likely that the mathematician communicates better.
3. Curiosity about math is easier to develop than curiosity about physics. I know this sounds counter-intuitive. But I’m talking about deep curiosity, the kind of curiosity that makes you explore answers yourself. Deep curiosity about physics requires a kind of naive curiosity about everyday things: you need to look around, go pick up things and play with them. This is socially visible and this kind of naivety is looked down upon; it is the opposite of nil admirari. But deep curiosity about math is easier to develop. You can do it in privacy. Just pen and paper. Thus, less people have developed a good intuition about physics.
4. Curiosity about math is more easily rewarded. The answers you get are clear and satisfying. But in physics, you are never sure if the explanation that you came up with corresponds to reality or whether you’re missing some important subtlety. To check, you have to find a way to test your hypotheses with real world observations. In the case of math you can get a crisp answer: a proof or a counter-example.
5. The physics education system isn’t very good at inculcating all of these abilities because they are harder to teach. Interestingly, on internet physics forums such as the old Orkut physics forum and Physics Stack Exchange (I’m not sure about physicsforums.com) the best explainers were, in some sense, outsiders (i.e. outside academia). Ron Maimon comes to mind. I forget the name of the best explainer in Orkut physics, but I remember clearly that he was a high-school dropout.
6. Historical reasons. Mathoverflow just became more famous because of all the famous mathematicians who came there. But, many famous physicists did try to come to Physics StackExchange as well. Examples: t’Hooft, Shor, Preskill, Gottesman.
This smells of opportunity. If these abilities: naive curiosity, thinking about more unstructured real life problems using hypothesis testing, intuition, and a mix of math and numerical estimation,and the ability to communicate clearly with both words and equations, are rare, then that means that this is a potentially a rare and valuable skill worth developing.