I just wish to point out a recurring observation... comparing the questions in physics SE and math SE (which you can also do by opening the math SE page), the math SE questions often seem more down to earth, as in they are usually very specific about what they want: suppose we know A and we know B, prove that we can also know C as a result, kind of questions... Why do physicists' math questions often seem more esoteric (abstract/symbolic) than even the mathematicians' math questions? I am interested to find out as to why there is this difference...
Your impression when comparing physics.SE and math.SE is likely a combination of several factors:
physics.SE's policy on homework-like questions is much stricter than any comparable policy on math.SE, i.e. you see a lot of "concrete" questions about solving math exercises on math.SE whose equivalent on physics.SE would be off-topic.
There are two SE sites for mathematics: math.SE and MathOverflow. The latter is where questions by professional mathematicans and advanced math students tend to go, so to get a proper comparison, you would have to compare the union of the questions on math.SE and MO to the questions of physics.SE. In other words, math.SE alone is not the correct sample for "mathematicians' math questions".
physics.SE gets "math questions" of a kind very rare on a pure math site: Questions by mathematicians trying to understand physics, and by physicists trying to understand a more mathematical formulation of their field. These questions tend to be very general questions about the mathematical structure behind a (sub)field of physics and thus might seem very "abstract" to you compared to questions focused on solving a particular problem of understanding one has encountered. Again, you probably need to compare these questions more to "general" questions on MathOverflow than anything on math.SE to get a proper comparison.