I think math is separated into two parts—the scientific and the language—and the scientific part is where I think mathematicians show a lot of variation. The language has to be standard, otherwise it could be ambiguous or even incorrect.

For example, back when we were doing our MSc degrees, my one colleague would start his day reading Mac Lane's old and new testaments [1]. I would start my day usually obsessing about the same things—what time is and its relation to space and orientation, whether everything can be expressed in a self-dual way, learning or improving language skills, writing music and playing soccer. Whenever I read mathematics I find it somewhat stressful and I've realised that I should write more than read. The "stress" part is maybe actually just the fact that in general I often don't like skimming things—not even story books. I also have Mac Lane's books, but I try to focus on one thing at a time.

Whether you replace every group by its permutation group as a habit or not, they may be isomorphic, but they are constructed differently—as are mathematicians.

[1] This was his joking way to refer to Algebra (old testament) and Categories for the Working Mathematician (new tastament).

There is certainly only one math (if you subscribe to this idea -- it is also the truth) but many ways of doing it. Given doing math (at least at the research level) requires a staggering variety in thought and being able to make connections through training (some might call this intuition), trying to understand the sensitivity of ways of thinking about abstractions, to neurochemistry, is definitely a nontrivial question. Now whether or not one is interested in answering this question, it is definitely complex enough to investigate.