Yeah, I get what you mean regarding the different types of thinking, I definitely agree with that, and no two types of thinking are the same, like even after a year of doing Medicine, I've started to wonder and think about many issues which were unknown to me before (both sociological and biological issues, in fact) - even though I probably won't have that much depth of knowledge, it's surprising what insights into the world education can give. You're right though, there are just many different sets of thinking skills which are obtained from different places for different purposes.
Second thing, ah yes, I meant that I am surprised there are no Maths majors in the QUANTITATIVE reasoning one. Ahh yes, not just verbal reasoning, but things such as writing, language and communication skills as well.