TITLE: The two distinct cultures in mathematics
QUESTION [7 upvotes]: I once read an article about two distinct culture within mathematics, "analysts" and "algebraists" when I was in high school. I am not still a graduate student, but I really want to hear what it feels to be an analyst or an algebraist. How different their tools are in research? And how different their takes are on the subject? Please share your experiences :)

REPLY [6 votes]: Here's a very soft answer to a very soft question: Are you familiar with the psychological notion of Rorschach inkblot images, designed to probe the human subconscious ?

When exposed, for instance, to the exact same pictures of various polynomial shapes, the algebraist mind immediately asks itself: Hmmm... I wonder if the curve has any rational points..., whereas the incorrigible analyst instantly thinks to himself: Hmmm... I wonder whether the arc length or area don't by any chance possess a closed form expression... Time to pull those integrals out of the trunk... :-) For the algebraist, $x^n+y^n=z^n$ means Fermat's last theorem and Beal's conjecture; for the analyst, it's a superellipse. The same object is approached from two different perspectives. Where the algebraist sees Wiles, the analyst catches a glimpse of Lam$\acute e$.