For alot of people, they either excel in one and suck at the other. I'm more of an algebra person even though I'm cutting my throat as I say that as its good to get exposed to other branches of math regarding geometry. So which do you consider yourself better in?
This is one of the things I am hoping to eventually study - if people truly tend toward one or the other. I always had to work my tail off in algebra, but geometry was a piece of cake. I think I skipped about a third of my geometry classes and barely cracked a book. It just all seemed very "obvious" if you knew the formulas and followed the logic.
I like algebra more than geometry, but I voted for geometry because I never had trouble understanding anything taught in my geometry class. I still don't conceptually understand inequalities and abolute value as much as I think I should.
I like geometry. It seems easy to me, as I am able to visualize things and just sit back and play with the concepts pleasurably for a long time. Algebra to me is work, but very elegant and powerful. I always felt weak and inadequate at algebra, but I worked at it enough to take first prize in a statewide algebra contest as a senior in high school.
In order to maximize my abilities and also my challenges, I chose to specialize in algebraic geometry, where I would be able to use my instinctive geometry gifts, and yet have to exercise my algebra muscles as well.
To an non algebraist I might seem like a fairly knowledgable algebraist, (I had one of the best possible algebra teachers, Maurice Auslander, and for some reason, maybe the name of my specialty I am often asked to write the algebra PhD prelim exam), but to me geometry is second nature, and algebra is somewthing to be learned. I am still trying to get the concepts of sheaf cohomology down into my pores where the geometry seems to have been stamped at my birth.
After decades of struggle I am beginnig to see that an equation has much more information than a mere geometric picture. This is the essence of scheme theory.
To me algebraic and moreso differential topology are relatively easy, being aspects of the most fundamental side of geometry. I love especially differential geometry, but feel challenged more by algebraic geometry, which uses the tools of essentially all other subjects, topology, differential calculus, complex analysis, and algebra, especially homological algebra, to study the most basic objects, the geometry of solutions of equations.
At times, even coding theory plays a role in algebraic geometry, but statistics not so much.
Algebra didn't get to be really interesting to me until I started reading on my own about Universal Algebra, and began to see the nesting structure (better terminology?) of specific algebras such as groups, monoids, groupoids, rings, loops and so forth.
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