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 knowledgeable 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 more so 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.
