Overview

Two of the more abstract branches of mathematics are homological algebra and category theory. Important progress was made in both during the first half of the twentieth century. Indeed, since the fields both arose in the latter part of the nineteenth century, virtually all work in them took place in the twentieth. While their practical effects may not be as great as their mathematical importance, research is still worth pursuing because the field of mathematics provides such an accurate description of the universe in which we live. This leads to the assumption that, even if these fields are seemingly of little import, the future may hold something more.

Background

According to the website Eric Weisstein's "World of Mathematics," category theory is "the branch of mathematics which formalizes a number of algebraic...