In my field of mathematics, there is a massive effort to unify/classify/generalize some of the mathematical structures discovered over the last 30-40 years. (fo

In my field of mathematics, there is a massive effort to unify/classify/generalize some of the mathematical structures discovered over the last 30-40 years. (for example, non-commutative geometry as presented by Alain Connes: http://www.alainconnes.org/en/ http://www.alainconnes.org/en/). The goal is to understand the non-trivial connections between the areas of algebra, analysis, geometry, number theory, physics, and topology. This effort is creating an entirely new branch of mathematics - one which comprises certain parts from each of these areas. I'm biased, but operator algebras (http://en.wikipedia.org/wiki/Operator_algebra http://en.wikipedia.org/wiki/Operator_algebra) are (IMO) the backbone of this effort. These are a type of topological algebra that serve as useful generalizations for a great-many things (such as topological and measure spaces).