Edward Frenkel talks about math:

From the outside, mathematics might look like one big lump. In fact, it is a huge subject that has many different subfields: algebra, number theory, analysis, geometry, and so on. In the world of mathematics, they look like disconnected continents. But the Langlands program connects different fields and, by doing so, tells us something about the unity of mathematics. It offers a glimpse of something beneath the surface that we don’t understand.

And (among much else of great interest):

Mathematical power is not the power of a bomb. You cannot see its effect as immediately as Hiroshima and Nagasaki. But a formula can be just as powerful in terms of controlling our lives. It can alter the course of history; it can affect millions of people. […] I think we mathematicians are a little bit behind the curve. We are not fully aware of the Frankenstein that we may have already created or could create.

(Wikipedia on the Langlands program.)