"The Unplanned Impact of Mathematics"

"Time and again, pure mathematics displays an astonishing quality. A piece of mathematics is developed (or discovered) by a mathematician who is, often, following his or her curiosity without a plan for meeting some identified need or application. Then, later, perhaps decades or centuries later, this mathematics fits perfectly into some need or application."

…and Peter Rowlett looked for (and talked about) more examples of such here:

http://travelsinamathematicalworld.blogspot.com/2011/07/unplanned-impact-of-mathematics.html