The Unreasonable Effectiveness of Mathematics in the Natural Sciences by Eugene Wigner

The Unreasonable Effectiveness of Mathematics in the Natural Sciences is one of those pieces of writing whose title really sums up the whole thing – basically it does what it says on the tin.  It started life as a lecture and was subsequently published in the mathematical literature in 1960.  It is about something that a lot of people have noticed.  It is really quite surprising how often a mathematical idea developed for a particular purpose, or for no other purpose than simple pleasure in the exercise of the mind, turns out to be a useful tool later for something completely different.