I blogged earlier about the "new age of empirical math", and how simulation complements deductive analysis as a math tool. For a recent client I've been doing queueing theory simulations with a Python library called SimPy. There a great tutorial on SimPy at http://simpy.sourceforge.net/SimPyDocs/Manual.html, but basically it's a discrete event simulation (DES) package. In the past I've only used DES to back up analytical results. For example, if you set the distribution of times between events to be exponential, then you get a Poisson process, which you can prove a lot of theorems about. But you can easily have the times between events be non-exponential. In that case you've got a snowball's chance in hell of proving anything, but it's perfectly easy to simulate it.
This blog features a series of mini-essays about the history and nature of math, and how it fits into the spectrum of human activity. I'm considering putting them together into a book, so comments are encouraged!