>>12703196Absolutely. Sometimes if I have no idea how to solve a problem I write a program to try to simulate what's going on. Oftentimes this illuminates some path forward to proving what I want to prove. For example, you might be to find the rate at which a solution to some PDE decays. It's easier to do this when you know what rate you're looking for right off the bat because you wrote a program that simulates solutions to the PDE and compares them to different asymptotics. If you know the rate, you have somewhere to start. If you don't, you'll need to get the rate out of your blind analysis which is way harder.
Stuff like this makes programming very useful for math.
