Item — HN Reader

And on the flip side, computers can suggest beautiful theorems to mathematicians by making it easy to run virtual experiments.

There's now a burgeoning field of pure math called "Experimental Mathematics," where they do just that. A good intro on how computer experiments can be used in algebraic geometry is here: http://math.uga.edu/~noah/files/spheres.pdf

(Disclosure: Noah was my college roommate and we published a paper with Henry Cohn on experimental mathematics for high-dimensional sphere packing, so I'm a biased participant.)

1 comments

I did my PhD in complex dynamical systems, and in that field, computer experimentation is invaluable. The favorite way to generate hypotheses is to explore with computer tools. Once you notice a pattern, then you trot out the theoretical tools to try to solve it.

Could you give some examples of the computer tools/software that are commonly used?

Could you provide or maybe point me somewhere where I could get an expansion of the ideas in your last sentence? Is it basically creating a simulation along certain non-linear parameters then running the simulation and watching what results? Like, "hmm... that looks like a phase transition, let me see if I can workout what is going on"?