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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 o
by brandonb 12y ago
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 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.)
- spacehome 12y agoI 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.
- cb18 12y agoCould 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"?