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I suspect computers can also help us get deeper. Stuff like computer algebra systems. Maybe some CAS-assisted work gets us into feedback loops allowing us to g
by danuker 4y ago
I suspect computers can also help us get deeper. Stuff like computer algebra systems.
Maybe some CAS-assisted work gets us into feedback loops allowing us to go indefinitely, as in a technological singularity.
But the "shallow" part is also quite wide.
You can teach people what you've learned forever, for instance.
- skyde 4y agodo you have experience with CAS? i would love to learn how to use CAS to write proof more effectively
- rowanG077 4y agoCAS can help with the more mechanical parts of a proof. I use it often to quickly check if something can be rewritten to something else I want. The sad part is that even if the CAS doesn't find a solution it doesn't mean there is no solution. It just didn't find it. But it can save a lot of work if the first thing you do is just quickly check, if you're lucky you just saved yourself a lot of work. I don't know what field you are in so it may or may not be helpful to you.
- dagw 4y agoOne very common and simple use case is looking for counter examples. If your theory states for example that "all Matrices with property X also have property Y" then it is quick and easy to generate a whole bunch of matrices with property X and check that they all have property Y. Of course that doesn't actually prove anything, but it can be used to disprove a statement and save you a bunch of time chasing down a dead end.
- danuker 4y agoTo be honest, my experience is limited to double-checking my algebra with the free Wolfram Alpha. I need it maybe a few times a year.