[danuker]

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]

do you have experience with CAS? i would love to learn how to use CAS to write proof more effectively

[rowanG077]

CAS 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]

One 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]

To 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.