ChatGPT will gobble up every symbolic manipulation task I give to it. At worst, sometimes I have to check its output and point out anything weird, then it’ll correct it.
I’m writing pages over pages of scary differential equations and the damn thing is saving me lots of time on it. And everything checks out! I wonder about GPT 4, since it is supposed to give correct answers without help as often as the average calculus student…
Well, it seems to struggle with really complicated equations without a bit of help, but it appears to have no trouble with complicated boundary conditions for simple equations. E.g., it solves most variants of the convection-diffusion equation on its own, given different boundary conditions, multiple regions, etc. While I haven’t managed to get it to actually write down the boundary conditions from an abstract description, that doesn’t really take much time to do oneself.
Also, I got it to successfully solve some statistics on differential equations using plain prompts, like “if the derivative of the average of this distribution with respect to time is equal to …”. Seems to work fine as long as it understands all concepts presented.