>>12875629most things you could write down are tough for computers. almost any equation is soluble numerically which is what computers do.
what is weird about mathematica and other symbolic math programs like e.g. sympy is that they try to code up symbolic math instead of doing things numerically. so they have a library of symbolic math that encodes some human system of math sitting on top of the numerical methods that computers are insane at. but what they have coded up in terms of the human symbolic math is not great. it only reflects how good the mathematica developers are at coding up the mathematical results that human mathematicians have proved.
this is an example of why Cleo on StackExchange is a legend. she just knew way more symbolic math than anybody who was coding for Wolfram. she breasted all these hard integrals that nobody coding for Mathematica could do, because she knew shit from the mathematical literature (or original but not groundbreaking extensions of it) that the guys coding mathematica were too dumb to figure out.
anyhow it is easy to find stuff like this that is hard computationally. it basically forms the essence of what mathematical physicists do: find weird equations mathematica can’t solve using a trick and then find the trick to do it using physics
