Big equations don't come out of the ether. Either they are derived some simpler set of underlying equations based on assumptions, or they are taken from a paper

Big equations don't come out of the ether. Either they are derived some simpler set of underlying equations based on assumptions, or they are taken from a paper/book that did that derivation. Usually, whoever does the derivation, or someone who wants to understand things properly, will do computations on multiple steps of the derivation from the start to the finish. A lot of these computations can be done by hand - you don't need a computer. A lot of computations should be done by hand - even if they could be done by a computer - because you only get a feel for the equations if you play with them with your hands. To quote Dirac, 'I consider that I understand an equation when I can predict the properties of its solutions, without actually solving it.' That comes from solving a lot of them by hand. Yes, oftentimes, doing numerical or symbolic computation with a computer helps. But is the pain point of that having to type the equation into the computer. Hardly. It would be nice, but nothing ground breaking.