It seems to be part of our habit in mathematics to first make many discoveries using brute-force and large enumerations, and then later extend the results with more sophisticated methods if we can find them. For one practical example, if you were doing a lot of computation in the 1960's you might carry around a book of trig functions, or a slide rule, but after microprocessors came about a pocket calculator could do all those functions with better precision. With proofs, many questions are proven up to some number n, which is only further extended by feeding the algorithm into a powerful computer. But occasionally we discover a way of reframing the problem so that it can be solved with relatively little computation.
I believe programming has some analogous quality to it: It's much easier to solve just one problem and gradually find ways to generalize it.
I believe programming has some analogous quality to it: It's much easier to solve just one problem and gradually find ways to generalize it.