Algebra is a symbolic pursuit, designed to enable you to define and then solve a problem. The rules of algebra define procedures for doing this. Thus, there are a great many corollaries between algebra and computer programming.

“Those seemingly-pointless geometric proofs” also have their importance, although I, too, did not realize it at the time. Once again, you are tasked with a problem to be solved, but given only limited tools and principles with which to solve it. Yet the solution, once arrived-at, must be rigorous and you must “debug” it.