"Common arithmetic and algebra rest on the same computational foundations and are directed to the same end.  But whereas arithmetic treats questions in a definite, particular way, algebra does so in an indefinite, universal manner, with the result that almost all pronouncements which are made in this style of computation-and its conclusions especially-may be called theorems.  However, algebra most excels, in contrast with arithmetic where questions are solved merely by progressing from given quantities to those sought, in that for the most part it regresses from the sought quantities, treated as given, to those given, as though they were the ones sought, so as ... to attain some conclusion-that is-equation-from which it is permissible to derive the quantities sought... . Yet arithmetic is so instrumental to algebra in all its operations that they seem jointly to constitute but a unique, complete computing science, and for that reason I shall explain both together."3

Isaac Newton