Mathematicians who thought that way are what led to formalisms: They couldn’t agree on if continuity implied the existence of a derivative, necessitating the n

Mathematicians who thought that way are what led to formalisms: They couldn’t agree on if continuity implied the existence of a derivative, necessitating the need for formal models and reasoning. Most software engineers don’t care about compiled assembly (and their work can be compiled to many flavors), yet it’s accurate to describe their work as creating streams of assembly instructions which can be automatically executed by a cleverly designed piece of silicon. The goal of formalisms has always been precisely what you say: a low-level backend that supports the high-level abstractions of working mathematicians. But just as with computers, it’s worth understanding “the stack” to appreciate what mathematics is.