Meanwhile, most of the stuff people actually love (and don't want to understand) about their software was invented by people pursuing the mathematical approach.
And those people get away with hacky code because most of the software core is rock-solid and mathematically valid, leaving an "error budget" for sloppy hacks.
But if it were just sloppy hacks all the way down, your gigabytes of source code would not work at all.
You have the luxury of not knowing what I know; that algebraic rigor, while frustrating, probably prevented bugs. And mathematics, while arcane and incomprehensible to you, prevents bugs. You don't want the truth because in places you don't talk about at standup, you want mathematicians writing on that chalkboard. You need them at that chalkboard. We use words like monad, monoid, endofunctor. We use these words as the backbone of a life spent proving something. You use them as a punchline.