[ux266478]

Math is great and should be well studied by programmers, but in general I oppose this idea. Mathematicians define things the way they do because they have neither flip-flops nor do they have a defined execution method as part of their foundational system. These two things radically change the interaction we have with any given formal system put on top of it.

> Functions map members of a set A to members of a set B.

> Something that has side effects all over the place should just not be called a function

Leibniz defines functions as a quantity that depends on some geometry like a curve. Bernoulli later defined it as a quantity that results from a variable. The latin word "functio" means process, not implying a mapping but an arbitrary sequential performance. Mathematicians are prone to taking words from elsewhere, either twisting their meaning or inventing wholly new meaning out of thin air, all according to their whimsy for their own particular needs. I do not think a reasonable case can be made to assert we have to respect ZFC's narrow conception of a function when we do not live in a ZFC world.

[dawnofdusk]

>Mathematicians are prone to taking words from elsewhere, either twisting their meaning or inventing wholly new meaning out of thin air, all according to their whimsy for their own particular needs.

True but one benefit of those guys is that they actually define what they mean in a formal way. "Programmers" generally don't. There is in fact some benefit in having consistent names for things, or if not at least a culture in which concepts have unambiguous definitions which are mandated.

[ux266478]

> they actually define what they mean in a formal way.

Sometimes yes. The big stuff is usually exhaustively formally defined down to the axioms. The further you get away from the absolute largest, most well-tread ground... the wood grows dark quite fast. Math, especially on the cutting edge, is intuitive like anything else and filled with hand-waives. Even among the exhaustively defined, there are plenty which only achieved exhaustiveness thanks to later work.

> "Programmers" generally don't.

On the contrary, all programming languages are formal grammars. I think the best way that I can underline the difference is that mathematicians are primarily utilizing formal grammars for communication to share meanings, and almost exclusively deal with meanings that are very well-defined. Programmers on the other-hand are often more concerned with some other pressing matter, usually involving architecting something unfathomably massive with a minute fraction of the man-hours used to construct ZFC, often dealing with far fuzzier things and with outright contradictory axioms which they have no control over.

They are as different as trophy truck rally and formula 1. As someone who lives in both worlds, I'm endlessly disappointed by shitflinging and irrational superiority contests between the two as though they even live in the same dimension.

> There is in fact some benefit in having consistent names for things

There is, in some contexts to some ends. Those are important and influential contexts and ends, and so the relevant math should be studied and well understood on an intuitive level. But they form a minority in both fields. I've known many mathematicians outside of programming contexts, and none of them have any grasp of category theory, type theory, the lambda calculus, etc. They might have heard of category theory, but they look at it with the same suspicion as you might expect from some fringe theoretical physics framework.

There is also the problem that these "consistent names" are built on a graveyard of previous conception. Mathematics is a history of mental frameworks, as are all ancient fields. As I underlined in my previous post, the formalization of mathematics gutted the idea of the function and filled it with straw. There's nothing wrong with how functions are defined within ZFC mind you. I just vehemently disagree with projecting it as a universal context, showing it any degree of favoritism.