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gspryesterday at 1:16 PM2 repliesview on HN

As a mathematician by training who does a lot of programming for a living: This is the biggest misconception about math I see coming from programmers. There's frequently a complaint about notation (be it that it is too compact, too obscure, too gatekept, whatever) and the difficulty in picking out what a given "line" (meaning equation or diagram or theorem, or whatever) means without context.

Here's the thing though: Mathematics isn't code! The symbols we use to form, say, equations, are not the "code" of a paper or a proof. Unless you yourself are an expert at the domain covered by the paper, you're unlikely to be able to piece together what the paper wants to convey from the equations alone. That's because mathematics is written down by humans for humans, and is almost always conveyed as prose, and the equations (or diagrams or whatever) are merely part of that text. It is way easier to read source code for a computer program because, by definition, that is all the computer has to work with. The recipient of a mathematical text is a human with mathematical training and experience.

Don't interpret this as gatekeeping. Just as a hint that math isn't code, and is not intended to be code (barring math written as actual code for proof assistants, of course, but that's a tiny minority).


Replies

keyletoday at 12:30 AM

Fantastic read, thank you. I was never explained it this way, nor imagined it this way.

I'll try keep an open mind and read more the surrounding content.

That said, there is a syntactic language, which many equations use, and they seem to vary or be presented differently. The big S is one, the meaning of `|` which is probably not "OR" etc. I wish there would be a cheat sheet of sorts, but I feel it would be death by a thousand paper cuts with 300 standards of doing things(?)

jayd16yesterday at 4:25 PM

Maybe you're right and maybe that's the culture in mathematics but we don't have to like it.