Mathematics feels like a giant old undocumented codebase in that, yes you could read the comments of each function, you would rather have a nice complete, well formatted docs page that in human terms explains how things work together, why they are here and where they came from.

I think its 'undocumented' nature comes from the fact that mathematics is supposed to be logical and thus intuitive enough if you dedicate thought on a certain matter.

@another-mariana code 'is supposed to be logical and thus intuitive enough if you dedicate thought on a certain matter.'

That has never prevented anyone from writing indecipherable spaghetti code.

I see that more as a cop out on actually writing the proper thing.

As Alexander Grothendieck said: 'One should never try to prove anything that is not almost obvious', similarly I would think of the field in general, show the obvious connections instead of just saying 'as is obvious' while it is not.

@ElectroArchiver code isn't logical enough to come to the answer just by thinking about it.

@another-mariana that's the very definition of code though..

you literally get a piece of paper, and move from one state to the next, one expression at a time, until you're finished.

That still doesn't excuse, why stuff isn't documented sometimes

ask for a glass of water, get a self-filling barrell of beer:

https://youtube.com/c/3blue1brown/...

enjoy.

also, afaik, it IS documented, but recursively. or cumulatively/additively, depending on how you look at it.

next steps/techniques of math are documented by previous steps/techniques.

can't think of better example, because i myself am not too knowledgeable about anything but the mostly basic math, but even multiplication is explained/documented via repeated addition.

code is just disguised math after all

@Midnight-shcode Thanks, I know 3Blue1Brown of course, the problem is that most of math is not documented on that level or anything near it, thanks to videos like that some topics have been made more accessible but that's just the tip of the iceberg sadly

@thebiochemic what i meant was the name of the functions or reserved words in any language need to be documented, you cannot come up with them. math is not an api.

@another-mariana math is very much an api

you define things, and prove them, to verify their truth and integrity with the rest.
The documentation is done through papers

if maths wouldn't be an api, it would be impossible to verify programming languages with it.

Mathematics has an unwritten rule that all syntax is correct as long as someone uses it to prove useful statements. As a result, the notation and naming scheme usually sacrifice everything in favour of conciseness.