Every programmer should know? None.
Middle school maths is "good enough" for the majority of programming jobs (85%+). There are of course niche programming jobs in: finance, statistics, AI, CS, gamedev, and so on but if you look at the programming industry as a whole those jobs are a tiny proportion overall (the majority are "boring" enterprise-style developers and web-developers: Java/Tomcat, ASP.net/MVC, PHP, RoR, and so on).
The thing is that the "boring"/average programming jobs are the silent majority. You'll likely read in this thread tons of obscure topics and how they apply to obscure jobs, but the reality is that few programmers work in those industries, but nobody [else] is going to post just to admit that for their job they don't need any maths day to day because it is boring and redundant.
This is JUST my opinion, but if you want to learn obscure topics, you're better off spending time learning CS topics (e.g. floating point number representation/bugs/limitations, encryption/hashing/etc, binary representations, assembly, kernel inner workings, CPU inner workings, and even borderline electronics). While advanced maths has a place in some jobs, advanced CS topics seem to be useful even on the web-stack/enterprise-stack to understand where bottlenecks might be materialising.
Maths is not useless. But most programmers won't use a lot of it day to day, if for no other reason that they have a library which does it for them (and they'd be foolish to reinvent the wheel).
Middle school maths is "good enough" for the majority of programming jobs (85%+). There are of course niche programming jobs in: finance, statistics, AI, CS, gamedev, and so on but if you look at the programming industry as a whole those jobs are a tiny proportion overall (the majority are "boring" enterprise-style developers and web-developers: Java/Tomcat, ASP.net/MVC, PHP, RoR, and so on).
The thing is that the "boring"/average programming jobs are the silent majority. You'll likely read in this thread tons of obscure topics and how they apply to obscure jobs, but the reality is that few programmers work in those industries, but nobody [else] is going to post just to admit that for their job they don't need any maths day to day because it is boring and redundant.
This is JUST my opinion, but if you want to learn obscure topics, you're better off spending time learning CS topics (e.g. floating point number representation/bugs/limitations, encryption/hashing/etc, binary representations, assembly, kernel inner workings, CPU inner workings, and even borderline electronics). While advanced maths has a place in some jobs, advanced CS topics seem to be useful even on the web-stack/enterprise-stack to understand where bottlenecks might be materialising.
Maths is not useless. But most programmers won't use a lot of it day to day, if for no other reason that they have a library which does it for them (and they'd be foolish to reinvent the wheel).