OKAY HI. I HEARD YOU HAD SHERIARTY TEACHER AU HEADCANONS AND STUFF.
YESSSS!!!! okay i realized that they are not simply teachers but professors at uni but it doesn’t change much
Jim teaches maths, while Sherlock teaches chemistry (especially biochemistry). From my personal experience I can say that there is always a little bit of rivalry between professors who study different scientific subjects, because they have different views on a lot of stuff. Maths is way too abstract and doesn’t have any real and concrete application, while biochemistry is very important and useful for a lot of things and has waaaay more applications. We all know how competitive and childish Jim and Sherlock are, so it’s not a surprise that they spend most of their free time arguing because “what you do is useless!!!!” “well if it wasn’t for us you couldn’t be able to do anything!!!! you should be grateful!!!”
Despite their little arguments they enjoy each other company and really admire the other because “wow what a wonderful brain”. They spend a lot of time talking shit about other professors and their own students.
At the same time they can be really proud of their students. “My students are better than yours!” is another argument that they have really often.
Sometimes they interrupt each other classes with some reandom excuse only to piss them off, what a couple of nerds.
Everyone knows about them. Some of the students ship them (and even write fanfics and draw fanart during classes) and the other professors can’t help but roll their eyes every time.
One time one of their colleagues actually told them to stop arguing like two children and just have sex. Jim grinned, while Sherlock was all ?????????????????????
After a while they end up together, but they never act like a couple in public. They don’t even hold hands. It’s not like they are ashamed, they just don’t want to give both their colleagues and their students the satisfaction.