Math and physics are different fields with different cultures. Some of those differences are obvious, others more subtle.
I recently remembered a subtle difference I noticed at the University of Waterloo. The math building there has “research rooms”, rooms intended for groups of mathematicians to collaborate. The idea is that you invite visitors to the department, reserve the room, and spend all day with them trying to iron out a proof or the like.
Theoretical physicists collaborate like this sometimes too, but in my experience physics institutes don’t typically have this kind of “research room”. Instead, they have “collaboration spaces”. Unlike a “research room”, you don’t reserve a “collaboration space”. Typically, they aren’t even rooms: they’re a set of blackboards in the coffee room, or a cluster of chairs in the corner between two hallways. They’re open spaces, designed so that passers-by can overhear the conversation and (potentially) join in.
That’s not to say physicists never shut themselves in a room for a day (or night) to work. But when they do, it’s not usually in a dedicated space. Instead, it’s in an office, or a commandeered conference room.
Waterloo’s “research rooms” and physics institutes’ “collaboration spaces” can be used for similar purposes. The difference is in what they encourage.
The point of a “collaboration space” is to start new collaborations. These spaces are open in order to take advantage of serendipity: if you’re getting coffee or walking down the hall, you might hear something interesting and spark something new, with people you hadn’t planned to collaborate with before. Institutes with “collaboration spaces” are trying to make new connections between researchers, to be the starting point for new ideas.
The point of a “research room” is to finish a collaboration. They’re for researchers who are already collaborating, who know they’re going to need a room and can reserve it in advance. They’re enclosed in order to shut out distractions, to make sure the collaborators can sit down and focus and get something done. Institutes with “research rooms” want to give their researchers space to complete projects when they might otherwise be too occupied with other things.
I’m curious if this difference is more widespread. Do math departments generally tend to have “research rooms” or “collaboration spaces”? Are there physics departments with “research rooms”? I suspect there is a real cultural difference here, in what each field thinks it needs to encourage.
4 gravitons 
If I understand well the way in which my university works (I’m an undergrad; my university is university of buenos aires), roles are switched un our physics and mathematics departament.
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I recently saw lots of math/science/engineering facilities at different institutions while out college tripping with my son (who didn’t go to any of the institutions we visited as it turned out). Harvey Mudd has some collaboration spaces, the University of Colorado at Boulder Engineering and Science buildings have a lot of them.
(One very weird feature of Harvey Mudd architecture is that the academic buildings are almost all connected by underground tunnels the way that buildings at the University of Minnesota-Duluth are in that case to make travel between classes easier in bitter cold and snow storms, even though Harvey Mudd in in Southern California where it never snows, temperatures are almost always mild, and it rarely even rains.)
Collaboration spaces are now the big thing in building design not only in academia across all sorts of disciplines (the recently completed law school building at the University of Denver has them everywhere you look, for example, as do most other new buildings on that campus), but also, according to my acquaintances in commercial real estate, in private sector start up companies especially in “tech” industries. The firm “Wework” which leases large amounts of unfinished unfinished office space and then sublets it finished and ready to go in smaller offices on shorter leases, has also been a big force in bringing collaboration spaces into the design of private sector office spaces especially in the start up and tech company worlds.
I honestly can’t say that I’ve ever seen a designated “research room” of the type that you describe in a math department (despite the fact that I was a math major myself). The place were you see rooms like that which are reserved in advance more often (indeed, in most colleges and universities) is in libraries (and also in most newer public libraries not affiliated with educational institutions), typically in and around writing clinics and mostly used by tutors and students to work on essays, or by study groups, cramming for tests, and to do work (especially at the initial planning stage) on group homework assignments (the University of Colorado at Boulder’s Engineering program assigns a room like that for a semester at a time for every group of seniors doing a required group project together).
When I’ve seen mathematicians collaborating, I’ve mostly seen it happen in individual professor’s offices. But, despite having seen many such institutions, my sample size is still small.
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