for example
Logopolis – The Calculated City
Logopolis was a civilization founded on the belief that mathematics was not merely a tool for understanding the universe, but the mechanism by which it remained intact. Its inhabitants were not rulers, priests, or warriors, but maintainers—mathematicians who devoted their lives to performing continuous calculations that stabilized reality itself. Through spoken equations and ritualized computation, they prevented entropy, spatial collapse, and cosmic decay, treating errors not as academic failures but as existential threats. Daily life revolved around precision, repetition, and restraint; emotion was considered a source of dangerous variability, and silence was valued as a working condition. Outsiders saw Logopolis as austere and joyless, but to its people, beauty lay in balance, and survival was proof enough of success. When the calculations faltered, the universe did not argue—it simply began to fail.
Is it more like the Vulcans in Star Trek with them all being 'logical'?
This seems like a kind of psionic* Tippyverse. Instead of walking out the door every morning and plowing a field, farmer Joe instead goes to his chalk board and works equations from the 'Food Acquisition' series of formulas. This puts food in everyone's larders (or cuts the middleman and makes people not need to eat). It's... certainly an interesting society to throw into a setting.
*or whatever. The math somehow making social survival happen without intermediary like physics, engineering, and eventually just plain old working to maintain life is a form of magic.
It also sounds maybe what D&D Vulcans would have their clerics do -- it always does seem weird how they have no gods and venerate logic, but have all sorts of temples and monasteries and sacred relics and practices and such.
The thing I'd like to point out is that, aside from having been pre-conditioned with things like Vulcans, there's no particular reason for such a society to be more 'austere and joyless,' or other things we tend to assign to such societies (reserved, quiet, having an over-fondness for beige robes). A math-based society could be overrun with jocularity, humor, sharp colors, atonal music, and unconventional art (so long as it is produced during designated off-hours).
This thread got me thinking about utilitarian philosophy as well. It's an interesting thought exercise though. How does society deal with it when the improbable happen? Unlikely doesn't mean impossible after all.
There aren't 'rules' on this per se, but in general moral philosophies judge the ethics of an action based on the reasonably expected outcome(s). Driving home drunk doesn't retroactively become acceptable because you made it home alright, etc. Mind you, being prepared for the eventual dice falling against you will tend to be part of the framing. Again, within 'reasonably expected' -- cracking someone's chest is reasonable if you are a trained surgeon, and you should be prepared for things you aren't trained for by having a cardiac specialist on call, but you don't need to be prepared for a meteor to fall through the top of the operating theater and kill your patient.
I don’t understand the question. What does a society based on maths mean?
It depends on the level we are looking for.
If a society is based on maths in the same way that, say, the classical/ancient Phoenicians were based on sailing or Dynastic eras China was a society based on bureaucracy (which is to say, in very broad strokes), perhaps that means it has an otherwise unexpected prominence, and everyone at least worries how well they do the thing and tries hard to get their kids to take their studies in the thing seriously (there are career opportunities in math, and those who are bad at math my get passed over for promotion in other fields, etc.).
If it is more along the lines of Plato's description of Atlantis, than maybe it is a society that thrives because of their adherence to math. This is much more at a 'living in a proper way provides good fortune' level than Shade's of Eternity's
City of Logopolis example. People still till fields to produce food and build canals to irrigate them, etc. It's just that the society as a whole prospers and sees good fortune because they keep their noses clean and their math accurate.
If it is indeed a society where doing math replaces other tasks directly (as exemplified above), it's going to come off one of two ways. The first is that it will seem like
Twilight Zone episode, where people are going about their lives doing very unnatural seeming activities and treating them as normal and you are just waiting for someone to say, 'wait a minute, something here seems off.' The other is that it will just seem like an alternate activity, and you have people going to work and working at desks instead of other vocations and it all feels kind of like IRL where most of us work at desks and maybe only through news feeds do you realize that there are still people who farm or maintain the roads and so on.