We still make everyday use of scientific and mathematical formulae that were derived centuries ago
I think there's a slight misunderstanding here. The
formulae are in use, yes. Yet the
language often is dead and buried.
When science is new and exciting, scientists will insist on coining and using big words and shiny new definitions; it's a natural thing to do, marking the property and all that. Most of that vocabulary is useless in the long run, though, and once a phenomenon is better understood, the excess terminology gets pruned.
Mathematics is abstract enough that people quite plausibly might still speak of "Laplacians" when using them a thousand years from now. Except that mathematics as a Starfleet officer tool should be even more abstract, outsourced and automated, involving no discussion of such "nuts and bolts" - even when the officer in question is an engineer. Any other field of science would be in constant iterative interaction with the world of applications, and old terminology would be quickly replaced by more accurate or useful words. Say, save for the primitive and unevolving application in telescopic terrestrial observations ("rectascension") the language of astronomy from the 18th century no longer survives - or where it does ("planetary nebula" or "nova"), it most definitely should not.
A work of fiction bridging eras can of course take liberties in facilitating the bridging. But works of fiction on Starfleet adventures tend to describe the end users, the people who deal with evolved science on the field and indeed participate in evolving it - and thus it's quite jarring to hear a supposed renaissance man from the 24th century use language that harkens back to the original rinascimento... That's something to spice (or buffer) a scientific paper with, not something to use in tackling a field problem so that the mission will succeed, the ship will be saved, and billions of lives will remain unaffected after all.
If anything, our heroes should be coining new phrases left and right to describe the wonders they see, and establishing bold new concepts that clarify, restructure and replace today's primitive notions (even if such semantic self-glorification perhaps is less common in the natural sciences than in the "unnatural" ones). When they do make use of today's immutables, they shouldn't raise them on the pedestal they hold today, given how old and ho-hum they will be at their time and age. But that's perhaps something for a different scifi realm, as Trek has always given us more entertainment value through anachronisms, through the wonderful sixties-in-space feel...
Timo Saloniemi