@MartinBrandenburg Out of curiosity, what do you mean by "it doesn't scale?" I agree that when theorems get sufficiently complicated, the difference between a semantic and non-semantic identifiers of bounded length becomes less substantial. But even granting this, it seems to me like there's a lot of "low-hanging fruit" that could be usefully given semantic names. And even when scaling laws are troublesome, I don't see what choosing an actually arbitrary identifier gives you over a weak semantic one. We typically never name functions in source code after people - why is math different?

@CyclotomicField That's the feeling I get from a lot of mathematical texts. It's like reading a piece of software where all of the important top-level calls are named "doThing()." But at least in software, there seems to be a broad agreement by working professionals that doing this is not ideal and you should strive to name things in a way that helps people understand what they're reading.

One problem is that all but the most recent texts and research papers (and this is assuming it actually catches on throughout the world) would still use the existing terms, so this change would still require knowing the original terms to read 99% (at least) of the literature. Another problem is that the vast majority of users of the terms have ingrained the traditional terminology for many years, and it's much harder to change at age 40 or 50 than at 18-25. See also my last 2 comments here for someone else wanting to change terminology.

@DaveL.Renfro Interesting links! They go a bit further than I had imagined though - I'm not super worried about reducing character counts (renaming "angle" to "nik" seems...unhelpful) per se, so much as helping people leverage intuitions they already have that are relevant to the math they're learning.

This is more or less what's done in Lean (a computer checkable theorem proving language.) Every theorem has a name. Some famous ones will be named after a person, but for the most part the names are descriptive. To pick a random example, the theorem that $x \to x^{-1}$ is differentiable for $x \neq 0$ is called differentiableAt_inv_iff.

'For example, it costs basically nothing to say "frequency decomposition" instead of "Fourier transform,"' though this might cause confusion when frequencies aren't involved. This strikes me as one of those 'if only everything were rational (the way I define rational), everything would be better (the way I define better). Take heart.

Several comments here are an answer to the question, not just a comment. Comments should only be used to clarify, not answer the question. See How do comments work for more information. Therefore, please post your answers as an answer. This brings extra visibility to the answers. (And please remember, an answer is allowed to be just one paragraph if it, well, answers the question.)

@user3716267 I have clarified this in my answer, and have deleted my (somewhat confusing) comment. I also address your analogy to computer science.

Though it ain't the same thing, why not start with an infinitely simpler problem: Get molecular biologists to use a semantic naming convention for genes they discover. In fact, it might be worthwhile, and humbling, simply to explore the extent to which this would work. In the meantime take comfort in Bourbaki.

@Aruralreader I'm not clear what you mean by "when frequencies aren't involved." Frequencies are always involved when doing Fourier analysis, for a sufficiently general notion of "frequency." There's ambiguity in "frequency decomposition" (series v. integral, etc) - but it seems to me to be a totally tolerable amount of ambiguity.

After which mathematician did they offensively name the Normal distribution?

@KurtG. "typical" and "universal" mean different things, last i checked ;)

@user3716267: I think many folks pass through this phase early in their studies. I imagine for ninety-nine percent of individuals working with mathematics, names are close to the least of their problems. Have a look at how the semantic web folks ended up dealing with naming of things.

The brain is good at remembering arbitrary names for things. Words are completely arbitrary to the things they name. We are able to remember hundreds of names of people (friends, family, etc.). By putting people's names to theorems, we allow concise and easy to remember names, while naming things with their properties would be too much ambiguous in maths, due to ever-expanding theories.

@Jean-ArmandMoroni The brain is pretty good at remembering things in isolation, but it's even better at remembering things when they're linked in a semantic schema. Look up the Baker/Baker paradox ;)

@user3716267 I perfectly agree with you. But this does not imply that things have to be named according to their properties. In no domain I know (typically music) are concepts named according to their properties. Another example: living species. They are typically named to honor someone; and when the name expresses some property, it is with latin that nobody understands anymore. A specific name is like an index in a database: it gives direct access to the thing. While a property description is like a database join: much less direct for the brain.

@Jean-ArmandMoroni There are lots of other fields that use semantically-empty signifiers in places where they (in my estimation) could do better, for sure. But I think this is a problem for those fields, as well. I'm not suggesting that mathematics attempt some sort of IUPAC-esque systematic naming of everything; but it still seems to me like mathematical convention leans really heavily into arbitrary signifiers even in places where there are similar-length semantic ones that would do better. We should, all else being equal, choose semantic signifiers when we are able.