- some words are loaned from another language like Eigenvector or group (sort of—I think it came from the French groupe). Also eg a blackboard-bold Z (for Zahlen) or Q (for quoziente) for integers or rationals
- other words are taken from the native language (eg rational or probability or field extension) though they may derive from Greek or Latin and have cognates in other languages.
- some symbols are quite universal and used in every language (eg the forall or exists or implies symbols)
- I don’t know whether letters that are typically used for things are the same (eg I don’t know why density is often rho. Is it referring to a word in a different language)
- the proofs are written in the native language and often that part matters a lot.
- so much stuff is named after people so words don’t need to be translated (eg noetherian domains or Cauchy–Schwarz)
- I wonder if some theorems get different names? (I assume in China they don’t call it Chinese remainder theorem)