Oh I've got many, many fancy terms in that realm. Been collecting some new ones lately too.
Here's a great joke that'll no doubt help you remember "abelian group":
What's purple and commutes?
An abelian grape!
With you on vocab, though in a lot of ways (especially math or maybe physics) knowing definitions is a big part of knowing anything; they are so precisely refined over time that they reflect the underlying well, or at least distill it. I dunno if that makes sense, but it's why I find all tech stuff infuriating to understand. Bunch of random terms, different flavors by manufacturer/developer, NOBODY understands any peace fully anymore, etc. gives me vertigo
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i barely even know what an arithmetic group is. i had a cute cryptographer girl explain it to me once in a presentation when i was working for a shitcoin building a zero knowledge smart contract engine. but i don't remember a thing about it, beyond that it's a set of numbers related to a specific set of operations, that lets you do cool stuff like ECDH