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Fantastic.

However, I wish that IPA pronunciations were also provided.

Ha ha, if you're a non-American take these pronunciations literally you will end up sounding like an American mathematician!

orthogonal: US: ohr 'thahg uhn uhl UK: or 'thog uhn ul

Or "beta", "theta" and "zeta", which I would rhyme with "beater" but Americans would rhyme with "data".

Except I'd rhyme "data" with "garter" rather than "dater" anyway so that's a bad example.

Wow, Barbie was right -- math is hard!

(Err, maths)

All those, and they couldn't even say which way "tuple" was supposed to be pronounced? I've been dying to know!
I've always pronounced it "toople" but I have never heard many people actually say the word. It's especially confusing as e.g. quintuple is different.
As far as I know "tuh-ple" is American programming jargon (Python jargon for sure), while everywhere else it's "too-ple", including American mathematics and European everything - programming and math. Correct me if I'm wrong.
I have no idea personally, but I say "tuh-ple" because it comes from "n-tuple" (think of how you pronounce "quintuple").
What about quadru(oo)ple?
I would pronounce it with the first syllable rhyming with "stew", not "too".

I admit the distinction would be lost on anyone with an American accent anyway since "too" and "stew" rhyme in American English.

Some of the Canadian/American computer-scientists I've spoken to say it as "tuh-ple", including Stephen Cook. I count them as mathematicians.

Honestly the only person I've known to say toople is, uh, me.

As a native french speaker, I'm not convinced at all about "zhah(n) bah teest zhoh zef foo 'Ryay" to say "Jean Baptiste Joseph Fourier" :D
But it's fun so fun to say
One that got stored in my brain faultily is χ (chi) as "key" versus "kai" - but the indicated pronunciation as ky is still ambiguous (think inky vs Kyle)! Wikipedia says kai. I still tend to pronounce it with a ch sound like Irish, German, Scottish "loch" etc. though.
When you learn that letter in Greek, it's pronounced "key." I don't know if you mathological folks decided to change that or not. ;)
I was excitedly hoping it would be a guide to how to pronounce formulae, alas not.