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Interesting! As an American I'd never heard that name for it. Usually it's called Collatz conjecture or the hailstone numbers in my experience.

All those names and more are included on the Wikipedia page it seems: https://en.wikipedia.org/wiki/Collatz_conjecture

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The French Wikipedia page about it is actually https://fr.wikipedia.org/wiki/Conjecture_de_Syracuse !

Going through the Wikipedia articles in all the languages (I can read), the French one is the only one primarily naming it after Syracuse. Could that be the result of the contentious relationship between France and Germany, Collatz being a German mathematician?

According to the French Wikipedia article, in 1952, after a visit in Hamburg, Collatz explained the problem to Helmut Hasse, who brought the problem to the US in the university of Syracuse, hence the name "Syracuse problem".

So this name appears after the 2nd World War, at a time when the relations between France and Germany are becoming friendlier (https://en.wikipedia.org/wiki/France%E2%80%93Germany_relatio...).

I guess that French researchers heard about the problem from someone from the university of Syracuse.

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