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How would you translate "united by mathematics" into Latin? Is the translation "civitatum a mathematica" correct? By "united" I mean united people.

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The suggested translation is not correct. It means something like "of societies from mathematics" and its meaning is unclear.

To find a better translation, we need a verb for uniting. I would go with the simple unire, but I'm sure there are other options too. The participle "united" is unit- with lots of different endings. As we are talking about people (and there is no such indications as "to the people" or "of the people"), we need the masculine plural nominative: uniti.

To say "by mathematics", you just need to put the word mathematica in ablative, which is conveniently also mathematica, although now the last A is long. You can choose to add the preposition a if mathematics is considered an entity that exercises its will to unite the people. If it is simply a tool or a circumstance of the union, the preposition should be left out. The latter is probably what you want to say, but I (happily as a mathematician) would also accept the former.

Thus: uniti mathematica or mathematica uniti.

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