I'm starting university soon and I'm going to major in math, and minor, at least, in philosophy. I'm also going to start a new language (I'm Finnish and I'm fluent in English), and the languages I've been thinking are Latin and French. I know that if you study a lot of philosophy, it's good to know Latin so that you can read the classics in their original language, but if I'm going to mostly focus in logic (and philosophy of language, but mostly logic), how much good does learning Latin do? Of course learning a new language is never a bad thing, but does knowing Latin help at all when studying mathematics and logic? In mathematics and logic I'd imagine there isn't that much that can be lost in translation.
If you're interested in history of mathematics, then Latin would very likely be helpful; until the 18th century or so, most mathematics done in Europe was written in Latin.
For studying modern mathematics, Latin isn't so useful. I'm a mathematician and have studied a little Latin, and it hasn't really been directly useful. Sometimes it helps a little in understanding a word's roots, but not much beyond that.
On the other hand, I do fairly often need to read a paper in French; there's a signficant amount of current and recent mathematics research written in French. However, this isn't too hard even though I've never formally studied French. The vocabulary and language used in mathematical writing, while specialized, is quite limited. And I know some Spanish, which is helpful in figuring out the grammar where needed.
So for mathematics, neither one is strictly needed, but given the choice I'd choose French.
I generally agree with Nate's answer. I was also a math & philosophy major as an undergraduate; I'm glad that I took Latin, and I feel that it gives me a good starting point into any other European language (plus it fits with the fantasy game development I do).
But I've never used Latin directly in any math work. If you think about math graduate school, a preponderance of programs I've seen require something like French, German, or Russian (or more than one). So in this case you may have to prioritize the math or philosophy pursuits, or decide to look medium-term (get French/German for immediate applicability to math research), versus very long-term (Latin as a foundation, and then multiple other European languages later on).
Latin (and related languages) is unusual in being highly structured, without much in the way of irregular formations. It's why much of Europe (and the Church) used Latin to intercommunicate. This may, or may not, help with math; in the same way that programming skill may help with language, as you have to grasp negatives, and combinations, and subroutines etc