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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.

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    A lot of logic up to the middle of the 20th century (think Frege, Hilbert, Goedel) was in German. – David Richerby Dec 9 '15 at 19:43
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    I believe this question is more about mathematics than about academia. – Oswald Veblen Dec 9 '15 at 20:46
  • To your points about reading philosophy: I would think being brand-new to the language would more than offset any advantage gained by reading the texts in their original language. Learning a new language is a GREAT thing to do, but I would think you would have to be fairly fluent before you're gaining anything by reading in anything other than your native tongue. – loneboat Dec 9 '15 at 21:26
  • I would suggest that you take a different approach to choosing a new language project. Why don't you seek out some foreigners in your university to be friendly with around some common interest, e.g. soccer, Eurogames, cooking, tennis, whatever you enjoy? If you happen to form a friendship with someone from Brazil -- then Portuguese will be a great language to study! Whatever romance language you learn will give you a good foundation for reading other romance languages such as French. My proposal would give you better language learning results, and more fun. – aparente001 Dec 10 '15 at 4:17
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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.

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    I absolutely agree: Latin would be useful only if one plans to pursue a career in the history of mathematics, but in that case Greek would be needed too. Instead, there is a great deal of mathematics literature in French, papers and (quite good) textbooks. A short-course or a few hours of self-study can be enough to understand the technical literature. – Massimo Ortolano Dec 9 '15 at 18:49
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    I agree that French is much more useful than Latin. But I think that describing the amount of current mathematics in French as "significant" is likely to be misunderstood as meaning that it would be quite hard to research mathematics without being able to read French. This answer on Math Overflow says that only about 1.5% of papers published since 2000 and indexed on MathSciNet are in French, with more than three times as much in each of Russian and Chinese. – David Richerby Dec 9 '15 at 19:39
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    @DavidRicherby: It could be my biased experience, but I personally have encountered a few French papers over the years that I really needed to read, and being able to do so was a great help. This hasn't happened for me with Russian or Chinese. Also, "since 2000" is not really representative; in mathematics, it's very common that papers are still relevant at 50, 60, 70 years old. – Nate Eldredge Dec 9 '15 at 20:16
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    @NateEldredge All very good points. All I'm saying is that, "a signficant amount of current and recent mathematics research written in French" sounds like a lot more French than "I... have encountered a few French papers over the years that I really needed to read." – David Richerby Dec 9 '15 at 21:17
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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).

  • There are graduate maths courses in English-speaking countries that require French, German or Russian? At what level? Why? – David Richerby Dec 9 '15 at 21:18
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    @DavidRicherby: Yes, indeed. I did my math PhD at a top-30 US university in the last 10 years, and one of the requirements was to pass a "language exam" in the student's choice of French, German or Russian. The level required is not very high, though. I chose French; the professor pulled a random French textbook off her shelf, marked a few pages, and told me to go home and translate them and come back in a week. I was allowed to use dictionaries, etc. At the end of a week she read my translation and quizzed me on a few specific sentences, and that was it. – Nate Eldredge Dec 9 '15 at 21:46
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    @DavidRicherby: I had no trouble with it, even though I had never studied any French. The goal is to ensure that students have some ability to read the literature in other languages. Of course, as English takes over, this is becoming less important, so it's also partly just a historical relic. Before I entered the program, students had been required to pass exams in two of the three languages, but this had since been reduced to one. My impression is that language requirements like this are very common in US math PhD programs. – Nate Eldredge Dec 9 '15 at 21:48
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    Such language requirements in US math PhD programs are still common, but they're getting less common all the time. (I looked into this several years ago when my department dropped our own requirement.) I strongly suspect that at many departments that still claim to require proficiency in 2 non-English languages, at most one is actually tested. – Mark Meckes Dec 10 '15 at 1:41
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    The University of Chicago required French, German, or Russian when I did my Ph.D. in math there (arrived 2006); I would imagine it still does. – Tom Church Dec 10 '15 at 8:54
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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

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