Last month, I attended the Cuartas Jornadas de Teoria de Numeros in Bilbao, Spain. This biennial conference is targeted at (but not exclusively for) Latin American and Spanish number theorists. This year, they featured an impressive international roster of plenary speakers, as well as a number of short talks by number theorists specializing in various disciplines (including yours truly). In this post, I would like to share what stood out for me the most at this conference: language. In particular, I want to share some of my thoughts on the difficulties of translating mathematical terms and the surprisingly-not-so-international nature of mathematics.

People say that mathematics is a universal language. Anyone can understand mathematics, no matter what language it’s in (OK, not *anyone*, but you know what I mean). I am inclined to disagree, since most mathematical objects have names that are very much connected to the language you are speaking. A vector bundle is essentially, as its name says, a bunch of vector spaces bundled up together. So if you don’t know how to say the word “bundle” in French, good luck getting across what you’re talking about. I do understand that given the formal definition, one would probably be able to tell if someone is talking about a vector bundle, even if you don’t understand some of the words. In reality, it seems like these days English is the default math language that we all use. Most books, journals, and conference presentations are in English. Of course, in the past it has been different, for example in the distant past it was Latin. But during this conference, there were many instances (even when the talks were fully in Spanish with Spanish slides) where someone would just use the mathematical terms in English, because they didn’t know how one would say it in Spanish.

Only one person, Edward Frenkel, from UC Berkeley, gave the whole talk in English. But like I said, this was not an issue since everyone there understood and spoke English. One of the organizers told me that since its beginnings, they have tried to invite at least one plenary speaker who is not from the Spanish speaking community. Frenkel turned out to be a perfect choice since he was already going to be in town for a conference on Mathematics and Art. For those of you who are wondering about this, Frenkel is a multi-talented fellow who not only publishes with Fields medalists but also dabbles in filmmaking. As a side note, during his talk, Frenkel mentioned a Turkish expression, “ya tutarsa”, which translates roughly to “keep the dream alive”. This expression was used initially by Langlands in his paper Beyond Endoscopy, and apparently according to him it was better left un-translated.

Initially (as you may have seen in my previous post), I was thinking of translating a 50-minute, English language talk into a 25-minute, Spanish language talk. In the end, I found myself scrambling for time even for the shortening of the talk (it is hard to do!), and I hadn’t even translated any slides yet. So, with the permission of the organizers, I decided I would leave the slides in English (although I translated the title slide and the “Thank You” slide) and give the talk in Spanish. This also turned out to be tricky, since I had to practice looking at slides written in English but saying the equivalent things in Spanish. There were some mathematical objects for which I had never learned the words in Spanish (for example, “vector bundle”, which turned out to be “haz vectorial” or “fibrado vectorial” depending on who you asked). So after I had researched every term I didn’t know and practiced many times in my room, the talk went pretty smoothly. I even made some people chuckle at my over-use of “chevere” (which means “cool” and is mainly used by Venezuelans).

This “multi-lingual slides” thing became a running joke at some point. I guess it started with Matilde Lalin, who warned that her first slide (the title one) was the last one in Spanish. I repeated this apology/warning in my talk. There were a few more people who did the same. And on the last day, two people wrote their title slides in Euskera, and they literally translated the math objects word by word (“towers of fields” became “columns of fields”, for example). But the funniest instance was when one of the plenary speakers, Carlos Vinuesa (also multi-talented), started his talk with a slide written completely in Hungarian. He followed that by saying “well, the math’s still clear, right?” (To which most of us replied, in our heads, “Um, no it isn’t!”). There were many looks of shock exchanged and I think I heard someone gasp. I guess the prospect of a 50-minute talk with slides written entirely in Hungarian was a little worrisome. He then explained all the different definitions on his slide and said “now it’s much clearer, right?”. And suddenly, the same slide appeared, but this time written in Spanish, and the whole room exhaled a sigh of relief.

I wanted to end this post with one last thought. It is easy to think that language matters a lot when one is talking about poetry, for example, and maybe this is not so obvious when talking about mathematics. But even though there are a lot of symbols and mathematical expressions that are easily understandable no matter what language you use, I think we should keep in mind that the mathematical language is in fact very complex, and inextricably linked to our own language. It was a great experience for me, after so many years of living in the U.S. and doing mathematics mostly in English, to have the opportunity to both give a talk and also attend talks in Spanish. It gave me a chance to be able to experience both how rich and at the same time how limited the languages we speak are, even when it comes to expressing mathematics.

I went to a Functional Analysis conference last month and they have two types of bases that receive different names, but if translated to portuguese or spanish these names would be the same: “almost greedy” and “quasi greedy”. If I want to talk about them, I would have to use their english names.

It should be noted that English does have a special place in mathematics in the Western world since a big percentage of papers are published in that language (and that is certainly true in Spanish-speaking countries). We’re used to reading papers in English and discussing them in whatever language we speak. Is it different with talks?Open question…

Why wouldn’t a conference geared to an international audience specify a common base language which all its presentations should be in, or translated into. From there if people needed further translation into a native language they can take either the natural language presentation, or the base language presentation and have that done for themselves.

I agree that English should be noted to have a special place in Mathematics, since almost all people are talking and understand this language.