By Guðmundur Heimisson, AMath Online MS Student
Math is often described as the "universal language", usually by non-mathematicians (or worse, physicists). Sometimes a quasi-mystical meaning is attached to mathematical notation, or even particular symbols, to the extent that the uninitiated might be forgiven for thinking that if aliens descended from the sky we would be able to communicate with them if we just used the Greek alphabet along with a few made-up pseudo-Greek symbols.
In reality, of course, mathematicians sometimes find themselves unable to understand the terminology of even a slightly different subfield (often while nodding along to a presentation). Far from being a universal language, math is like any other field in that it requires a shared natural language for any meaningful conversation. As it turns out, sometimes even sharing a natural language is not sufficient.
I moved to the US at the age of 15, and since then all of my math education has been entirely in English. I have often found myself in the strange position of being unable to explain what I am studying to someone in my native language of Icelandic, and when asked by relatives or friends for basic math tutoring I find myself using an English to Icelandic math dictionary extensively. This is not because my Icelandic has atrophied, but rather because of Icelandic's vigorous rejection of loanwords.
Like many European languages, Icelandic has a national language committee whose job is to standardize its usage, introduce neologisms for new technologies or concepts, and publish alarmist articles bemoaning the state of language education. Unlike many other European language communities, speakers of Icelandic often actually use the neologisms propagated by the language committee, and the Icelandic school system in particular is enthusiastic about promoting their usage.
So, for example, while in many European languages the words for 'smartphone', 'computer', and 'television' are loanwords from English, the Icelandic words for these are 'snjallsími', 'tölva', and 'sjónvarp'. Usually the new Icelandic word is simply a calque, for example 'snjall' means 'smart', and 'sími' means 'phone', but occasionally more inspired choices are made, like with 'computer', where the word 'tölva' is a portmanteau of the words for 'numbers' ('tölur') and 'oracle' ('völva').
As it turns out, this tendency to reject foreign loanwords and create Icelandic neologisms in their stead is not just applied to more recent English loanwords. Many European languages (including English) have a fondness for Greek and Latin roots for academic or scientific vocabulary, so the words for things like 'biology', 'mathematics', and 'politics' are basically identical across many European languages. However, in Icelandic these would be referred to as 'líffræði', 'stærðfræði', and 'stjórnmál'. Additionally, as you might have guessed by now, every concept within a field is also neologized with Icelandic roots, usually by some professional association or university department.
Because of this national obsession with linguistic purity, there is a distinctly Icelandic word for nearly any math concept you would care to use, from 'absolute continuity' ('alsamfelldni') to 'zero set' ('núllstöðvamengi'), a dictionary of which is maintained by the Icelandic mathematics association. So, while a math lecture in English would contain a lot of words with Greek or Latin roots whose meanings would be opaque to most English speakers, the same lecture in Icelandic would consist entirely of words with Icelandic roots whose meanings would be transparent to an Icelandic speaker (or at least easier to recall once learned).
Unfortunately, this effort to keep the language free of loanwords is hampered by a lack of textbooks in Icelandic on advanced subjects. Icelandic is spoken by less than half a million people, so there are only a few thousand students in any one school year, and for specialized subjects at the university level the number of students can be counted on the fingers of one hand. Add to this the fact that many university classes are taught in English (often because of international students who very rarely speak Icelandic), and as a result there is a severe lack of advanced Icelandic textbooks in math (or most any field). In fact, even at the high school level, where classes are taught entirely in Icelandic, occasionally textbooks will be in English because no textbook exists in the native language (this is especially true for advanced high school subjects like calculus).
I got a vivid example of how this can affect students a few years ago, when I tutored an Icelandic friend of mine in introductory calculus. It turned out that the textbook was in English, while all the lectures and class notes distributed by the professor were in Icelandic. Like many students, my friend preferred to learn from the professor's lectures and notes, and so had only a hazy connection between the Icelandic terms and the English terms, while I only knew calculus in English. At the time, I was not aware of the online Icelandic math dictionary, which meant that we wound up spending most of the tutoring trying to figure out the English translation of basic terms such as 'tangent' and 'polynomial' (in Icelandic: 'snertill', and 'margliða' respectively).
I do wonder whether Icelandic students would be better served by a less aggressive regimen of replacing loanwords in academic disciplines. I don't know if referring to a 'parabola' as 'fleygbogi' helps Icelandic speakers learn geometry, but mutual intelligibility and cognates can serve a useful purpose when students need to use resources that are not in their native language, or when trying to learn another language. In any case, it's been a long time since I've lived in Iceland, and so it would be unwise for me to formulate too strong of an opinion on this topic, especially given how important conserving the language is to many Icelanders. What I will say is that if we are lucky enough to meet extraterrestrials, instead of trying to communicate with them using math, we would be better off using the real universal language, IKEA furniture assembly instruction manuals.