# Resources for reading mathematics out loud in different languages

Are there reference books or online material for reading mathematics out loud in different languages? For example, the expression1) $$\int x^2dx=\frac13x^3$$ is understandable to anyone who has studied mathematics, independently of their language skills. But reading it out loud or writing it in words only is highly nontrivial for someone without mathematical education in the respective language. I can express the equation above in English2) or Finnish3), but not in any other language I speak. I find students occasionally having trouble verbalizing formulas even in their mother tongue in which the courses are taught.

For a complicated formula there need not exist any sensible way of reading it out loud; one has to explain it in some other way than reading through. There rarely is a single correct verbalization of a mathematical expression. Therefore I don't expect a "complete and perfect set of rules", but just some guidelines and examples in different areas of mathematics.

Main question(s): Where can I or my students learn to pronounce mathematics in different languages? What material for reading mathematics out loud do you suggest? Can I find examples of mathematics spelled out in different languages? Resources for all languages4) are welcome.

Side questions: Are there sources about reading mathematics out loud (or spelling it out) in general? Is there any research on how reading formulas aloud affects learning mathematics?

1) I don't want to discuss if this is good notation or whether I should have a constant.

2) "The integral of x squared equals one third x to the third."

3) "x:n neliön integraali on yksi kolmasosa x kolmanteen."

4) I don't speak all languages, but I think it would be useful to collect a list of mathematics pronunciation guides in one place. My personal interest is mainly in Latin, Finnish, English, Italian, French and Swedish.

• For Latin, you might try the manuscripts between the times of Newton/Leibniz and Cauchy. It might be useful to see how certain expressions changed over time. Although it won't help as much with the language aspect, Florian Cajori's work on historical notation may help you with finding sources. Gerhard "We're Talking Really Old School" Paseman, 2015.04.29 – Gerhard Paseman Apr 30 '15 at 2:14
• I doubt you're going to find much. Just think about the situation with English: books don't often explain how notation is supposed to be read. You usually need to be in a class and listen to what the teacher says. This becomes a serious problem if you want to give a lecture in a new language, and the most realistic solution I can think of is to sit down with a native speaker and have them explain to you how notation is pronounced. – KCd Apr 30 '15 at 6:28
• @KCd, I know that most books don't explain how to read notation at all. But I thought that I'm probably not the first one to think of this issue and there are so many books in English that pronunciation guides must exist somewhere. Reading out loud or spelling out is something that could be learned by just reading (if there only was some material), so I was hoping I wouldn't need to speak with a native speaker. – Joonas Ilmavirta Apr 30 '15 at 6:52
• This is only one language, but at Kahn Academy en Español you can listen to math being spoken in Spanish. Similar teaching videos in other languages are available. – Joseph O'Rourke Apr 30 '15 at 11:59
• In your example of how to pronounce the equation, you included "x" in the English version rather than writing out how it sounds. Pronouncing mathematical notation includes pronouncing the letters too. For instance, in Russian math the letters a, b, c, ...., x, y, z are pronounced for the most part as in French, not English. – KCd Apr 30 '15 at 14:17

As Joseph O'Rourke pointed out in the comments, teaching videos are a partial solution. As a practical test, I went to the Wikipedia page about complex numbers and browsed through the side panel to know the translation to some other languages. I then searched YouTube for "complex numbers" in English, Italian, French, Spanish, Finnish, Swedish and Latin, and for all but Latin I relatively quickly found a video in which equations or other expressions are read out loud. (Frankly, I would have been surprised by a Latin video about complex numbers, but I couldn't resist trying.)

Videos have some drawbacks, though. If you already know the topic and just want someone to read out loud many expressions, the videos are slow. In some languages it is difficult to catch the correct pronunciation or the corresponding way to spell out the expression. Videos don't make a good reference material; it's not easy to check how to pronounce some specific thing in, say, Italian. If I want to give my students a guide to pronouncing formulas in a particular course, videos are not very useful.

I would prefer written lists of examples, but they seem harder to come by.

For French (my answer is based on the examples of http://www.rpi.edu/dept/math/ms_graduate/resources/SayingMath.pdf, and on my experience as I’m a native speaker) :

• $2^2$ deux au carré
• $2^3$ deux au cube
• $2^4$ deux puissance quatre
• $2^n$ puissance n-ième de 2
• $\sqrt{25}$ racine de 25
• $a^2+b^2=c^2$ a deux (ou carré) plus b deux égal c deux
• $a^2, 2a$ a deux, deux a
• $1/2, 1/3, 1/4, 1/5$ un demi, un tiers, un quart, un cinquième
• $x/2$ x sur deux
• $\sin^2 x$ sin carré (de) x
• $\tan^{-1} x$ tangente moins un de x ou arctangente de x
• $\ln 2$ L N de deux
• $\exp x$ exponentielle de x

Finally, your example would be:

Une primitive de x carré est x cube sur trois

Ou plus simplement:

Intégrale de t deux dt [dété] (de 0 à 1) égale à un tiers