5
$\begingroup$

I don't know if this is the best stack exchange for this question, but I couldn't think of a better one. Please migrate it to an appropriate stack exchange, if this one is not appropriate. Anyway, my question is, are some human languages better for expressing mathematical concepts than other languages? I am asking because it is my belief that German is better than English for expressing mathematical concepts and doing mathematics. Even if that is not true, I am certain that not all languages are equally suited for every single purpose. Also, has anyone in the academic literature discussed this question? I would like some references.

$\endgroup$
7
  • 4
    $\begingroup$ What makes you believe that German is any better at expressing mathematics than English? Why do you believe that some languages are better than others at expressing mathematical ideas? $\endgroup$
    – Xander Henderson
    Commented Jan 9 at 1:54
  • 1
    $\begingroup$ There is research on how much better Chinese is for understanding place value. Eleven is something along the lines of ten-and-one. Thirty one would be three-tens-and-one (thought English isn't so bad for this one). $\endgroup$
    – Sue VanHattum
    Commented Jan 9 at 2:30
  • 9
    $\begingroup$ As a German native speaker who publishes all his research in English, I find the idea that one of the two languages were better suited for expressing mathematical concepts really far-fetched. $\endgroup$ Commented Jan 9 at 3:11
  • 1
    $\begingroup$ @fedja: Indeed, there's an institute in Israel that invents new word in Hebrew. $\endgroup$ Commented Jan 9 at 5:14
  • 1
    $\begingroup$ When you say "German is better than English for expressing mathematical concepts", it suggests to me that German is your own native language. $\endgroup$ Commented Jan 12 at 22:20

4 Answers 4

3
$\begingroup$

Perhaps taking things to their extreme there are languages which lack simple numbering like the language of the Brazilian Amazonian people the Pirahã which appears to have only words for one and two (or small quantity and large quantity) according to some authorities. This obviously restricts their ability to count and to compare sizes of groups.

$\endgroup$
3
$\begingroup$

This question reminds me of the so-called Hopi time controversy. In 1958, Stuart Chase asserted (see page 3) that a person whose native language is Hopi has less trouble grappling with the "fourth dimension" than does somebody whose native language is, for example, English. Although intriguing, the theory is unfounded and not widely accepted by linguists.

I think the same negative conclusions will apply to any speculation that there is a particular language which is best suited for learning mathematics.

A narrower but well supported phenomenon is Spatial-Numerical Association of Response Codes (SNARC effect) of Dehaene et al. Admittedly, this has more to do with cognitive parsing of numerical data than high-level mathematics. The idea is that when presented with small numbers, a person will parse them faster if they are presented on the left, while larger numbers should be presented on the right, as we think about a number line. However, there is research explaining that this effect is reversed for people whose native language is one where writing proceeds from right to left, i.e., "right-starters."

$\endgroup$
2
  • 1
    $\begingroup$ Indeed. The idea that language shapes thought is very much tied up in the works of Whorf and Sapir, and is largely discredited in modern linguistics and neurology. As an (irrelevant) aside, about 10% of my students are Hopi, and they seem to do no better (nor worse) than any of my other students. :D $\endgroup$
    – Xander Henderson
    Commented Jan 10 at 17:26
  • $\begingroup$ I guess I'll need to brush up on linguistics. My sense, from having lived in a 2nd language at 16, is that our language is shaped (somewhat) by what language we're thinking in. $\endgroup$
    – Sue VanHattum
    Commented Jan 10 at 20:29
1
$\begingroup$

Let me give you an example in two languages: English (Dutch), and let's talk about tables (tafels [ˈtafəls]) and tables (tabellen [taˈbɛllən]):
A table (tafel) is the piece of furniture at which you can sit and eat and pile stuff on.
In primary school, you learn about multiplication tables (tafels van vermenigvuldiging), and apparently, children have no problems accepting that the word "table (tafel)" is used for this purpose.
Later on, you learn about tables (tabellen) as grids on a piece of paper, containing information, grouped by columns and rows.
In fact, the tables of multiplication (tafels van vermenigvuldiging) are not actual tables (tafels) but more like tables (tabellen), so that's a very fine nuance, getting "lost in translation".

$\endgroup$
1
$\begingroup$

There is mathematics and then there is mathematics.

Languages do presumably affect the speed at which children learn basic number words.

It is known that children learn Danish (in general, not specific to mathematics) slower than Norwegian and Swedish while very young, but then catch up and soon there is no difference. I also just now read a book about mathematical difficulties in the Norwegian context, which specifically names the "-ten -numbers"; tretten (13), fjorten (14), and so on, up to nitten (19). Children might instead write these as for example 31, since the three (tre) is named first.

What follows is guessing on my part based on the two known things above. I guess that most children understand and get past these issues fairly quickly, and afterwards there are no significant differences. In particular, once one gets all the way to research mathematics, there is almost certainly no difference. However, there might always be individual issues that might be caused by the language to a single person, or maybe at a given age a given language has a minor edge.

In addition to number words, we might consider a word like "polygon" in English, which is Greek (also to most English-speakers), and compare it to monikulmio, mangekant, månghörning, and so on, which specify that there are many angles or sides, and do it in a language the speakers understand.

Some languages might also have concepts and ways of stating things others lack: like "puolet enemmän" and "puolet vähemmän" in Finnish and the corresponding expressions in at least one Sami language. But, again, I doubt these make a difference in the long run.

$\endgroup$
1
  • 1
    $\begingroup$ German native speaker here, we have those -ten numbers as well. I remember that when we were in elementary school, a friend would write the 3 of dreizehn (temporally) before the 1, but (spacially) in the correct place, like 713: 7 -> 7 3 -> 713. $\endgroup$ Commented Jan 18 at 20:38

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.