# Mathematic reasoning in nonEnglish/non Western languages

I am teaching in an Eastern Asian environment (precisely, teaching Mathematics using English in Korea, with Asian students) and I figured out that my reasoning is a lot based on my language proficiency in English and latin languages. As a latin languages speaker, mistakes in the difference between definite article “the” and indefinite article “a” hurt me a lot, whereas these articles do not exist in my students' mother language (at least, in Korean). I also have a quite efficient writing style for proofs, organizing my reasoning on the multiple logical connectors that Western Europe languages provide: so, then, hence, therefore, as a consequence,...; the actual content of my sentences being as simple as possible to convey the mathematical content in the most straightforward way. More elaborated sentences are used for broad introduction of ideas, and conclusions. But other languages have a completely different structure.

I would be interested in references on how the structure of a language influences the logical reasoning. For example, I believe that the importance given on existence problems and unicity problems is mostly due to the emphasis on definite and indefinite articles in Western languages. When introducing a new mathematical object in class, I feel very uncomfortable having to say “a” until unicity is proved. For practical reasons, I am mostly interested in Asian languages (mainly Korean, and also Chinese and Japanese), but references for other languages may also be useful.

• I am a native Chinese speaker, but I don't find any considerable difference from the reasoning you describe in the question body. Maybe it is because mostly I think in English? :D – awllower Apr 23 '15 at 6:06
• There's a big problem with your premise that uniqueness is (necessarily) connected to definite articles: in English the definite article "the" can precede a plural noun. You can write about "the zeros of the Riemann zeta function" or "the prime factors of this number". While there are no definite article in Chinese per se, the sense conveyed by definite articles certainly can be clearly conveyed in Chinese. – Willie Wong Apr 23 '15 at 11:59
• Note that Russia (not sure whether you count that as Eastern or Western) also has a strong mathematical tradition in which existence and uniqueness problems are studied in detail, but the Russian language has no articles whatsoever. // In any case, a random Google search brought up this PhD dissertation which you may find interesting. – Willie Wong Apr 23 '15 at 12:12
• Your premise about existence and uniqueness being related to definite or indefinite articles is bogus. As Willie wrote, Russian has no articles and also has absolutely no problem conveying ideas related to existence or uniqueness. In English we may distinguish between "the algebraic closure" and "an algebraic closure" while in Russian they just don't care that much about it (since, frankly, it's usually not as important as you might think). If there truly is a need to speak about a choice of an algebraic closure, say, then in Russian you could just use their word for "choice." – KCd Apr 24 '15 at 16:38
• As a general remark: It may be helpful to check out a topic's Wikipage in English and then compare it to the corresponding language page of your choice. I have certainly done this for Chinese in order to see how various terms are defined and discussed. A difference in the use of (in)definite articles may influence a non-native writer's exposition, but there is certainly no insurmountable obstruction inherent to any of the languages mentioned... – Benjamin Dickman Apr 25 '15 at 1:48