——By Ryan Strugnell（石室中学剑桥国际高中课程中心物理及数学老师）
在第三期《学科大讲堂》中，生物老师Kevin Gayle为我们讲述了生物与英语学习之间的联系， 认为学科的学习离不开语言，而在本文章中，Ryan Strugnell将数学列为自己习得的第五门语言。我们能将数学称为一门语言吗？数学与语言学习之间又有着怎样的区别与联系？本期剑桥国际高中课程中心数学老师Ryan Strugnell为你解答。
课程中心物理及数学老师Ryan Strugnell
I have journeyed on this planet for more than 35 years now. In that short time I have visited 19 countries spread over 5 continents. I have attempted to learn 5 languages including English, Afrikaans (South African), Mandarin Chinese, Korean and Mathematics. I can communicate reasonably fluently in English. I have communicated successfully using Mathematics and basic numbers as my foundation in many countries and thankfully I have been understood!
Let us look whether we can really call Mathematics a language:
Here are some definitions of language:
a systematic means of communicating by the use of sounds or conventional symbols (from WordNet)
a system of words used in a particular discipline (from WordNet)
the code we all use to express ourselves and communicate to others (from Speech and Language Therapy's "Glossary of Terms" )
a set (finite or infinite) of sentences, each finite in length and constructed out of a finite set of elements (from Noam Chomsky)
The grammar of mathematics
Mathematics in formulas has its own grammar, recognised internationally by mathematicians regardless of the language they grew up speaking or mother tongue. This includes the assumption that Mathematical formulas are written from left to right; even though some writing systems have a foundation direction from right-to-left or top to bottom. Another commonly held assumption is that the Latin alphabet is commonly used for simple variables and parameters. Formulae such as Cos(2A)=2Cos^2 A-1, or SinX + ACos(2X) ≥ 0 are understood by Chinese and Israeli mathematicians alike.
Such mathematical formulas can be a part of speech in a natural-language phrase, or even assume the role of a full-fledged sentence. For example, the formula above, an equation, can be considered a sentence or type of phrase in which the greater than or equal to symbol has the role of a verb. In careful speech, this can be made clear by pronouncing "≥" as "is greater than or equal to", but in an informal context mathematicians may shorten this to "greater or equal" and yet handle this grammatically like a verb.
Mathematical formulas can be spoken aloud. The vocalization system for formulas has to be learned, and is dependent on the underlying natural language. For example, when using English, the expression "? (x)" is normally pronounced "eff of eks", where the insertion of the preposition "of" is not suggested by the notation per se. The expression "dy/dx", on the other hand, is vocalized like "dee-why-dee-eks", with complete omission of the fraction bar, in other contexts often pronounced "over".
The Meaning of Mathematics
Mathematics is used to communicate information about a wide range of different subjects. Here are three broad categories:
Mathematics describes the real world: many areas of mathematics originated with attempts to describe and solve real world phenomena - from measuring farms (Geometry) to falling apples (Calculus) to gambling (Probability). Mathematics is widely used in modern Physics and Engineering, and has been hugely successful in helping us to understand more about the universe around us from its largest scales (Physical Cosmology) to its smallest (Quantum Mechanics).
Mathematics describes abstract structures: on the other hand, there are areas of pure mathematics which deal with abstract structures, which have no known physical counterparts at all.
Mathematics describes mathematics: mathematics can be used reflexively to describe itself-this is an area of mathematics called Metamathematics.
Mathematics can communicate a range of meanings that is as wide as (although different from) that of a natural language. Paraphrasing English mathematician R.L.E. Schwarzenberger:
My own attitude is simply that mathematics is a language. Like English, or Latin, or Chinese, there are certain concepts for which mathematics is particularly well suited: it would be as foolish to attempt to write a love poem in the language of mathematics as to prove the Fundamental Theorem of Algebra using the English language.
Alternative Views:
Some definitions of language emphasize the spoken nature of language. Mathematics would not qualify as a language under these definitions, as it is primarily a written form of communication. However, these definitions would also disqualify sign languages, which are now recognized as languages in their own right, independent of spoken language.
Other linguists believe no valid comparison can be made between mathematics and language, because they are simply too different. Mathematics would appear to be both more and less than a language for while being limited in its linguistic capabilities it also seems to involve a form of thinking that has something in common with art and music. - Ford & Peat (1988)
So be encouraged! You can already speak at least 3 languages! If you are at Chengdu Shishi Cambridge A-Level School then you can speak Chinese (or German) as your first language, English as a second language and you can communicate in Mathematics, too!
To conclude, here are some of my favourite quotes about Mathematics:
- "Mathematics is like love; a simple idea, but it can get complicated."
- "Small minds discuss persons. Average minds discuss events. Great minds discuss ideas. Really great minds discuss mathematics."
- Arithmetic is numbers you squeeze from your head to your hand to your pencil to your paper till you get the answer. ~Carl Sandburg, "Arithmetic."
Acknowledgement: This article is a paraphrasing of selected works found on the internet, largely from Wikipedia.com