Math as a Language 1

Until now, we have discussed many aspects of math. What perhaps was not apparent to many was that many of these are aspects of what we can call the “Language of Math”. Math is a language for expressing patterns & relations in numbers & shapes.

We will now see the different elements which make up the language of math. You will see that in spirit it is similar to the daily language (Tamil, Hindi, English etc). It also has most of the parts of speech. But the contents are different. Chapter 14.6 gives the details in a tabular format.

Language of Precision

The language which we use for daily communication is meant for describing things & events in a qualitative way. We will describe a tree by calling it “tall”. But math is meant for quantifying and conveying it in a very precise manner. We may say that the tree is “4.50 mts” tall. It is a language to describe size & order.

Hence in daily language, many words have multiple meanings and the exact meaning may have to be derived from the context in which a word was used. The word “tall” is a good example. But words in math have very precise and objective meanings.

The alphabet of math are the numerals 0 to 9 and the symbols of operation & comparison. All numbers which can be written down with the numerals & symbols are words. 234.5 and 34 are such words, each with a specific meaning. Hence the math vocabulary is infinitely large.

Words Borrowed From Daily Language

Math vocabulary also contains many “daily use” language words, but they have very precise meanings. An “odd” number is precisely defined and it has no relation to the word “odd” used in daily language.

Math vocabulary also has special words which are only used in the classroom. Obtuse, scalene are some examples. Students need a lot of time to internalize the meaning of these unfamiliar words.

Parts of Speech in Math

All numbers & math words are like nouns. They define a particular math object. ‘Nine’ & ‘division’ are nouns.

All the operators have both a noun form and a verb form. ‘Divide’ is a verb. Division is a noun which identifies the operation.

Daily language has conventions like punctuation & paragraph rules. May also has such conventions. The order in which operations in an expression have to be evaluated, like the BODMAS rule, is one such convention

Math has phrases and statements. 2 + 3 = 5 or x2 + 3 = 7 are sentences in math.

Truth Values & the Idea of Proof

Unlike daily language statements, many math statements can be clearly identified as “true” or ‘false”. 2 + 4 = 7 is clearly a false statement. Hence in math a series of statements can be written down such that the “truth” of one statement logically confirms the “truth” of the following statement. Such a series of statements is called a “proof”.

Internally Dictated Grammar (Logic)

We can say that “grammar” in a daily use language is a human construct and can vary in the same language from region to region. In math, its grammar is decided by its internal logic and is same all over the world.

Language of Modern Science

Today, many sciences like atomic physics, molecular chemistry & cosmology have become so complex that words are not sufficient to communicate about them. Because of its universal & internal logic, math has become the language in which many concepts in higher level science are being expressed.