The Language of Math

Jan 17, 2020 | Littleton

It is often assumed that there is a dichotomy between math and language arts – that if one has a brain built for math, they are most likely less linguistically driven or talented or that there is preference for one or the other, but not both. But what if they are more closely connected than people think? What if there are such similarities between language arts and math that you could see the same patterns in both? What if math actuallyisa language? 

The famous Italian astronomer Galileo Galilei perhaps said it best when he said to understand the Universe, you must understand the language in which it’s written, the language of Mathematics.” Perhaps he was talking about shapes like circles, triangles and other geometrical figures being letters? Or perhaps he was referring to the sequence of letters, numbers and shapes that are often a part of equations and answers. In order to determine whether math is an actual language similar English, German or Mandarin, it helps to look at how language is defined and what makes vocabulary and grammar, particularly when it’s used to construct math sentences. 

There are a lot of definitions of what language is and there is a bit of a division between whether languages have to be verbal or whether they can just be written communication. There are also two schools of thought when it comes to whether the elements used to construct a sentence should only be finite in their meaning, or whether language can include just abstract concepts. Outside of those two different discrepancies in order to be considered a technical language, a method of communication must have grammar, syntax, vocabulary and a group of people who understand it and share the meaning. And using this criteria, math is totally a language. Mathematicians, physicists and scientists around the world use the same symbols, their meanings, grammar and syntax to communicate concepts that describe finite and abstract concepts. The vocabulary of math uses alphabets and symbols from other languages around the world to form something unique to math and equations can be written or spoken out loud. Take 9 + 7 = 16. It’s clearly written already, but it can also be stated as “nine plus seven equals sixteen” when spoken. 

Understanding how mathematical sentences read and their meaning is imperative for teaching and for students to comprehend. Imagine looking at Arabic if you only speak English and trying to read it fluently. It would be impossible and intimidating without exposure to any Arabic at all. Looking at math equations – especially more difficult ones – can be really similar for kids. If they haven’t had the right building blocks to help them break down the equation into bit sized, more manageable parts. The better students become at math as a language, the more numerical fluency and better number sense kids will have and one way to help with learning the actual syntax of the language of math is by word problems. Extracting verbs, nouns and everything in between from a spoken/written language and translating them into an equation helps comprehension.  

With all of this said, let’s review the technical aspects of what’s considered what in the language of math to help give a visual. Nouns in math include:

  • Variables (x, y, z, a, b, c,)
  • Numerals (0, 5 etc.)
  • Expressions ( 7x, x2, 3 + x) 
  • Fractions (1⁄3, 5⁄9, 8 1⁄4)
  • Pi (π)
  • Infinity (∞)
  • The speed of light (c)
  • Imaginary numbers (I, -i)

Verbs in math are these:

  • Actions that happen between numbers, letters and symbols, like multiplication, division, subtraction and addition. (*, ÷, -, + or /).
  • Inequalities or equalities (<, >, =)
  • Other functions (cos, tan, sin, sec) 

Syntax and grammar, the structure of how all the language comes together is also the same. Here are examples of this:

  • The Latin alphabet is used to represent parameters and variables. Integers or numbers look like i, j, k, l, m, n versus real numbers are represented by a, b, c, y. Larger, more complex numbers are represented by wand zand unknowns are x, y, z. Names of functions are usually f, g, h
  • The Greek alphabet is used to indicate more specific concepts.
  • Formulas always read from the left to the right. 
  • The way that everything is phrased is standardized. 
  • Brackets and parentheses universally denote the order in which the symbols interact with each other.

All in all, not only is math a language, it’s a universal one that can bring together many cultures in the world. Formulas have the same meaning, regardless of what primary verbal language people speak and because of this, math can help people communicate with each other through other language barriers, which is a beautiful thing.