Sunday, June 1, 2014

Nature of Mathematics - Math as a Language

Think about it.  Math as a language.  Some say, "math is like a foreign language" - Greek, in fact;  they "don't get it" - don't understand it.  Setting aside the fact that mathematics actually has many great Greek contributors (and Islamic, Indian, Italian, to name a few more), if you look at the components of a language, math really is a language.

All languages have:
  • symbols (alphabet)
  • nouns, verbs, and descriptors (words)
  • rules, methods, and practices that are related to the use of these symbols (grammar)
  • sentences
  • people who use that system of symbols in order to communicate
So does mathematics -
  • numerals and variables are the symbols
  • the way the numerals and variables are used give us nouns (numerals, constants, and representations that are fixed), verbs ((in)equalities, operations), and pronouns (variables),
  • conventions of usage
    • variables a,b,c... usually indicate constants
    • variables i,j,k... usually indicate counting numbers
    • variables x,y,z ...usually indicate unknown variables to be obtained
    • sentences read left to right
    • order of operations
  • sentences are in the form of equations and formulas (2x + 4 < 20)
  • people around the world use this system of numbers to communicate about real world issues both informally and formally -  counting, measurement, money, data, statistics, probability, reasoning, geometry, calculus, physics, engineering
Some say mathematics is not a language in itself because
  • Math is primarily a written form of communication (really?)
  • Math is an art (it is created by it's own rules, it is beautiful)
  • Math is a science (it is experimental, it explains realities according to set rules)
I would argue that mathematics is a sweet combination of all of these.  I think math is a language, with it's own set of symbols, conventions, and means of communicating; it is an art that is beautifully created from it's own set of rules; it is a science that is experimental in nature, explaining realities of the real world.  Just because math is an art or a science, doesn't mean is is not a language.  I believe that mathematics IS a language.

1 comment:

  1. Good essay. Made your point, & supported it well.
    Does that have any teaching implications for you, math being a language?