Maths, it is Greek and Latin to me

‘I was good at Maths until the alphabets decided to get involved’ is a meme that I came across on a social medium and this had me amused.  Looking back at my own journey with Maths so far, I began in primary school with numbers and arithmetic, graduated onto using English letters with the coming of algebra, got my first taste of Greek letters with trigonometry (remember sin theta?) in middle school and have now ended up using 10 times more Greek letters than I use numbers. Isn’t it paradoxical that mathematics is about numbers, but the higher up you go in school the less numbers are used in Maths. Or, is it?

A whiteboard over which few PhD Economics students had a discussion.

One could argue that Maths is but a language to communicate general facts. To the extent that these facts are general, numbers only serve to limit Maths in its generality.  I am convinced that numbers are limiting and therefore we need letters to be used in Maths. But I wonder if using Greek letters instead of English alphabets was a choice made by few genius mathematicians (or economists) to draw admiration by confusing the audience along the lines of “That person must be a genius, for I couldn’t even read what was on their slides”. I was wrong, but not entirely.

Mathematics, and every field that uses mathematics have their own conventions regarding what symbol should be used for certain concepts. For example, W stands for Watt in Physics, K stands for Potassium in Chemistry or E is Expected value of a variable in Statistics.  The exposure to maths that I have is through its applications in economics.  And boy, do economists use Maths ! This blog is my exploration (and scouring the internet) on why economists use Greek letters. I divide my answer into three parts – clarity, need for more symbols, and legacy. 

To avoid confusion

While the use of Greek alphabets contributes to an article looking cryptic (Remember the economist working on some algebra for his research being removed from a flight because a co-passenger thought he was writing something in code language for a bomb), it actually reduces confusion. Economists have to use English sentences along with mathematical equations and using the same alphabets for both could potentially be confusing in the text.

No English alphabets left

Another reason why English alphabets cannot be used is quite simply that English alphabets are all taken. There are 26 English alphabets which give 52 symbols to use when we consider both uppercase and lowercase letters. While 52 symbols is a lot, the economist has to respect existing norms regarding certain letters.  A reader who sees the letter ‘d’ will think differential and an economist will like to avoid this letter to denote anything else. Similarly, some widely accepted norms are:

  • A & B for sets. a & b for constants.
  • c denotes consumption
  • d for differential
  • e is the Euler number while 
  • F,G,f & g for functions
  • I is the identity matrix
  • i & j  are used as an index for a collection of things, 
  • N and n, denote population
  • O, well this is already confusing with 0 (zero)
  • P,Q, p & q are probabilities
  • q denotes quantity
  • t is time
  • U, u denotes utility
  • X,Y,Z for random variables. x,y,z for observations of random variables. y also denotes income in economics

Now, that leaves us with much fewer English letters to use as symbols.

Legacy and why I may not be entirely wrong

Given that using alphabets from a language other than English is less confusing and needed for want of symbols, the question then is ‘Why Greek?’. Why not alphabets from Hindi or Malayalam? Greek and Latin were languages that were part of a curriculum considered a ‘classic education’ in Europe in 1700s. Many scientific works were written in Latin until the late 1800s in Europe even though Latin had long ceased to be a commonly spoken language. Knowledge of Greek and Latin was thus a signal of being educated So, when economists started using mathematics and statistics as tools, we inherited the symbols used by mathematicians and statisticians.  It would be outlandish to claim that economists today are being elitist in their use of Greek alphabets; it is simply necessary. But the use of Greek letters in particular could be a relic of a past where it was a medium to distinguish one from the masses and signal elitism.  

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