The Story of ‘X’

One of my favourite anecdotes from my days teaching in an English secondary school involves the variable x. I was introducing the concept of a linear equation. Specifically the y=mx+b that kids in Ontario learn all about in Grade 9.
I was explaining how you plot the line on a graph when a young boy got out of his chair threw his hand up and toward the board, palm open, indicating with a wild gesture the third last letter of the alphabet written plainly in the equation. “But Sir!” he exclaimed, “What Is X!”
For my students, up until this point a letter had represented some unknown quantity, and it was their responsibility to divine its value. To Solve For X! But this was a new concept. In y = 2x + 1, x isn’t a quantity to solve; it’s a variable, a symbol of all the possible numbers to which we could multiply by 2 and add 1. I was amused and did my best to explain the nuanced differences of this new concept masquerading as an old familiar one.
But how did X become the symbol of anything in the first place? Who was the mystery person who decided that we needed to use letters to represent numbers?
His name was François Viète.

François Viète

Viète was born in Fontenay-le-Comte, France, in 1540. He grewup to be a lawyer like his father before him. Most of his life was marked by the French Wars of Religion which lasted from 1562 to 1598. He made quite a name for himself in his career. Early on he was tasked with looking after the interests of Mary, Queen of Scots. Viète went on to serve as a code-breaker for both Henry III of France (of the House of Valois) and later for his successor Henry IV (of the House of Bourbon).
Viète was the first person to use letters as symbols for unknown quantities.
Up until this point Algebra had been a tedious and time consuming assortment of algorithms all described in common language. By contrast, Geometry was pleasantly axiomatic with universal rules and easily followed instructions. By creating a system where letters represented both the coefficients and the unknowns Viète was able to axiomatize algebra and make a system as nice and neat as Euclid had for Geometry some 1800 years earlier.

Vieta's Isagoge

Viète’s system wasn’t perfect. He didn’t yet have the “=” that was invented by Robert Recorde in Wales around the same time. He also made the strange decision to use vowels to represent his variables and consonants to represent the coefficients. It would have to fall to the great Descartes to create the tradition of using the last letters (x, y, z) for variables and the first letters (a, b, c) for coefficients. However his system allowed him to become one of the most powerful mathematicians in Europe.

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