Chapter 1 told how letters entered mathematics: al-Khwarizmi’s thing, Viète’s vowels and consonants, Descartes’s $x$, $y$, $z$, Euler’s $f(x)$. This chapter asks what a letter does when it appears in a formula.

The answer is: many different things, and the text hardly ever says which. In $x+3=7$, the $x$ is a number being sought. In $a+b=b+a$, the letters are arbitrary numbers. In $y=ax^2$, the $a$ stays still while $x$ and $y$ move. In $\sum_{k=1}^n k^2$, the $k$ could be replaced by $j$ without changing anything. Reading algebra is, above all, recognising the role of each letter. It is also where many pupils stumble, and not for lack of arithmetic.

Texts in this chapter

  1. One letter, five roles
  2. The unknown: a place for what is being sought
  3. Letters that generalise: from 3 + 5 = 5 + 3 to a + b = b + a
  4. The variable: the letter that moves
  5. Parameters: letters that stay still while others move
  6. f, f(x) and x ↦ x²: three ways to name a function
  7. Dummy letters: the k of the sum and the t of the integral
  8. When the letter misleads: students, professors and apples
  9. How to read a letter: a guide and a glossary
  10. References and credits