The earlier chapters almost always treated notation as if it were a single thing: the script learned at school, heir to the Indian numerals, Viète’s algebra and Leibniz’s calculus. This chapter recalls that this script is one among many, and that each one was born of a place, a tool and a community.

The Chinese calculated with rods on a board, and the red and black rods gave them negative numbers centuries before Europe. The Maya counted in twenties and had a sign for zero. The Inca kept numbers in knotted cords. On the other side, the same European script that conquered the world also lost battles: the French Revolution imposed the metre, but could not impose the hour of a hundred minutes. A notation wins when a community adopts it, and communities have reasons that mathematics alone does not explain.

The chapter also looks at the present: at physicists who stop writing the summation sign, at Kenneth Iverson, who championed notation as a tool of thought, at the $x = x + 1$ that is not an equation but an order, at the names that theorems carry, and at the market boys of Recife who calculated better in the street than on paper. And it ends with the most demanding script of all, that of proofs checked by computer, in which nothing can be left implicit.

Texts in this chapter

  1. Other scripts, other mathematics: rods, dots and knots
  2. The metre won, decimal time did not
  3. Tribal conventions: Einstein, Bourbaki and the initiated reader
  4. Notation as a tool of thought: Iverson
  5. The equals sign that gives orders: x = x + 1 and programming languages
  6. The names on theorems: Stigler’s law
  7. Street mathematics and school mathematics: mathematics off the page
  8. Notation for machines: proofs the computer checks
  9. Notation and culture: a guide and a glossary
  10. References, credits and the end of the book