The first six chapters looked at notation as it is: who invented each sign, what it means, what it lets us do. This chapter looks at the people who learn notation. No sign is transparent. Reading $\frac{dy}{dx}$, or even $304$, requires knowing what each part does and in what order the parts combine, and that knowledge is acquired slowly, over years.
Written mathematics is a second language with a grammar of its own, and it is almost always learned mixed up with the first one. A child hears “three hundred and four” and has to write three digits, not five. A student reads “three times more” and has to decide whether it means triple or quadruple. An adult sees $6 \div 2(1+2)$ on social media and discovers that two sensible people can read the same line in two ways. The errors that appear along the way are rarely laziness: they almost always follow a rule, only the wrong one. That is why they are a window onto what the reader has understood.
The chapter also looks at the other side: writing. Gauss and Ramanujan filled notebooks with writing so compressed that other mathematicians took decades to decipher it. And Abraham Nemeth, who was blind, showed that mathematical writing can be read with the fingers and with the ears, provided one says aloud what the page shows only through position.
Texts in this chapter
- Counting, saying and writing numbers
- Read before you calculate: Bogdanov-Belsky’s painting
- Two languages in one sentence: the mathematics register
- The captain’s age: from word problem to equation
- The conventions nobody writes down
- Errors that make sense: false rules
- Writing to think: the notebooks of Gauss and Ramanujan
- Reading with the hands and the ears: Braille and the Nemeth code
- How to learn to read and write mathematics: a guide and a glossary
- References and credits