Further reading

  • Martzloff, Jean-Claude. A History of Chinese Mathematics. Berlin: Springer, 1997.
  • Shen, Kangshen; Crossley, John N.; Lun, Anthony W.-C. The Nine Chapters on the Mathematical Art: Companion and Commentary. Oxford: Oxford University Press, 1999.
  • Ifrah, Georges. Histoire universelle des chiffres. Paris: Robert Laffont, 1994.
  • Ascher, Marcia; Ascher, Robert. Code of the Quipu. Ann Arbor: University of Michigan Press, 1981.
  • Alder, Ken. The Measure of All Things: The Seven-Year Odyssey and Hidden Error That Transformed the World. New York: Free Press, 2002.
  • Einstein, Albert. Die Grundlage der allgemeinen Relativitätstheorie. Annalen der Physik, 49, 1916, pp. 769–822.
  • Weil, André. Souvenirs d’apprentissage. Basel: Birkhäuser, 1991.
  • Iverson, Kenneth E. A Programming Language. New York: Wiley, 1962.
  • Iverson, Kenneth E. Notation as a tool of thought. Communications of the ACM, 23(8), 1980, pp. 444–465.
  • Knuth, Donald E. Two notes on notation. American Mathematical Monthly, 99(5), 1992, pp. 403–422.
  • Graham, Ronald L.; Knuth, Donald E.; Patashnik, Oren. Concrete Mathematics. Reading: Addison-Wesley, 1989.
  • Backus, John et al. The FORTRAN automatic coding system. Proceedings of the Western Joint Computer Conference, 1957, pp. 188–198.
  • Stigler, Stephen M. Stigler’s law of eponymy. Transactions of the New York Academy of Sciences, 39, 1980, pp. 147–157.
  • Carraher, Terezinha N.; Carraher, David W.; Schliemann, Analúcia D. Mathematics in the streets and in schools. British Journal of Developmental Psychology, 3, 1985, pp. 21–29.
  • Carraher, Terezinha N.; Carraher, David W.; Schliemann, Analúcia D. Na vida dez, na escola zero. São Paulo: Cortez, 1988.
  • D’Ambrosio, Ubiratan. Etnomatemática: elo entre as tradições e a modernidade. Belo Horizonte: Autêntica, 2001.
  • Gerdes, Paulus. Geometry from Africa: Mathematical and Educational Explorations. Washington: Mathematical Association of America, 1999.
  • Appel, Kenneth; Haken, Wolfgang. Every planar map is four colorable. Illinois Journal of Mathematics, 21, 1977, pp. 429–567.
  • Hales, Thomas et al. A formal proof of the Kepler conjecture. Forum of Mathematics, Pi, 5, 2017, e2.
  • Moura, Leonardo de; Ullrich, Sebastian. The Lean 4 theorem prover and programming language. CADE 28, Springer, 2021.

Image sources

Image Source Licence
Rod numerals in Qin Jiushao’s Shushu jiuzhang (1247) Wikimedia Commons public domain
Page 62 of the Dresden Codex, reproduction by Sylvanus Morley Wikimedia Commons public domain
Inca quipu in the Larco Museum, Lima Wikimedia Commons CC BY 2.0, bobistraveling
Decimal time dial by Hanin (c. 1793) Wikimedia Commons public domain
Albert Einstein in 1921, by Ferdinand Schmutzer Wikimedia Commons public domain
Punched cards with Fortran Wikimedia Commons public domain
The triangle in Zhu Shijie’s Siyuan yujian (1303) Wikimedia Commons public domain
Ubiratan D’Ambrosio receiving the Kenneth O. May Medal (2001) Wikimedia Commons CC BY-SA 4.0, ICHM
Map coloured with four colours Wikimedia Commons CC BY-SA 3.0, Inductiveload

The interactive figures (the three scripts of a number and decimal time) work in all four languages of the site. The record of the downloaded images, with the hash of each file, is in data/semiotica_imagens.json.

The end of the book

This book began with the side of a square turning into $\sqrt{\ }$ and ends with a line of Lean that a machine can check. Along the way, notation appeared in many forms: as the invention of people with names and dates, as a system of signs with rules of its own, as a language learned slowly, and as the product of cultures that counted in twenties, with rods of two colours or with knots in cords.

The thread running through the eight chapters was the distinction between active notation and sterile notation: the kind that helps us think and the kind that only records. It is not a property of the sign alone. The same $\frac{dy}{dx}$ is active for someone who can read it and sterile for someone who only memorised it; the same $=$ asserts on one page and gives orders on the next. A notation is active for someone, in a community, with a tool, at a moment in history. Learning mathematics is, to a large extent, entering these communities, and teaching mathematics is opening the door.

Chapter index · ← Notation and culture: a guide and a glossary · Start of the book