History of Mathematical Notation

For a quite extensive overview with many examples, you might want to check out The origins and development of mathematical notation. I also enjoyed reading Stephen Wolfram's take on Mathematical Notation – past and future, with a great variety of illustrations.

The OP asks specifically for the evolution of one formula, "to see the big picture". Here is one example, taken from Math through the ages:


I think that the most complete source is still :

  • Florian Cajori (1859-1939), A History of Mathematical Notations (1928 - Dover reprint).

We can easily find there examples regarding the evolution of "algebraic" symbolism through the modern era :

  • §122 page 90 : Leonardo Piasano (Fibonacci) (c.1170 – c.1250), from Liber abaci

  • §130 page 101 : Nicolas Chuquet (c.1445 – c.1488), from Triparty en la science des nombres

  • §132 page 103 : Estienne de La Roche (1470–1530), from L'Arismetique (1520)

  • §134-on page 106 : Luca Pacioli (c.1447–1517), from Summa de arithmetica, geometria, proportioni et proportionalita (1494)

  • §140 page 117 : Gerolamo Cardano (1501 – 1576) ), from Artis Magnæ, Sive de Regulis Algebraicis Liber Unus (1545)

  • §151 page 139 : Michael Stifel (1487 – 1567), from Arithmetica integra (1544)

  • §162 page 154 : Simon Stevin (1548 – 1620), from De Thiende ('the art of tenths'), first published in Dutch in 1585 and translated into French as Disme

  • §170 page 169 : Leonard (c.1515–c.1559) and Thomas Digges (c.1546 – 1595) , from An Arithmetical Warlike Treatise Named Stratioticos (1579)

  • §176 page 181 : François Viète (1540 – 1603), from Zeteticorum libri quinque (1591)

  • §191 page 205 : René Descartes (1596 - 1650), from La Géométrie (1637).


"The big picture" that can be seen in Carlo Beenakker's example is

Rhetorical (verbal); Syncopated (abbreviated words); Symbolic.

However, this well-known picture is very algebra-oriented and does not say anything about the use of notations in say geometry as discussed here " The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History " or as asked here Uppercase Point Labels in High-School Diagrams. Thus, at least for me, the interesting answers to OP questions would be those that are not related to algebra.

Tags:

Ho.History Overview

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