Evolution of Algebraic Symbolism

Diophantus (c. 250 A.D.) of Alexandria was probably the first to use abbreviations in mathematical formulas. Until then, problems and their solutions have been written in pure prose. This stage of development is known as rhetorical algebra. With Diophantus begins the period of syncopated algebra in which stenographic abbreviations are used for the more frequent quantities, relations, and operations. Diophantus used Greek letters to denote integers. A thousand years after introduction of the Hindu-Arabic numerals, we still follow in his footsteps when using Roman letters for the same purpose. Hebrew years are usually written in the same manner by employing letters from the Hebrew alphabet. In symbolic algebra, notations used are virtually arbitrary and often little related to the entities they represent. Introduction and evolution of algebraic notations, as we know them today, was due to the invention and spread of printing. Standardization of symbolic notations was a lengthy process that took about 3-4 hundred years.

Below is a table of various forms in which the modern day equation 4x2 + 3x = 10 might have been written by different mathematicians from different countries and at different times.

Nicolas Chuquet148442 p31 égault 100
Vander Hoecke15144 Se + 3 Pri dit is ghelijc 10
F.Ghaligai15214 e 3c° - 10 numeri
Jean Buteo15594 p 3 p [ 10
R.Bombelli1572 p equals á 10
Simon Stevin15854 + 3 egales 10
François Viète15904Q + 3N aequatus sit 10
Thomas Harriot16314aa + 3a === 10
René Descartes16374ZZ + 3Z 10
John Wallis16934XX + 3X = 10

Transition to symbolic notations was neither fast nor painless. Not only various groups of mathematicians used different notations, there was real resistance to the symbolization of mathematics in principle. For example, Thomas Hobbes (1588-1679), a renoun English philosopher, insisted that Wallis (1616-1703) "mistook the study of symbols for the study of geometry," and referred to the "scab of symbols" in Wallis' geometry of the conic sections. (Wallis severely ridiculed Hobbes, but, at the end, refused to include his responses to Hobbes into his collected works.)


  1. Encyclopædia Britannica
  2. H. Eves, Great Moments in Mathematics Before 1650, MAA, 1983
  3. From Five Fingers to Infinity, F. J. Swetz (ed.), Open Court, 1996, Third printing

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