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 Chuquet	1484	4² p3¹ égault 10⁰
Vander Hoecke	1514	4 Se + 3 Pri dit is ghelijc 10
F.Ghaligai	1521	4 e 3c^o - 10 numeri
Jean Buteo	1559	4 p 3 p [ 10
R.Bombelli	1572	p equals á 10
Simon Stevin	1585	4 + 3 egales 10
François Viète	1590	4Q + 3N aequatus sit 10
Thomas Harriot	1631	4aa + 3a === 10
René Descartes	1637	4ZZ + 3Z 10
John Wallis	1693	4XX + 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.)

References

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

Language of Mathematics, Language of Science and Plain Language

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