The Origin of the Plus and Minus Symbols

By Wesley Fenlon

The + and - symbols are universally recognized, but they're also far younger than the origins of mathematics.

If math is the only universal language, as the saying goes, then it's a language more or less like any other. And approaching it like a language makes us think about elements of mathematics that we normally take for granted. For example: When and how did the symbols for addition and subtraction come from? Astrophysicist Mario Livio was curious and decided to find out the answers for himself, and the resulting blog post is an interesting mathematics history lesson.

Though mathematics has been around for more than two thousand years--famous mathematician Pythagoras lived in the 6th century BC--Livio traced the + sign back to the 1300s.

"There is little doubt that our + sign has its roots in one of the forms of the word 'et,' meaning 'and' in Latin," writes Livio. "The first person who may have used the + sign as an abbreviation for et was the astronomer Nicole d’Oresme (author of The Book of the Sky and the World) at the middle of the fourteenth century. A manuscript from 1417 also has the + symbol (although the downward stroke is not quite vertical) as a descendent of one of the forms of et."

The - sign, meanwhile, hasn't been around as long--Livio writes that it first appeared in 1481 in a German algebra manuscript. Neither the + or - symbol appeared in English writing on math until 1551. And, like any other language, the writing of mathematics has evolved over the years. Livio notes a few examples of how the symbols have changed into the forms we now know:

"[Johannes] Widman himself introduced it as a Greek cross + (the sign we use today), with the horizontal stroke sometimes a bit longer than the vertical one. Mathematicians such as Recorde, Harriot and Descartes used this form. Others (e.g., Hume, Huygens, and Fermat) used the Latin cross '†,' sometimes placed horizontally, with the crossbar at one end or the other. Finally, a few (e.g., De Hortega, Halley) used the more ornamental form '.' "

The practices of denoting subtraction were somewhat less fanciful, but perhaps more confusing (to us at least), since instead of the simple –, German, Swiss, and Dutch books sometimes used the symbol '÷,' which we now use for division. A few seventeenth century books (e.g., by Descartes and by Mersenne) used two dots '∙∙' or three dots '∙∙∙' for subtraction."