25/08/2021

In Folha de S.Paulo, the origins of mathematical terms.

James Joseph Sylvester, que criou vários termos matemáticos/ Crédito: Johns Hopkins University/Divulgação

Reproduction of Marcelo Viana's column in Folha de S.Paulo

The Book of Genesis recounts that, after creating the world, God made the animals and brought them to Adam, and "the man gave names to the livestock, the birds of the air, and the wild animals." In an article published in the journal Nature in 1888, the Englishman James Joseph Sylvester claimed for himself an equivalent distinction in the field of mathematics: "Perhaps I may claim without immodesty the title of 'Mathematical Adam,' since I have given more names to creatures of mathematical reason than all other mathematicians combined."

Perhaps the best known (and most ingenious) of the mathematical terms coined by Sylvester is "matrix," which he first used in 1850. The word comes from the Latin "matrix," meaning "womb" or "uterus," and is therefore widely used in animal husbandry. Sylvester adopted it for his purposes, arguing that a mathematical matrix is "a rectangular arrangement of numbers from which different systems of determinants can be generated, starting from the womb of a common mother."

Incidentally, mathematicians love to take common words and use them for their own purposes. For example, there's a theorem in topology that says "every compact Hausdorff space is normal." Aside from "Hausdorff," which refers to the German mathematician Felix Hausdorff (1868-1942), all the words in the statement are in common use. But the only ones with their usual meaning are "every" and "is."

Other mathematical terms are the result of errors and confusion throughout history. Years ago, a colleague from Madrid tried to convince me that the word "sine" in trigonometry meant "breast" (in Spanish the two words are identical) and referred to the rounded shape of the function's graph.

The true origin is the word "jya," which means "bowstring" in Sanskrit and was first used in a mathematical sense in the work "Aryabhatiya," published in 499 by the Hindu Aryabhata the Elder. The corresponding word in Arabic is "jiba." However, it was written "jb" because the Arabs usually omitted vowels. As a result, it was confused with "jaib," which means "bay," and therefore was translated as "sinus" ("bay") in Latin. From this came "seno" in Portuguese and Spanish.

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