# Where do mathematical terms come from? – 08/24/2021 – Marcelo Viana

The book of Genesis tells that, after creating the world, God made the animals and brought them to Adam, and “man named the domestic animals, the birds of the air and the wild animals”. In an article published in the journal Nature in 1888, Englishman James Joseph Sylvester claimed for himself an equivalent distinction in the field of mathematics: “Perhaps I can apply without immodesty the appellation ‘Mathematical Adam’, since I have given more names to creatures of mathematical reason than than all other mathematicians together”.

Perhaps the best known (and ingenious) of the mathematical terms created by Sylvester is “matrix”, which he first used in 1850. The word comes from the Latin “matrix”, which means “womb” or “womb” and hence , is widely used in livestock. Sylvester adopted it for his own purposes, arguing that a mathematical matrix is ”a rectangular array of numbers from which different systems of determinants can be generated, from the womb of a common mother.”

In fact, mathematicians love to take common words and use them for their own purposes. For example, there is a theorem in topology which says that “every compact Hausdorff space is normal”. Except for “de Hausdorff”, which refers to the German mathematician Felix Hausdorff (1868-1942), all the words in the utterance are in routine use. But the only ones that are in the usual sense are “all” and “is”.

Other mathematical terms are the result of errors and confusion throughout its history. Years ago, a colleague from Madrid tried to convince me that the word “sine” in trigonometry would mean “breast” (in Spanish the two words are identical) and would refer to the rounded shape of the graph of the function.

The real origin is the word “jya”, which is “bowstring” in Sanskrit and which was first used in the mathematical sense in the work “Aryabhatiya”, published in 499 by the Hindu Aryabhata the Elder. The corresponding word in Arabic is “jiba”. Only it was spelled “jb”, as the Arabs used to omit vowels. The result was that it was confused with “jaib”, which means “bay” and, therefore, it was translated to “sinus” (“bay”) in Latin. This resulted in “seno” in Portuguese and Spanish.

We don’t really know who made this mess, or when, but “sinus” has already been used in the Latin translation of the Arabic mathematician al-Khwarizmi’s “Algebra” published in 1145 by the Englishman Robert of Chester. I will come back to them.

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