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

The book of Genesis says that after God created the world, he created the animals and brought them to Adam, and “man called the domestic animals, the birds of the air, and the wild animals.” In an article published in Nature in 1888, the Englishman James Joseph Sylvester claimed for himself an award in the field of mathematics of equal value: mathematical reason than all other mathematicians combined ”.

Perhaps the best known (and most 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 is therefore widely used in livestock. Sylvester has adopted it for his own purposes, arguing that a mathematical matrix is ”a rectangular series of numbers from which various systems of determinants can be generated from the womb of a common mother”.

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

Other mathematical terms are the result of mistakes 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 that it would refer to the rounded shape of the function graph.

The actual origin is the word “jya”, which means “bowstring” in Sanskrit and which 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”. Only “jb” was written because the Arabs left out vowels. The result was that it was confused with “jaib”, which means “bay” and therefore translated as “sinus” (“bay”) in Latin. This led to “seno” in Portuguese and Spanish.

We do not know exactly who created this chaos and when, but “sinus” was already used in the Latin translation of “Algebra” by the Arabic mathematician al-Khwarizmi, published in 1145 by the Englishman Robert of Chester. I’ll get back to you.

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