22/09/2021

In Folha: Porta dos Fundos, Descartes and the question

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

In the excellent video "Romans," the comedy group Porta dos Fundos makes fun of the fact that the letter x is used in many different ways in mathematics: as an unknown in an equation, as a multiplication symbol , and even as the numeral 10 in Roman numerals. It's worth checking out.

The habit of using the last letters of the alphabet (z, y, x…) as unknowns, and the first ones (a, b, c…) to represent known quantities, began in the book "Geometry," published in 1637 by the French mathematician and philosopher René Descartes (1596–1650). He offered no explanation, and the matter remains a subject of discussion to this day.

But the reason why x prevailed over yez is known and very curious. When preparing the book for printing, the typesetter noticed that some typefaces were running out. Since Descartes said that it didn't matter which of the three was used in each case, the typesetter prioritized x in the equations, because yez are more commonly used in French.

The x as a multiplication symbol was used in "Key to Mathematics," a work by the Englishman William Oughtred (1574–1660) published in 1631. The same had already happened in 1618, in an anonymous appendix to the Latin-to-English translation of the work "Description of the Admirable Table of Logarithms," by the Englishman John Napier (1550–1617). But it is believed that Oughtred himself was the author of this appendix.

Oughtred was also the first to use a pair of sliding rulers with logarithmic scales to perform multiplications and divisions, in 1622. Rulers with logarithmic scales had been invented by another Englishman, Edmund Gunter (1581–1626). The "slide rule" was an essential tool for engineers and scientists until the 1970s, when it was gradually replaced by the electronic calculator.

Gottfried Wilhelm Leibniz (1646–1716) agreed with the Porta dos Fundos group and therefore advocated the use of a dot (·) to represent multiplication. “I don’t like the symbol x for multiplication because it is easily confused with the unknown x. In general, I use one dot to indicate multiplication and two dots for division,” he wrote in a letter to Johann Bernoulli dated July 29, 1698.

To read the full text, visit the newspaper's website.