A hallmark of mathematical language, which impresses and sometimes intimidates the layman, is the use of rather mysterious symbols. They are what make mathematical discourse so concise and effective: “a formula is worth a thousand words”.

The infinity symbol (∞) is one that arouses the most emotions. The form itself has a long history, going back at least to the Middle Ages. The first to use it in a mathematical sense was the English priest John Wallis (1616 – 1703), in 1655.

Wallis did not explain the choice, but it is believed that it was based on the Roman numeral thousand, which at the time was spelled CƆ and which was also used in the sense of “many”. It is tempting to think that he might have been inspired by the esoteric symbol of the serpent biting its own tail, which represents eternal rebirth. But this theory does not seem compatible with Wallis’s religiosity.

Another popular symbol is the equality symbol (=). It appears to have been used for the first time by the Welsh Robert Recorde (1512–1558) in 1557, but it also appears in a manuscript dated between 1550 and 1568 which is preserved at the University of Bologna. Unlike Wallis, Recorde gave an explanation: “I use a pair of parallel lines of the same length because no two things look more alike.” It used quite long lines, but over time the symbol was shortened.

The symbols of minor (<) and major (>) appeared for the first time in the book “Analytical Art Applied to the Solving of Equations”, by English Thomas Harriot (1560–1621). Historian Art Johnson claims that the inspiration would have been a mark combining the two symbols that Harriot saw on the arm of an American Indian. But Harriot never used the symbols of inequality in his works: the book was only published ten years after his death, organized by other people.

The first to use √ to represent square root was the German Christoff Rudolff (1499-1545), in 1525. According to Leonhard Euler (1707–1783), it would be a modification of the letter r, initial of ‘radix’ (root, in Latin) . In fact, Leonardo of Pisa, better known as Fibonacci, had already used an R to represent the square root, in 1220. Even so, Euler’s explanation is not consensual. In 1637, René Descartes (1596–1650) gave the square root symbol its current shape, adding a horizontal segment to the symbol √.

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