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2 + 2 = 4: Mathematical symbols

01:00 Fri 22nd Mar 2002 |

Q. What symbols are we talking about here

A. The symbols for addition, subtraction, multiplication, division and equals (+ - x � =). They are familiar enough to us today, but, at least in terms of how long we've been dabbling in mathematics in one form or another, they are relatively recent innovations.

Q. How recent

A. Less than 500 years, which, when you consider that humans have been doing sums and accounting on various substrates for around 4,000 years, isn't so very long.

Q. Why is this

A. For the most part calculations were undertaken on counting machines, particularly the abacus, rather than on paper. There was an ongoing debate in the Middle Ages as to which was faster, the abacus or pen and paper. There were even names for the supporters of each method, abacists and algorists, and competitions were regularly held to try to pin the conundrum down once and for all.

Q. So, where and when did the symbols originate

A. They didn't all appear at once. The plus and minus symbols first turned up in Leipzig in 1489 in a textbook on commercial arithmetic by one Johann Widman, called Rechnung uff allen Kauffmanschafften. However, he didn't use them as we do now but as symbols for surpluses or deficits in accounting. There is some suggestion that they were around in the commercial world before Widman adopted them, possibly as a quick way for merchants to mark barrels to indicate whether they were full or not. It seems that the plus sign started out as an abbreviation for the Latin et ('and'), but nobody seems to know for sure where the minus sign came from. The symbols were gradually adopted throughout Europe in the century after Widman's book was published.

The person responsible for introducing them to England was a 16th-century mathematician named Robert Recorde. In his most famous work, the Whetstone of Witte (1557), he introduced the two signs: 'There be other 2 signes in often use of which the first is made thus + and betokeneth more: the other is thus made - and betokeneth lesse'. In the same book he introduced our modern equals sign: 'I will sette as I doe often in woorke use, a paire of paralleles, lines of one length, thus: =, bicause noe 2 thynges, can be moare equalle.'

The multiplication sign seems to have been invented by the British mathematician William Oughtred, and it appears in his Clavis Mathematicae (Key to Mathematics) which was published in London in 1631.

The symbol for division was first used by Johann Rahn in Teutsche Algebra in 1659 and was known at the time either as the obelus or the obelisk, from the Greek for a roasting spit. The symbol itself wasn't new, as it had been used to mark passages in writings that were considered dubious or spurious. As for why this symbol became employed for division, a strong argument runs that it's a minus sign with added dots. This is supported by its having survived in Denmark until very recently as a symbol for subtraction not division, though the Danes have now adopted international usage.

Q. So, what did people use before the introduction of these symbols

A. For those who did calculations on paper, it was common throughout Europe in medieval times to indicate plus and minus by the letters 'p' and 'm', each with a bar or a wavy line over the top.

For more on the history of mathematical symbols go to

For more on Phrases & Sayings click here

By Simon Smith

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