There is no mathematics without signs and symbols. Signs aid in the workings of mathematical concepts in a theoretical manner, and are essential tools for counting – the core purpose of mathematical thought.
In the introduction of integral signs that revolutionised mathematical reasoning, the contributions of 16th-century Welsh physician and mathematician Robert Recorde are immense. Among his many achievements, is the invention of the equals sign (=), alongside pre-existing ideas of plus (+) and (-), for English speakers.
After a brief stint as a maths teacher, Recorde trained as a doctor, researching on urology. Later, he embraced life as a writer, publishing theological tracts, poems, and textbooks on astronomy, geometry, and arithmetic in English. Meanwhile, mathematical works were predominantly written in Latin, and with lengthy expressions, which few people could comprehend. Recorde’s writing in English for the British learner, led to his greatest invention. In his final book, The Whetstone of Witte (1557), is where we see ‘=’ for the first time.
Horizontal and parallel
Recorde introduced a pair of horizontal parallel lines to show ‘equality’ between two mathematical conditions, and the succeeding result. Earlier, Latin had a word for the concept of equality – ‘aequalis’, and if more elucidation was necessary, people would shorten it to ‘ae’ or ‘oe’. Recorde found it tedious to have to repeatedly state that one side of an equation was equal to the other side. Hence, to make it simpler for English speakers, in The Whetstone of Witte, Recorde introduced the equals sign, alongside the use of German symbols ‘+’ and ‘-’. In combination, these signs allowed people to express mathematical equations quickly and with minimum use of ink. For eg. Instead of writing, “A factor added to a quantity of three is equal to a different factor from which is taken away a quantity of four,” Recorde’s breakthrough meant that this same thought could be simply written as: “x + 3 = y – 4.”
Today, the equals sign is also known as the equality sign, with its 500-year-old symbol ‘=’, which continues to be in use to indicate equality between two conditions. In an equation, it is placed between two expressions that have the same value, or for which one studies the conditions under which they have the same value. And ‘=’ also denotes the result or culmination of a mathematical problem or puzzle. For eg. 1 + 1 = 2, and 5 - 3 = 2. In both cases, ‘=’ is used to explain ‘2’ as the result of the two problems. Hence, the equals sign also means totality, and an equation cannot be expressed without it.
Centuries later, Recorde’s most famous invention became a stepping stone for the computer age, helping write computational language. The sign was first used in 1957, as part of a computer programming language in FORTRAN I. With maths being an important subject to propel technological advancement, the equals sign has entered almost every stream of use. Over the years, its simplicity and logic allowed variations (such as == and ===) to be invented, to make calculations more seamless, and to allow more numbers to see each other as equals.