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Roots: All things being equal

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Imagine the scene: The year is 1557. Henry VIII’s eldest daughter, Mary, is on the English throne. It’ll be another year before her younger sister, Elizabeth, becomes queen. You’ve published a fair few mathematical texts, and you’re halfway through writing your latest book ‘The Whetstone of Witte‘, the second in a pair of books on Arithmetic (the title was a pun about sharpening your mathematical wits).

You’re determined to only use English language in the book but you are getting really frustrated with having to write ‘is equal to’ every time you note down an equation. Then it dawns on you! Why not use a symbol to represent ‘is equal to’? It’ll save time. It’ll save ink. After all, isn’t mathematics all about efficiency? But what symbol to use?

It occurs to you: no two things are more equal than two parallel lines, so to ‘avoid the tedious repetition’ of the words ‘is equal to’, you introduce the symbol ‘=’. You have invented the equals sign.

We’ve all been there – LOL, BRB, </3 – finding short ways to express yourself to save time and effort.

Robert Recorde

Robert Recorde

The equals sign was invented as shorthand by Robert Recorde, a Tudor mathematician and doctor who published widely on a variety of topics. He was born in Tenby, Wales in around 1510, and died in Southwark in 1558 whilst in prison for not paying a fine.

During his life, he took on many roles. He was in charge of the Royal Mint and taught mathematics at both Oxford and Cambridge universities. He was a qualified medical doctor, and worked as the court physician for both Edward VI and Mary. The following is an excerpt from the original text of ‘The Whetstone of Witte’, published 1557:

“Howbeit, for easy alteration of equations. I will propound a few examples, because the extraction of their roots, may the more aptly be wrought. And to avoid the tedious repetition of these words: is equal to: I will set, as I do often in work use, a pair of parallels, or Gemowe [twin] lines of one length, thus: =, because no two things, can be more equal”

Recorde initially used this new symbol to set up a system of six equations:

whetstoneofwitteeqs

The symbols within the equations have meanings, and Recorde provides us with a key:

wwsymbol1 – an absolute number,

wwsymbol2 – an unknown, or root,

wwsymbol3 – a square number.

We can rewrite Recorde’s equations to make them look more familiar. Here are the first three:

$14x+15=71,$

$20x-18=102,$

$26^2+10x=9^2-10x+213.$

It is easy to appreciate how useful this new symbol was. Up until Recorde’s notation, the most common way to write ‘equal to’ was to use the Latin ‘aequales’ or ‘aeq’. Recorde was very keen on promoting English vocabulary in an English mathematics textbook. He believed that everyone should be able to access mathematics. The + and – signs had not been used in England previously, and with Recorde’s invention of =, the equations included in his book look like they could have been written this week, not 450 years ago. Robert Recorde was a trailblazer.

recordeplaque

Memorial plaque to Robert Recorde in Tenby, Wales.

However, whilst abbreviations in common use currently spread like wildfire, the spread of Recorde’s equals sign was much more sedate. In 1631, three separate books were published – including Trigonometria, the influential book by Richard Norwood – all using the parallel lines equals sign. Sir Isaac Newton (1642–1727) then picked up on the notation and used it in his works, and so on, until it became the ubiquitous sign that mathematicians now use on more than a daily basis. This was hardly a viral spread with the scale or speed of ‘FTW’ or the hashtag, but the slow and steady acceptance of = as the universal sign of equality is clear to see.

Red Human Rights Campaign logo

Red Human Rights Campaign logo

Indeed, the Human Rights Campaign unveiled the equals sign as their logo in 1995, and it has become synonymous with the LGBT community’s equal rights movement. Inscribed on a memorial plaque to Recorde in St Mary’s Church, Tenby,  is the line ‘invented the sign of equality’, and I am astounded how prophetic this statement turn out to be.

In ‘Mathematics’ by David Eugene Smith (1923) Recorde is referred to as the founder of the British School of Mathematics, but I hadn’t heard of him until I embarked on the research for this article. That needs rectifying. We now know that when it comes to impact and influence on the brevity and efficiency of mathematics, Robert Recorde is without equal.

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Emma Bell is a maths teacher at Franklin College in Grimsby, UK.
You can follow her on Twitter, or email her at emma.bell@franklin.ac.uk.
Twitter  @El_Timbre    + More articles by Emma

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