More Equal than Others

In his scientific best-seller, A Brief History of Time, Stephen Hawking remarked that every equation he included would halve sales of the book, so he put only one in it, Einstein’s equation relating mass and energy, E=mc2.

There is no doubt that mathematical equations strike terror in the hearts of many readers. This is regrettable, as equations are really just concise expressions of precise statements. They are actually quite user-friendly and more to be loved than feared.

An equation indicates that whatever is to the left side of the “equals” sign has the same value as whatever is to the right. For Einstein’s equation, E is the energy and it is equal to the mass multiplied by the square of the speed of light. In ancient times, equalities were expressed in verbal terms like this.

It was Robert Recorde, a Welsh-born mathematician, who introduced the symbol “=” for “equals”. In his book The Whetstone of Witte, written in 1557, Recorde wrote that he chose this symbol consisting of two parallel lines “bicause no 2 thynges can be moare equalle”.

Robert Recorde (c. 1512 – 1558), a Welsh physician and mathematician.

Robert Recorde (c. 1510 – 1558), a Welsh physician and mathematician.

The first equation to appear in symbolic form was in Recorde’s book, and was 14x + 15 = 71. The quantity x is called the unknown (although early writers on mathematics called it “the thing”) and the equation states that if we take 14 times x and add 15 we get 71.

How might such an equation arise? Suppose you need a hammer and some nails. A hammer costs 15 euros and a packet of nails is 14 euros. If you buy a hammer and x packets of nails, the total cost is 14x + 15, the left side of Recorde’s equation. If you have just 71 euros to spend, how many packets of nails can you buy? The answer is the solution x of the equation.

 The first equation written in symbolic form. Equivalent in modern notation to 14x+15=71.

The first equation written in symbolic form. Equivalent in modern notation to 14x+15=71.

Recorde explained the transformations that can be made to an equation to ‘solve’ it, that is, to find the unknown quantity x. In the present case, you can subtract 15 from each side to get a new equation 14x=56 and then divide both sides to get another one, x=4. This is the solution, and you can afford four packets of nails.

Recorde is credited with introducing algebra into England with his book. But he had other talents in addition to mathematics. He was physician to Edward VI and Queen Mary and, in 1551, was appointed Surveyor of the Mines and Monies of Ireland.

Alas, he ended his days in prison, for reasons that are unclear. Perhaps he became embroiled in a religious controversy, or ensnared in some political intrigue. Or perhaps some of the ‘Monies of Ireland’ went astray!

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