Multiplication Is Vexation

Four lines of homework grumbling survive from about 1570, which makes this one of the oldest recorded complaints in the English language about maths lessons. Somebody in an Elizabethan schoolroom wrote down that multiplication was irritating, division was no better, the Rule of Three was beyond him, and something called Practice was sending him round the bend. Nothing in it is invented for comic effect. Every one of those four things was a real, named part of the arithmetic syllabus he was being made to learn.

That is what makes the verse unusual. Most old nursery rhymes need a footnote before a modern reader can see the joke. This one lands immediately, because the pupil's position has not changed in four and a half centuries, and the only obscure words are the names of the lessons themselves.

Origins

The rhyme is traced to an anonymous English manuscript dated to around 1570. No author, no school and no town is recorded with it. The manuscript is nearly always quoted secondhand in later books rather than reproduced, so the date is best treated as approximate rather than exact. A handful of sources credit the Scottish mathematician John Napier, who was about twenty years old in 1570 and who later invented logarithms, but nothing links him to these lines and the attribution reads like a later guess attached to a famous name.

The early wording is not quite the version children learn today. One recorded early form runs "Multiplication is mie vexation, / And Division is quite as bad, / The Golden Rule is mie stumbling stule, / And Practice drives me mad", with spelling that shifts from printing to printing. "The Golden Rule" was the standard nickname for the Rule of Three. Hodder's Arithmetick of 1702 gives the reason without embarrassment: "as Gold transcends all other metals, so doth this Rule all others in Arithmetick." The nickname faded, the plain name replaced it in the verse, and the internal rhyme of "Three" and "me" made the swap easy.

Meaning & Interpretation

The four complaints are not in random order. They climb. Multiplication, then division, then the Rule of Three, then Practice is exactly the running order of a period arithmetic course. Cocker's Arithmetick, published in 1678 and the most popular English arithmetic book for the better part of a century, works through numeration, addition, subtraction, multiplication and division, arrives at the Rule of Three and its variants, and finishes with rules for commercial practice. The rhyme is a syllabus rewritten as a list of grievances, and the grievance gets stronger as the syllabus gets harder.

The escalation of the verbs does the work: vexation, as bad, doth puzzle me, drives me mad. It starts at annoyance and ends at breakdown, in twenty-three words.

What is the Rule of Three?

The Rule of Three was a method for solving proportion problems. Given three numbers, you found the fourth that stood in the same ratio, by multiplying the second by the third and dividing by the first. If four yards of cloth cost twelve shillings, how much do seven yards cost? Multiply twelve by seven to get eighty-four, divide by four, and the answer is twenty-one shillings. It was drilled by rote, with no algebra involved, and for centuries it marked the practical ceiling of an ordinary education. Abraham Lincoln summed up his entire schooling in his 1859 autobiography by saying he could "read, write, and cipher to the Rule of Three; but that was all." A harder Double Rule of Three handled problems with more variables. English schools began abandoning it in the 1880s in favour of the Method of Unity, on the argument that pupils were following a recipe instead of reasoning.

What does "vexation" mean?

Vexation means annoyance, irritation or distress. It comes from the Latin vexare, to shake or harass, and it survives in ordinary English in the adjective "vexing" and in the legal phrase "vexatious litigant". In the rhyme it is deliberately the mildest of the four reactions, the starting point that the remaining lines build on.

What was "Practice" in old arithmetic books?

Practice was not practising sums. It was the name of a specific technique, and of a chapter in the textbooks, covering short methods for working out the value of a quantity of goods. The trick was to break a price into convenient fractions of a larger unit, called aliquot parts. Under pre-decimal money, where twelve pence made a shilling and twenty shillings made a pound, two shillings and sixpence is exactly one eighth of a pound, so ninety-six items at that price come to ninety-six divided by eight, or twelve pounds, with no long multiplication at all. Cocker's Arithmetick devotes a chapter to the Rules of Practice, and eighteenth-century trade manuals described them as short methods of finding the value of any quantity of goods. Fast and elegant once the tables of aliquot parts were memorised. Maddening before that.

Who wrote Multiplication Is Vexation?

Nobody knows. The lines are anonymous, and the manuscript they come from carries no name. What can be said is narrower and more interesting: an English speaker sitting in front of an arithmetic book in roughly 1570 disliked it enough to put the complaint into verse, and somebody thought the verse worth copying out.