Shakespearean Numbers

Shakespeare’s era was abuzz with mathematical progress, from the new concept of “zero” to Galileo’s redraft of the heavens. Now, Rob Eastaway uncovers the many surprising ways math shaped Shakespeare’s plays―and his world―touring astronomy, code-breaking, color theory, navigation, music, sports, and more.

The excerpt below is from the first chapter of Eastaway’s book, Much Ado About Numbers: Shakespeare’s Mathematical Life and Times, which has been selected a Bloomberg Best Book.

A Playfulness with Numbers

The notion that Shakespeare’s work might have any links at all with math might come as a surprise. In an era of Spanish Armadas, the arrival of tobacco, and the suppression of Catholics, you might think that math would have been the last thing on people’s minds.

Yet what is striking is that Shakespeare’s plays and poems are full of mathematical ideas, and in particular numbers. He quantifies just about everything: hours, years, distances, the size of an army: you name it, if Shakespeare can put a number to it, he generally does.

The more I’ve investigated the numbers he uses, the more impressed I’ve been by just how creative he is in expressing them. And, as you might expect, he is often poetic with numbers, too. One of my favorite examples appears in Othello, a tragic play about love and jealousy. In Act 3, Scene 4, Bianca is sorry that her lover Cassio has been away for a week. She begins:

What, keep a week away? Seven days and nights?

OK, we get it. But she decides to ram it home with another way of expressing just how long a week is:

Eight score eight hours?

Bianca is demonstrating some nifty mental arithmetic. She’s letting the audience know that there are 7 × 24 = 168 hours in a week (or, as she puts it, 8 × 20 (a score), plus 8, which comes to the same thing).

Of course it’s not Bianca who does this calculation; it’s Shakespeare who has figured it out and then put the words into Bianca’s mouth.

Did you already know that there are 168 hours in a week? I certainly didn’t, until I worked it out. This would have been just as obscure a number fact in Shakespeare’s time as it is today. It takes some mental agility to both calculate the number of hours in a week and then express it in a poetic turn of phrase. “Eight score eight” sounds so much more elegant than “one-hundred and sixty-eight.”

“Score” (meaning twenty) was one of Shakespeare’s favorite numbers. The word comes from the Old Norse word skor meaning a mark or notch. One theory for why it came to represent twenty is that it was used for counting large numbers of, for example, sheep and making a notch in a stick for every twenty. Its meaning slowly changed to cover a reckoning or total amount, and by 1670 it had become a mark made to record a point in a game, which continues to this day.

The words “sixty” and “eighty” were very much in use in Shakespeare’s time, but he hardly uses them, opting for “three score” and “four score” instead (sometimes hyphenated, sometimes a single word).

This use of multiples of twenty to express numbers was particularly popular in Elizabethan times. It’s an idea that still lives on in the French numbering system. You may know that once French counting goes past 69 it becomes eccentric. The French 70 is “sixty-ten” (soixante-dix) and 80 is “four twenties” (quatre-vingts). Four score is the English equivalent of quatre-vingts.

Curiously, the French don’t seem historically to have referred to 70 as “three-twenties-ten”—but the English did. Shakespeare himself does so in Macbeth when the nameless “Old Man” declares that he can remember “three score ten” years of his life.

Shakespeare would have been well versed in the Bible and was no doubt familiar with Psalm 90, which includes the famous line that dictates the natural lifespan of an adult, the so-called allotted span. The King James Bible, published in 1611 (late in Shakespeare’s career), puts it this way:

The days of our years are threescore years and ten; and if by reason of strength they be fourscore years, yet is their strength labour and sorrow; for it is soon cut off, and we fly away.

From the author: The Greek and Hebrew Bible texts referred to “seventy” and not “three score and ten,” as did the first English (Wycliffe) translation of 1382, which says: “The days of our years be seventy years”. However, by 1535, the Coverdale Bible was referring to “three score and ten,” as was the Geneva Bible of 1599. So, whichever English Bible Shakespeare read, the allotted lifespan would have been “three score years and ten.”

In other words, you can expect to live to 70, and if you somehow make it to 80, you’ll be shuffling off your mortal coil pretty soon afterwards. Thankfully in modern times we’ve pushed a bit further beyond these limits.

There’s plenty more number-play to be found in Shakespeare if you search for it. This includes, for example, referring to ten as “half a score” (The Taming of the Shrew), and “twice five” (in three plays). He also expresses fifty as “half a hundred” (Coriolanus).

Shakespeare was also fond of compounding numbers and leaving the audience to imagine how big the result would be. In The Tempest, instead of describing himself as a complete idiot, Caliban says he is a “thrice-double ass.” Thrice-double is six. Shakespeare does something similar in The Merchant of Venice, but on a bigger scale, when Portia suggests that a payment should be “double six thousand and then treble that,” which ends up as 36,000.

And there’s also what I would call exponential wordplay, which exploits the fact that if you keep doubling a number you reach a vast total very quickly. In Macbeth, a wounded captain is reporting how he saw Macbeth and Banquo fighting on the battlefield. He tells how

they doubly redoubled strokes upon the foe.

That sounds like a lot, but just how much is it? Double one cannon ball and you have two. Redouble and you have four. If you doubly redouble, you redouble twice, and four doublings means multiplying by sixteen. Shakespeare clearly liked this phrase because he’d used it before in the play Richard II, when John of Gaunt encourages Henry Bolingbroke to “let thy blows doubly redoubled fall . . . on thy enemy.”

And Shakespeare wasn’t averse to a little numerical sleight of hand. Here is the Fool addressing King Lear:

. . . Leave thy drink and thy whore,
And keep in−a−door,
And thou shalt have more
Than two tens to a score.
—King Lear, Act I, scene 4 

In other words, live wisely and carefully, and you’ll end up in profit, and two tens will end up being worth more than twenty. That’s creative accounting for you.

About the author

Rob Eastaway has authored and coauthored several bestselling books that connect math with everyday life, including Why Do Buses Come in Threes?, How Many Socks Make a Pair?, and Maths on the Back of an Envelope. Since 2004, he has been the director of Maths Inspiration, an interactive lecture series encouraging higher math education that has reached over 250,000 teenagers in the United Kingdom, New York, and Sydney. For five years, he was also the editor of New Scientist magazine’s weekly math puzzle. He has over 30 years’ experience presenting on math to audiences of all ages, including as a keynote speaker at educational conferences and as a regular guest on BBC Radio. In 2017, he received the Zeeman Medal for excellence in the public communication of mathematics, jointly awarded by the London Mathematical Society and the Institute of Maths and its Applications. In 2025, he delivered the BSHM Gresham College Lecture on the subject of Shakespeare and mathematics. He lives in London, roughly two-score-and-eight furlongs from Shakespeare’s historic Globe Theatre.

Learn more at robeastaway.com.