# US vs. UK: Mathematical Terminology

I’m an American, born and bred. I revere the 14th Amendment, root for the New England Patriots [dodges rotten fruit], and can rattle off all 44 presidents.

Yet here I find myself, in Birmingham.

Not Alabama. England.

In some ways, it’s not so different. As my friend John advised before I moved: “The British speak English, care about money, and yell about politics. You’ll barely notice you’ve left.” But it’s not quite like home: the spellings, the roundabouts, the big red buses—and, most relevant for a teacher like me, the sometimes startling differences in the ways our two countries educate kids.

In less than a year of teaching, I’ve encountered some surprising disparities, each of which prompts the obvious question: Which way is better, the British or the American?

I have nothing to gain by these comparisons. If I favor America, my judgments will be dismissed as jingoism (just like 97% of the other things I say). And if I favor Britain, I will have my surrender lorded over me for months to come by English teenagers. Thus, I find myself in a predicament similar to many facing America today: a lose-lose situation. And, in the true American spirit, I shall plunge forward anyway.

In the future, I hope to tackle trivial little issues, such as university majors and the nature of secondary education. But this week, I began with the big stuff: mathematical naming conventions.

These are interchangeable. If you find anyone claiming a strong preference for one or the other, tell them to do take a deep breath, walk away, and go do something beautiful. Watch a sunrise, listen to a Beatles album, punch an investment banker—anything to remind you that life has meaning beyond misplaced pedantry.

Winner: Draw.

Yeah, this isn’t a mathematical difference so much as a linguistic one, but z is the third-most common name for a variable, so it comes up daily. Six months in, I’m already loving the “zed.” The alphabet is overloaded with “ee” letters (B, C, D, E, G, P, T, V). “Zed” is fresh. It’s different. It’s like the single onion ring in your order of French fries.

Winner: UK.

Welcome to my nightmare.

Multiplication comes up a lot in mathematics. Like, a lot a lot. To save time, we’ve developed the convention of omitting the multiplication symbol altogether (hence “2y” for “2 times y”). Sometimes, of course, this isn’t possibly (you can’t write “23” for “2 times 3”), but writing traditional symbol X would be confused for the variable x. So we use a simple dot instead.

Here’s the problem: My British textbooks still use that central dot to represent a decimal.

What does this mean? It means that multiplication haunts my days. When I tried to introduce the dot for multiplication, my students freaked out. (Even if they hadn’t, I’d still be wary of putting them at odds with their own countrymen by forcing different conventions on them.) So I settle for X instead. To avoid confusion I must (grudgingly) change the way that I write the letter x. I hate it.

After seeing this post, some colleagues (aged 23 and 28) pointed out to me that they never put the decimal in the middle. “Maybe it’s a generational thing,” they suggested. But if that’s the case, then it’s not just me who prefers the American way; it’s British people too.

Winner: US.

Many problems in America are diffuse. Cultural. Institutional. It can be hard to assign blame to specific people. But there’s a single villain behind the word trapezoid: Charles Hutton.

Historically, “trapezium” referred to a four-sided shape with one pair of parallel sides, while “trapezoid” referred to a four-sided shape with no parallel sides at all. As the erudite John Cowan explains: the “trapezium” looks like a trapeze, and the “trapezoid” has a shape “analogous to, but not the same as, a trapeze (as with humanoid, planetoid, factoid).”

So what’s Hutton’s problem? When he wrote his (otherwise wonderful) mathematical dictionary in 1795, he switched the two words. Americans inherited the blunder.

(Or, as the British would say, “blundre.”)

(Yes, I know the British don’t say that. I’m just trying to divert attention towards a debate where we’re on better footing than the trapezium thing.)

Winner: UK.

You know who uses this notation? Scientists, that’s who.

And you know what standard numbers look like? They look like numbers, British people. There’s nothing “standard” about this.

Winner: US.

This is unforgivable. The word “index” already has a perfectly distinct mathematical meaning, and the word “exponent” has none. It would be like referring to “division” as “subtraction.” We already have a meaning for that word, British people. You do Shakespeare a dishonor.

(In their defense, the British also recognize the word “exponent,” but they seem to default to “indices.”)

Also, most gratingly, the plural “indices” is often gives rise to the bastard singular “indice.” What the heck is an indice, Britain? Will you please stop saying that?

Winner: US.

Americans revise their essays and review for tests.

The British review their essays and revise for tests.

It’s a disarming adjustment to make when you hop the Atlantic. But since “vision” and “view” mean basically the same thing, it’s hard to pretend that this makes one iota of difference.

Winner: Draw.

This happened with friends: Some Americans and some Europeans were sitting around, shooting the breeze, when the topic of measurement came up. “How many feet in a mile?” a European asked. “It’s about 5000, right?”

“Five thousand, two hundred, and eighty,” the Americans all recited in unison. The Europeans broke into laughter that was spontaneous, derisive, and utterly justified.

There’s no defense. We are fools.

Yes, it’s hard to change systems, but the rest of the world managed it, whereas we in America continue to rear the next generation in our own scientific filth. 12 inches per foot, 3 feet per yard, 1760 yards per mile… 8 ounces per cup, 2 cups per pint, 2 pints per quart, 4 quarts per gallon… Our teachers have to teach this stuff. Our kids have to learn it. I love America’s spirit of independence and individuality, but this is ridiculous. Mothers like to ask, would you jump off a bridge if everyone else was doing it? The question here is, why are we jumping off the imperial measurement bridge when no one else is doing it? I guess we want to be special, distinctive little bridge-jumpers.

Yes, I expect to have my passport revoked in retaliation for such anti-American blasphemy, but there we are.

But, before we bow down before our British overlords, guess what? They don’t always use the metric system either! Yes, they use Celsius instead of Fahrenheit, but that one doesn’t really matter, because in daily life you never do unit conversions involving temperature. When it comes to the big ones, the Brits are wildly inconsistent. They mostly use kilograms, but will occasionally bust out “stones” (which are 14 pounds each). They use “metres” for short distances, but revert to miles for long ones. Yes, they’re “more metric” than Americans, but has no one told them that the whole purpose of standardized units is, you know, standardization and consistency? At least we’re sticking with our system, instead of hopping back and forth.

Winner: Draw. Or, well, both nations lose, but in different ways.

Whereas Americans refer to “The Pythagorean Theorem,” the British simply invoke “Pythagoras.”

I don’t really care. The British version is less of a mouthful, I suppose. It’s also wonderfully insane: When you say, “We can solve this using Pythagoras,” you’re effectively suggesting that a Greek man who’s been dead for 2500 years will personally stop by to help solve your math problem.

Winner: Draw.

THE FOLLOWING ADDED 5/21/2015… or is it 21/5/2015? ANYWAY, THANKS TO COMMENTERS/COMMENTRES FOR THE SUGGESTIONS:

What I love is that these both capture the insanity of irrational numbers. Americans think they’re radical; Brits think they’re absurd; and according to legend, the Pythagoreans find them so disturbing that they’ll kill anyone who dares discover them.

These words also perfectly capture the flavor of their respective countries, which is to say, the US is a nation of skateboarders, and the UK is a nation of Latinists.

Winner: Draw.

To the British, ( ) are just a special case of the many types of brackets, also including { } and [ ]. To the Americans, they’re different.

Yes, the singular “parenthesis” is often mislaid by Americans. But I like the adjective “parenthetical,” as in “a parenthetical remark” or “when it comes to discussing important mathematical issues, the choice of symbols is, at best, parenthetical.”

Winner: Draw. I apologize for my indifference; it’s far too British of me, innit?

I’ve been proctoring tests for years, and only this year did I get the distinct pleasure of invigilating one.

It’s delightful, invigilating. You hold vigil. You, in fact, bring the vigil. You inject vigil into an otherwise vigil-less exam room. It’s like being an Invigorator.

Winner: UK.

You hear both words in both places, but the UK leans towards -ising, whereas the US is happier to use “factor” as a verb.

If you care about this, then congratulations! You are probably the sort of person who can turn on any sport – up to and including the Little League World Series and youth cricket – and immediately find yourself a passionate supporter of one team or the other. Which is to say, you care too much about stuff, dude.

Winner: Draw.

Hey Britain, what’s the point in having an easy-to-remember mnemonic if everyone uses a different one? BIDMAS, BODMAS, BEDMAS, BIMDAS… yes, you could argue that the variety of acronyms reflects the arbitrariness of the convention, but that’s a cheap argument. You’re better than that.

Winner: US.

FINAL SCORE: USA wins! At least, until someone points out to me another difference that “favours” the UK, at which point it will be back to a comfortable stalemate.

## 127 thoughts on “US vs. UK: Mathematical Terminology”

1. In progressing through a podcast series called “The History of English Podcast”, I have learned the concept of vowel and consonant shifts. Many of these shifts have occurred because, say the experts, a particular sound combination was hard to pronounce for a majority of the people speaking the language. I think that the sound at the end of “maths” – the “th” followed by the sibilant “s” – is one of those hard-to-form sounds, and thus we should advance the language by dropping the “s” sound. So there.

1. Stijn van dijk says:

In progreing through the podcat erie called “The hitory of Englih Podcat”, I have learned the concept of vowel and contonant shift.Many of thee shift have occurred becaue, ay expert, a particular ound combination wa hard to pronounce for a majority of the people peaking the language. I think that the ound at the end of “math” – the “th” followed by the ibilant “” – i one of thoe hard-to-form ound, and thu we hould advance the language by dropping the “” ound. O there.
je hebt kleine geslachtsdelen! 😊

2. Sk says:

Love the article. An amazing read but a quick question if I may? Out of all the places why Birmingham?

1. Ha – spoken like someone not from Birmingham! I politely decline to answer this question on the grounds that moving to Birmingham ought not to require any special justification. We do it for the love of Brum.

3. Mario Bourgoin says:

It’s not just the US staying away from metric units. There’s also Liberia and Myanmar, and the latter country is making plans to switch to metric units.

4. When I watch Numberphile videos (a lot of Brits doing maths…) they often write the variable x as if it was constructed with mismatched parentheses, like this: )(

I’ve never done that or seen that in the US, so I figured it was a British thing. But I recently wondered if it was a mathematics thing that I never noticed – to distinguish it from the multiplication times?

And maybe that’s what you are referring to when you say “To avoid confusion I must (grudgingly) change the way that I write the letter x”…

Love this post.

1. Mysterious Clive says:

Yes, us Brits tend to use )( instead of x so that we can differentiate between the multiplication and the variable.

1. Fynn Bernhard says:

Gutentag dercksack 🏳️‍🌈
You definitely the type of guy to send )( instead of x to ur bf.
Schlaffe blödsinn😊

5. Alan Knight says:

My grandson in Portugal asks, Why should I have to learn fractions? Nobody uses them. What would your answer be?

1. Adolfo pablo diego josé francisco de paula juan maria de los remedios cipriano de la escobar says:

Hello from Spain 🇪🇸,

Please inform your grandson that he must learn the ways of the fractions because he can ONLY provide a fraction of the satisfaction a woman needs in the bedroom.
Dañarse.

1. 黃宏成台灣阿成世界偉人財神總統 says:

Don’t worry Alan, I’ll be your Knight in shining armour bby.

6. Richard moss says:

Just found this page by accident. I was going to suggest you cover dates properly, but I can understand why you don’t. MM/DD/YYYY format is absurd and evil and would negate every other US ‘win’ on the entire page and then some.
Then again, we would not have Star Wars day without it.

1. Richard moss says:

Bad form to reply to own comment, but my other pet hate is saying “December 4” instead of “December the 4th” or “the 4th of December”. The exception? Yep, Star Wars day 🙂

1. Luke says:

Surely you want to say May the 4th on Star wars day, and not “May 4”?

Otherwise I wholeheartedly agree with everything you’ve said

7. Steven Stowers says:

I just saw this column, thanks to a link from the most recent. I’m going to resist the temptation to address the “math vs maths” controversy (or, as the Brits say, conTROversy). But one that isn’t on here, unless I missed it, is “sums.” To me, as an American, sums are the results of addition. But as far as I can tell, in the UK “sums” refers to any sort of calculation, whether or not addition is involved. I’m not sure what the exact US equivalent would be.

1. Yes – someone just raised this on Twitter!

I think the closest U.S. analog for “sums” would be “calculations” or “computations.” Which is to say, it really has no equivalent.

For what it’s worth, Brits also recognize that “sum” has a more specific technical meaning (as the result of an addition operation), they just also use it more generally (e.g., any student doing a bunch of problems for homework might be said to be “doing their sums”).

1. 1010BINARY_CODE1010 says:

No, in London we tend to say algorithms or nibbles instead of ‘sum.’ It has more mathematical meaning to us.

8. Christina says:

In the Uk, we tend to say horizontal and vertical axis instead of the hotdog and hamburger axis. Personally, the Uk version is more intellectually correct .

1. Piére Bouhraua says:

Oui oui, as a french citizen I agree completely with you, the American terms for some of the words are quite estupidé if I do say so moiself. We share many similarities with le british linguee

2. Otto says:

I don’t know if I’ve ever heard of the hot dog or hamburger axis (US math teacher here)

9. Nat Santorelli says:

Loved this article but have to disagree with the position of the decimal point. When it’s placed at the bottom it makes the end of sentences very confusing. Ten divided by three is 3.33.

See my point … literally 🤣

10. Hi Ben! I love your blog and the illustrations really make me chuckle. I sent you a note on Linkedin to ask if you might be free to talk about some of the things you mentioned here. Hopefully we can find time to speak. Alex

1. Hmm – I’m not seeing the message on LinkedIn, but I’m happy to chat! Want to send me an email? It’s just the name of the blog at gmail

11. Otto says:

Don’t forget about system of equations vs simultaneous equations.

1. Mmm, true – I guess that one didn’t jump out at me because you occasionally hear “system” in the US, but I suppose “simultaneous” isn’t said in the UK

1. I’m British and have only EVER said/heard “simultaneous equations”. I suppose I’d be able to work out what someone meant if they said “system of equations” but I don’t remember ever having heard it.

12. Rob says:

TIL that in American English the term “whole numbers” doesn’t include negatives. The term “integer” does. What does the word “integer” mean? That’s right, “whole”. And in every other language, including British English, “whole numbers” includes negatives. The discussion on Stack Exchange has a link to this post 🙂 https://matheducators.stackexchange.com/questions/18948/why-don-t-american-school-textbooks-recognize-negative-numbers-as-whole-numbers

1. Ah, fascinating! Always intrigued to learn the depths of our weirdness. I guess this Americanism doesn’t really come into the light because by the time you’re working across the Atlantic, you’re rarely talking about “whole” numbers, but instead using the unambiguous terms “natural” (to exclude negatives) or “integer” (to include them).

13. matt says:

Nice article. I was actually looking up a field of mathematics that’s called something different in the US but couldn’t remember what it was but nonetheless i found your article a good read. What I like to remind my US friends is that they aren’t using different terms to the British .. they’re using the ones we used to use in many cases. Like calling curtains drapes or a tap a faucet .. these are all words we used to use in England but forgot about or changed but the US did not. It’s not their fault we changed the language.

1. Yeah, I find it a fascinating and mysterious fact of linguistics that languages tend to change faster closer to their points of origin.

14. Mohamed Mohamed says:

when you describe win-lose situations, it is fair to use the word “tie” instead of using the word “draw” all the time.