# 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.

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

1. I’d like to jump in here and say that neither of the trapeze-conventions is on solid footing. While Mr. Hutton may have flipped the definitions, we mustn’t lose our grip on the actual meanings of the words.

I agree that we should reason through the question rather than leaving it up in the air, but I think you’ve swung too far one way here—or perhaps not far enough. Yes, a trapeze has two parallel sides, but its other two sides have equal length. So “trapezium” is a perfectly good word for the isosceles version of the shape.

Now what looks similar to, but not quite the same as, a trapeze? Well the figure you drew does, what with its two parallel sides and unequal other two sides. So any shape of that ilk ought to be called a “trapezoid” just as we have them in America.

1. James or heyeme says:

What about the daring young man in the flying trapeze

2. This is interesting. Being a former member of Her Majesty’s empire, with language we tend to lean towards the British vocabulary, spelling and general usage in South Africa. But from these samples it would appear we lean more towards US conventions when it comes to math (except for imperial measurement, really, what’s wrong with you people?).

As for the multiplication, we were taught to use the x-symbol (or brackets) for multiplication and to use a cursive “x” when indicating the variable. I’m familiar with using a dot for multiplication, but I don’t think we ever actually used it that way, in either math or physics.

It’s funny, really, that even with Math, which is considered the true universal language, there are such big differences from one place to another.

1. Jonathon Dough says:

American’s can’t handle IMPLIED MULTIPLICATION. Just search the internet for 6/2(1+3)=?

1. Jonathon Dough says:

Urgh … Americans

3. I usually go with the Americans, even though I was brought up with the British terminology. I learned “standard form”, and I vividly remember questioning my teacher in class about the meaning behind this term. I never saw how this way of representing numbers is “standard”, as opposed to having all the zeroes behind. I saw its convenience, but never really picked up the idea of “standard”. Anyway, it is the scientists who primarily use this notation, so I guess it has always been better to call it scientific notation.

1. AJ5025 says:

I think the point is that you are making all the numbers look the same – n.nn x 10^m. In this way you are standardizing all numbers into the same form. Hence standard form.

4. Clearly, the US won, except that you considered the last challenge a draw. Pythagoras is a bit too dead to stop by for tea, unless you have an Imagination Station (1 in 8000 people will get that reference). I’ll keep my theorem alive and well, thank you.

1. Curtis den Otter says:

I got that reference. Yay me!

1. Is this an IStation party, I assume? God, I hate IStation…

5. As a Canadian, I use ‘zed’ to refer to the letter of the alphabet, but ‘zee’ to refer to the variable (i.e. a complex function f(z) would be ‘eff of zee’ and the derivative d/dz would be ‘dee by dee zee’). I blame this on having an american as my PhD supervisor.

1. Ariel says:

I did the opposite, briefly, in college in California, when my advisor was Australian. The other Americans all knew what I meant. They also all laughed at me.

6. And don’t forget about slope/gradient and roots/surds! I’m an American teaching in a British Curriculum school in China. The learning curve was quite steep for some of the terms. And what do you do when you monitor a test? (proctor/invigilate)

1. And we can’t forget about Aunt Sally! PEMDAS vs BODMAS/BIDMAS/BEDMAS depending on if you want to use order, exponent, or indices.

1. Irene says:

I’m currently taking A Level mathematics and can say that I have never heard of BEDMAS in my life.

7. You didn’t even mention the billion/trillion thing.

1. Unfortunately, the UK changed to short scale in the 80s, IIRC.

1. Stuart says:

UK switched to short scale in 1974.

Confusion in mathematics terminology is ‘fun’, but it’s the English language teachers I feel real pity for. With the admixture of British and American language influences on the ‘younger’ generations it must have them tearing their hair out at times.

One of my favourites (aside from spelling.. heh heh) is the American predilection for continued use of antiquated idioms in common parlance. ‘Go ahead’ is a nautical term, you’ll still see it in common parlance in such places as Liverpool (A port city). Americans tend to include this idiom when adopting a presentational style of speech. “Let’s go ahead and..” Rather than simply “Let’s….”. In the UK we value the succinct, whereas in American spoken English verbosity seems to indicate the erudite.

In British English the tolerance for the mis -applied suffix or prefix is low, whereas in America it seems a bit of a free for all. I personally think this is due to the relatively recent mixing of multi-language populations. The need to fully explain your meaning seems to have lead to the American habit of including preamble, caveat and example in everyday speech, a habit which has the average UK listener tapping their foot or rotating the wrist and thinking. Yes, yes, get on with it.

I would advise Americans coming to the UK to pay attention to subtitles in broadcast media. Notice how you may hear a foreign language spoken for several seconds (even up to minutes sometimes) and yet the subtitle includes a perfectly accurate translation using only 2 or 3 words of English.

8. I had all of my maths(!) education here in Britain, and I can’t recall ever seeing a decimal point in the middle, they’re always at the bottom to me. I would instinctively treat a dot in the middle as “dot product” though, so that doesn’t help much…

9. The problem I have with the whole metric vs imperial thing is that in daily life it doesn’t actually matter – if you’re travelling at 100kph and have 100km to go, you can figure out that’ll take you an hour just as easily as 60 miles at 60mph. There’s never really a need to convert from miles to feet or kilometers to meters. And there’s certainly never a need to convert between the systems.

I’d be fine with switching if it weren’t for two things: human height and temperature.

Unlike the rest of the metric system, Celsius doesn’t have the advantages of multiplication or division by 10, and it’s a narrower scale. Fahrenheit offers more granularity.

And for height, I think feet and inches are pretty handy. I know I’m a little under six feet tall. It’s a good division that you just don’t get with centimeters or meters.

1. Well… your arguments about feet/inches for height only make sense because you grew up with them. Ask anyone from Europe, and it’s not like they’re wandering around confused about their heigh, crying “if only I knew imperial, I’d understand how tall I am!” as they hit their heads while passing through too-short doorways.

They’re handy for you, but if you grew up with metric, you’d also think it was pretty handy for you.

And really, how often do you really need the granularity of 71 degrees vs. 72 degrees? I’d take water boiling at 100 degrees vs. 212 any day.

1. I’ll agree that it’s at least partly because I grew up with them, but if you grew up with metric, where are the divisions?

We talk about people being over or under six feet tall, and occasionally over or under five, and sometimes even over seven. I know they’re arbitrary, but by dividing height into two separate measurements, some divisions exist.

If height is measured in meters or centimeters, it’s just a continuous scale with no convenient divisions. As far as I know, metric height isn’t given in say, a round number of decimeters and the remainder in centimeters, right? Maybe that’s all that’s needed to provide similar break points. (Possibly a little TOO granular, though, with a decimeter being about 4 inches.)

And honestly, it doesn’t really matter to me what the number is when water boils – when I see bubbles, I put the pasta in. 🙂

1. Six feet is pretty close to 180cm. If you need distinctions, that’s a pretty simple one.

Also, I should note that you’ve contradicted yourself a little here: You prefer Fahrenheit because of its decreased granularity, but prefer feet/in because of its increased? Isn’t that a little strange?

Are you sure you don’t just prefer these because you grew up with them, and are providing post-hoc justifications? 🙂

2. Sorry, can’t nest threads any deeper than this…

I prefer Fahrenheit because of its increased granularity. There’s MORE detail in Fahrenheit than Celsius.

3. Yes, but that’s the opposite of your reason for preferring feet and inches, which was my point 🙂

4. I’m still not seeing a contradiction, I think because I like the two measurements for different reasons.

Fahrenheit I prefer because there are more degrees. Maybe it’s to do with where I live, too – our temperatures range from usually about 10 to about 100, which would be about -10 to 37 in Celsius. If I lived in a place with a narrower range in the first place, maybe I wouldn’t care as much. 🙂

Feet and inches I prefer because there are well defined divisions due to the use of two units. You could do the same with decimeters and centimeters, too, but as far as I know, people don’t. (I assume the “Wow, they’re really tall!” point is 2 meters? What’s the “Wow, they’re really short!” point?)

Maybe that’s the difference. Americans are more into classifying and grouping people. 🙂

2. Emma says:

1.5m is really short

2. Roy says:

Celsius is not part of the base units of the metric (SI) system. The base unit for temperature is Kelvin, which I believe is used in both US and UK, just not among so much by “commoners”. Regarding Celsius, I find it quite logical that 0 deg C is the freezing point of water, and 100 deg C is the boiling point. Body temperature around 37,4 deg C (Celsius can be just as acurate) is just an arbitrary value that “everyone” knows. I acknowkedge though that this is just a personal preference, and I would never bake my pizza in a 437 degree oven.

3. The place where the metric vs imperial difference really does matter, in daily life too, isn’t conversion between the two: it’s in conversions within them. If I do arithmetic with quantities and even moderately big numbers, I have to change units and invoke the correct conversion factor. In metric, this is always trivial. With imperial, as a child, I had to memorise 18 different units of length between a third of a millimetre and two km, with diverse conversion factors between them and no rhyme or reason to the naming or the ratios. With metric, all lengths are just various quantifiers modifying metre; and the same quantifiers are used to modify other quantities, vastly reducing the mnemonic price of the system. In contrast, with imperial, I had to learn a plethora of names and conversion factors for each type of quantity, all independent, all essentially arbitrary. Inflicting all that tedious memorisation on young minds is a vast waste of time and effort, both for them and for their teachers; and making it a prerequisite of other studies is a wanton impediment to learning. (For when I need to interact with archaic units, I now have software to do the conversions …)

As to the “higher granularity” of Fahrenheit: the temperature I most often care about is that of my immediate environment; and any precision finer than that of Kelvin (shared with Celsius, a.k.a. Centigrade) is illusory. The thermometer at my bedroom window reports (to tenths of a Kelvin) a value; but by the time I emerge onto the street 10m below the morning has warmed and I’m in a different part of the street’s air-flow, with a different ambient temperature. So finer granularity than about a Kelvin is of little use to me. Meanwhile, having freezing be where the temperature changes sign makes plenty of sense to me – but then, I live in Norway, where the winters are long and cold, and I ride a bicycle to and from work. When the temperatures drop down to single digits in autumn, I want warmer clothes; when they flip sign, that matters, but I don’t need the *really* warm clothes until we get back up to two digits again.

For “dividing height” at “convenient divisions” – you only find those divisions convenient because they’re what you’ve grown up with (like I did). The light nanosecond (or foot) is about 30 cm anyway, so you can classify just fine in metric, if you care to. In any case, such divisions are an artificial discretisation imposed on a genuinely continuum quantity; if you’re going to classify, it’d make more sense to set the boundaries at positions specified in terms of statistics of your population; since those shall vary between populations, it’s best to not use them as the actual units, but use some other unit, measure them in terms of it and classify with respect to the measured data (which you can do in any system).

By the way, the reason for UK and US pints and gallons differing is that, back in about 1700, when UK law was standardising units, the diversity of “gallon” units – between different trades, towns and individual practitioners – presented practical difficulties too great to eliminate all of the diversity. They got rid of all but two: the “wine gallon” (of 231 cubic inches), also called a “Winchester gallon”, and the “beer gallon” (the volume of 10 lb of water). Both survived in use until after various trans-atlantic colonies cast off the inept rule of the home country (thereby helping it to learn how to do at least some things less ineptly); since then, the UK has settled on the beer gallon while the US has settled on the (smaller) wine gallon. Both divide the gallon in eight to get pints; but they sub-divide the pint by different factors to get their fluid ounces *almost* equal (the US pint/16 is a 4% bigger; the UK pint/20 is (because 10 lb = 8*20 oz) the volume of one ounce of water).

10. Mathnerd says:

the singular of indices is index….

11. vigneshv0408 says:

To be fair to the British, 5 day cricket is the least common version of cricket these days. The game has gotten a lot shorter but the shorter formats (the ones that end in < 6 hours and never ends in a draw/tie) are wildly unheard of in America.

Great post as always! 🙂

12. Joseph says:

Saying “indice” (in-di-see) instead of “index” is horribly bad, indeed. But we Americans are no better; I often hear my math students say “matrice” instead of “matrix”, and “vertice” instead of “vertex”. I think this one’s a draw.

1. Roy says:

That is weird. In my linear algebra books, they use the words matrix and matrices, and in my 3D graphics books the words index, indexes/indices, vertex, vertices. All the books are from the USA.

2. Emma says:

We British don’t accept ‘indice’. Students say it but it isn’t right, it’s not in textbooks or dictionaries.
I think the Pythagoras example is the same; we say ‘Pythagoras’ as (slightly lazy) short-hand for Pythagoras’ theorum.
Just to screw with your minds, the Oxford University exams, which are highly British (and include dressing up in a special exam uniform called sub-fusc) are supervised by Proctors.

13. I was also going to suggest PEMDAS vs. BIMDAS. I give a slight edge to the British, as spelling the plural word “brackets” is a whole lot easier than spelling “parentheses.”

Another difference in nomenclature is GCD (greatest common divisor) vs. HCF (highest common factor); I would declare this a draw.

1. Ronald Lohse says:

Haven’t heard of either. I do refer to the GCF, the greatest common factor. But not the GCD nor the HCF.

2. Roy says:

Oh dear, I use parentheses (), brackets [], and curly braces {}.

1. Jonathon Dough says:

Only learned this recently when my romanian friend got on my nerves about using brackets for everything.

round brackets = ()
curly brackets = {}
square brackets []

Oh dear …

14. Zed, by the way, is an abbreviated form of zeta.

15. Chris McClain says:

Can we please invent a new symbol for multiplication of two numbers? It is a pain to help students “unlearn” the use of “x”, the dot is often written poorly or lost in writing, and the use of parentheses to allow for omission has unfortunately convinced students that parentheses are a symbol for multiplication. Let’s adopt a new symbol!

1. Chris McClain says:

I’d even accept the tensor product symbol of a circled x as a new symbol for numerical multiplication.

2. Emma says:

I used a filled in circle for multiplication and a dot for a decimal point.

Also, good maths teachers should teach the curly x as soon as they introduce letters for variables.

3. Brian says:

As a former developer (programmer), I typically use the asterisk (*) for multiplication. Several programming languages use it and it just carried over. I suspect that needing a non-ambiguous symbol was the reason there, too.

16. I have two more that have struck me this year as an American following some British “maths” teachers on Twitter.

1) Suppose you are solving these two equations to find the x and y values that make both equations true:

x + 2y = 8
y = 2x – 6

British: you’re trying to find the values that make them simultaneously true, so this is a simultaneous equations problem.
American: this is a systems of equations problem because… um… because… you need a system to solve it?

What the heck, American math teachers? This topic didn’t freak kids out enough, so we needed to give it a big scary nonsensical name?

Winner: UK.

2) Studying units and unit conversion in the US may be more of a pain, as outlined above, but at least we get to call it measurement. I just cannot imagine why British educators would agree to talk to pre-teens and adolescents about something called mensuration. That is just setting those poor teachers up for a really bad day.

Winner: US.

I am having a sudden flashback to when I was 20 and spent the summer working in a chemical factory in West Bromwich (near Birmingham) and I asked someone where they kept this product:
http://www.flinnsci.com/store/Scripts/prodView.asp?idproduct=14056
which we routinely talked about in American labs without batting an eye. My British coworkers just about expired from laughing so hard.

1. Oh yeah! That and PEMDAS vs. BIDMAS/BODMAS/NO MAS POR FAVOR.

I’ll try to add ’em tomorrow!

17. Leo says:

My take as an Italian:
1) At least you have a common abbreviation, “matematica” is quite the mouthful. However, I must admit that “mate” (mah-teh, not your best companion) isn’t unheard of, but only between students and basically only when messaging.
2) “Zeta” has a cool ring to it, believe me.
3) Bottom, what’s wrong with you guys? Why would you put that in the middle? Also, since high school, we’re taught to use the dot to multiply.
4) “Trapezio” is way better, in my humble opinion. However “trapezoide”, as in “trapezio”-like exists, so I’ll side with the British here.
5) “Notazione scientifica”, which I think you might guess it means “scientific notation”.
6) “Esponenti”, once again, with ‘murica.
7) Too much of a language stuff, but we use “ripetere” (repeat) for “study for a test” and “controllare” (to check) for a writing.
8) … (I want to meet the guy who thought of imperial, that’s way too crazy)
9) “Teorema di Pitagora”, I’m sure you can guess who we are with.
11) Ok, so, now it comes to the strange stuff. We call those “parentesi” (both for singular and plural), however those specific ones we call “parentesi tonde” (round parentheses), then [] are “parentesi quadre” (square parentheses) and {} are “parentesi graffe” (don’t ask me what it means). However, out of middle school many just drop quadre and graffe and go with tonde even when we have parentheses inside of parentheses [middle school ex.: {2[5x(4b)]}; high school ex.: (2(5x(4b)))].
12) Ah, no particular name, just our “professore”.

1. I think that braces {} are called graffe because they look like they clamp (graffare) their contents, or because they look like clips (also graffe). In French and Dutch they are accolades, embraces, a variant of the same idea; in Spanish llaves and in Portuguese chaves, keys, presumably from the shape.

18. Many years ago I tried to coin “surdation” to mean that operation which is to exponentiation as division is to multiplication (that is to say, exponentiation with a reciprocal exponent.)

Somehow I don’t see “radicalisation” as a serious proposal…

(BTW, with regard to the blog post as a whole, I can, being Australian, take a relaxed attitude.)

19. NickT says:

For dates, even as an American, I prefer 22 May 2015. Why “we” ever thought that the “least significant” part of the date should go in the middle makes no sense. However, my real preference is for 20150522, so that I can simply sort lexicographically.

1. Americans put the date in the middle (as Britons once did) because that’s the usual order of saying a date in words: July fourth, seventeen seventy-six.

1. Only we don’t say it that way in Australia (not sure about Britain). We say “The fourth of July”.

2. Emma says:

Fantastically US-centric, in the UK we would more commonly say fifth of November, sixteen oh five

1. yes always day month year since primary school, even through military service, it’s so confusing when there are low numbers in a date as you have to check if it’s from English or American background unless both day and month are the same, 2/2/1999, 5/5/2011.

2. Mick says:

Or if the Day is above 12

20. Mark Goldman says:

Your description of “zed” as the onion ring in an order of french fries is a fantastic, poetic image and almost convinced me the UK won that battle. BUT you forgot something critically important: “zed” ruins the lovely rhyme to end the alphabet song! The swinging syncopation, internal rhyme and graceful closure of
“tee you veeeee
double you ex [pause]
why and zeeeee”

would clunk to a crash landing if you sang “why and ZED.” Yuch! Sounds like you clinked your head while singing. If they sing it that way in the UK, I bet it makes the little children cry.

USA WINS!!!

1. Mark Goldman says:

2. Emma says:

We have a different song [similar words] that works with a zed.

21. Kelly says:

I am a french Canadian math teacher. Sort of related but thought you might think it interesting. I like to say for fractions such as 2/3 or 4/5 2 ‘on’ 3 and 4 ‘on’ 5. My students make fun of me (english students) but the 2 is sitting ON the 3 !!!

22. Himanshu says:

As an Indian student, what I want to say is that we receive the best of (or sometimes the worst of) both worlds. In a country where you find Feynman’s lectures on physics and Oxford english dictionary in the same desk, what else do you expect? Here one makes every attempt to get a distinct edge over the other owing to the intense competition for the limited number of higher education opportunities and hence, just for that distinct edge we are bound to engulf as many good books as possible. We are quite familiar to both British and American writers right from junior high school. As such, we are comfortable with both ‘factoring’ and ‘factoris(z)ing’ , both parentheses and brackets , both radicals and surds, both exponents and indices, both scientific notation and standard form. And so far the metric vs imperial systems are concerned, any mathematics or physics student who make it to the graduate level is comfortable with both the systems. And we are also taught the differences between American and British English right after we complete a few years of primary education. So, in spite of starting kindergarten with ‘zed’ we learn to get comfortable with ‘zee’. However, we are monitored by invigilators and we review our essays, revise for tests.

23. Eric Smith says:

I’d like to point out that there are 3 feet in a yard.
5 1/2 yards to a rod,
40 rods to a furlong,
8 furlongs to a mile,
and
3 miles to a league.
If you end up reading any old literature, particularly involving ships – this might help.

24. I have to say that when I came from Romania to Uk to study the most annoying thing for me was the decimal notation. It took me ages to understand that teacher were referring to 3 point 50 and not 3 multiplied by 50. I still do not understand why the dot is in the middle…
Anyway, the post is really funny 😛

25. Here’s a little poem by Lewis Carroll (a British mathematical logician, of course) featuring two of your favorite terms:

Yet what are all such gaieties to me,
Whose thoughts are full of indices and surds?
x^2 + 7x + 53
= 11/3

(It’s a riddle whose solution is quadratic.)

26. quintopia1 says:

Both sides lose on the order of operations mnemonic. PEMDAS is just as terrible as BIDMAS or any of the others. Have you taken a stand against them all yet?

27. An Australian perspective.

math vs maths:
Australians tend to be protective of “maths”. For me, it’s because in our accent, where vowels are very soft, it feels like there’s no end to the word, so you might as well be saying “mah”. Plus lots of other school subjects finish with a hard sound (“physics”, “english”, “science”) so it’s nice to end the word for our subject with a bit of force to be noticed in such a list.

zee vs zed:
Most of us say zed, unless we’re singing the alphabet, then it’s zee, because of years of conditioning through watching Sesame Street. I prefer zed and still sing zed even though I know it doesn’t rhyme. Suck that Bert.

decimal points:
As far as I can tell, most people in Australia simply don’t care. I think we lean towards dot at the bottom but only because of typing on a computer. As to the multiplication sign, I use it all the time, but perhaps that’s because many of my students haven’t done high school algebra and the dot freaks them out. Sometimes I think we should all start using an asterisk, since that’s what you use when typing on a computer anyway.

trapezoid vs trapezium:
Everyone here uses trapezium — it’s just fancier-sounding, especially when your daughter at kindergarten says her favourite shape is a trapezium. Another thing that grates me is “cuboid”. It perfectly describes the thing it describes, but somehow just sounds weird. Here in Australia we call it a “rectangular prism”,.

scientific notation vs standard form:
Before reading this, I had never ever heard this called standard form. How bizarre.

exponents vs indices:
Oh my yes the horror of the indice, and it’s much more common friend the matrice! Though I can hardly expect anything better in a land where the plural of “you” is “yous”. As to the preferred terminology, well most of us just call them “powers” — you do say “two to the power of five” after all. Textbooks still list the “index laws” though. Most of us tell students about all the terminologies, just to be safe.

revise vs review:
To be honest I’ve never thought about it at all. In Australia they’re pretty much interchangeable, and most of the time we’ll just say “edit” and “study”. Revise and review sound so formal!

imperial vs metric:
Get with it USA. Honestly. Interestingly in Australia lots of people still state their height in feet (if they know their own height at all that is, which is rare). Also, we’ll use imperial in language when we want to be imprecise or poetic: “But that’s miles away!”, “I could drink gallons!”, “We’re inching along”.

pythagorean theorem vs Pythagoras:
We never ever call it “the Pythagorean theorem”, but instead “Pythagoras’s Theorem”. I like that it explicitly belongs to someone. Often we will day just “Pythagoras” for short like the Brits do. We’ll do that for lots of things though. For example, we won’t say “by Rolle’s theorem” in calculus, but simply “by Rolle”. I kind of like the idea that it’s the person who asserts this truth for us.

Most people here have never heard of radicals, and at school we call them surds. I like surd. It has no meaning outside maths and therefore sounds like a nonsense word.

parentheses vs brackets
Australians are way to lazy to call them parentheses! And yes we’ll call all of the shapes brackets. If we want to distinguish we’ll call them “round brackets”, “square brackets” and “curly brackets”. I quite like this approach to things, considering that all the shapes are doing the same general job of holding things in.

proctors vs invigilators
I had never heard the word proctor in my life before reading this. What a meaningless word! Invigilator has inside it a description of what the person is doing at least!

factoring vs factorising
We say factorising here in Australia, and I reckon it’s because verbing nouns is not the sort of thing most Australians are comfortable with!

pedmas vs bodmas/bidmas
The most common acronym here in Australia is BEDMAS. What I hate is how people here refer to it as if it’s a thing in its own right rather than a mnemonic. Teachers and students here will say “just use BEDMAS”. The horror! Interestingly, my school teachers never gave us an acronym at all, and just called it “the order of operations”. And I agree with their approach wholeheartedly.

AND ONE EXTRA
What’s with the practice of calling things “Algebra I” and “Algebra II” as if anyone has the slightest clue what topics they might contain? And what the hell is “Precalculus”? Just list the topics, people!

28. Emma says:

Also forth vs quarter for 1/4.

Forth (Fourth?) wouldn’t work in the UK as it is already too busy being a river and used as in ‘go forth and multiply.’
Quarters is already used as a portion (e.g. living quarters of a house or military base or the Jewellery Quarter of a city); and is a great nod to the Latin roots of our language(s). I only wish we had more special fractions (Octer and Septer anyone?)

1. Americans use both “fourth” and “quarter,” with a preference for the latter. Do Brits really never say “fourth”? Didn’t realize that was regional.

1. Emma says:

Nope, I’ve never heard a Brit use it. I worked it out from context the first time I heard it but thought it was an error rather than someone else’s right way.

1. Ken Maltby says:

Why do you think Americans use the term quarter for 25 cents – because it’s a quarter of a dollar. SO even you guys use it. The term a ‘fourth’ is never used for the fraction 1/4

2. only in the last quarter which would be a whole so not realy

“exam papers” in the US, “scripts” in the UK; “marking” in the UK, “grading” in the US.

30. Factorising? Never heard of it like that. I’ve always been used to factoring.

As a Canadian who has been to two different universities in Ontario, my undergraduate university had “proctors”. When I went to graduate school at a different university, they called them “invigilators”. I am not sure if it is a US or UK thing. Is it a Canadian thing?? (Who knows?)

31. I came here after googling to see if there was a difference between standard form and scientific notation, to find they are the same thing. For some reason I use the term standard form mostly, but I think in Australia scientific notation is the standard term.

Also, we just have exam supervisors now, rather than proctors or invigilators. The term proctor is never used, but invigilator sometimes.

32. Came here to find out why my students are confused by my multiplication and decimal dots. Now I am wondering how they learn ANYTHING from me!

33. MaryAnn says:

I really appreciate this post! I’ve an American in the beginning of my first year teaching IB mathS… and had a mini panic attack when my supervisor mentioned surds! Like… what? and “metre” ?? slope vs gradient?? practise ??

34. Bob Brenchley says:

Hi, very good article, to which I would like to add a little of my past experiance (I’m 62 years old by the way, so experiance goes way back).
First, mathmatics is a plural noun so ‘maths’ is more correct.
The decimal point. I was taught to write it in the middle, but typewriters/wordprocessors and the computers did not have the ‘middle dot’ so the convention moved it lower. I can remember back in the 60s typing a paper where every time I needed the decimal point I wouls adjust the typewriter down half a line to get the mid-point decimal – hard work I recall 🙂
I’ve always used Scientific Notation and exponents, but then I am a scientist.
I’m old enough to have been taught almost exclusively in feet and inches, pounds and stones, pints and gallons (but not cups, that rarely gets used as a messure in the UK even when cooking). I can work in metric but still think in imperial.
Never used the term ‘surd’, not ever.

Ok. Dates written as just numbers should use the internationa for YYYY/MM/DD because this makes sorting into date order soooooo much easier.

And finally ‘ize’, preferred in the US and preferred by the Oxford University Press (publishers of the Oxford English Dictionary) and by me (I published magazines for many years and my house style was always ‘ize’. (see https://en.wikipedia.org/wiki/Oxford_spelling). Until about 10 years ago the BBC used ‘ize’ while commercial broadcasters used ‘ise’. These days the BBC have dumbed down and now use ‘ise’ as well.

Sorry to take up so much space 🙂

Bob.

1. my big bugbear about the differences in UK and US liquid measurements is in the volume of a pint! the british gallon is 1/5th more than the American gallon I think some poor American teacher forgot that 20 fluid ounces go into an imperial pint!

35. Sameer says:

Nice article. I am from India and we tend to stick to British English more often than not.

I want you to add 1 more point to this post. And, that’s none other than the term “billion”.

American English takes it as “a thousand million” (10^9) while British take it as “a million million” (10^12).

I would like to know the winner in this case who could be a “billion”aire 😁

36. Very nice article… I put myself here as a student in an English school (but born as a Japanese; actually until the age of 11 I was a native Japanese pupil). I have been interested, and also irritated, by the difference between British English and American English, especially because our [Japanese] English textbooks strongly adhere to the, to quote their words, “more common” American English. Based on that, I would be interested in adding a couple of points for you to argue which one is “better”.

The reference the number “0” other than “zero”: would you prefer “ou” or “nought”?
The reference to the notation used to mark complement sets or derivative functions: would you prefer “dash” or “prime”?
The reference to the numbers marked with their positive/negative signs: would you prefer “directed” or “signed” numbers?
The reference to the largest number that can divide all numbers, in a certain set of integers, with no remainders: would you prefer “GCF” or “HCF”?
The full name of the term “LCM”: would you prefer “Lowest” or “Least” Common Multiple?

Also, for this one, I’m not even sure whether this is an American/British thing, but what’s with the tradition of referring to the fact of an integer being a factor of another integer as “this GOES INTO that” (e.g. “2 goes into 6”)? My classmates, almost every time, use this terminology, and I get really frustrated by the inaccuracy of the expression, just trying to imagine the picture of a number “going into” another.

Anyway, thank you for bothering to read this comment.

37. Anon says:

Math vs Maths. As a Maths teacher from England I went to Chicago to apply for a job. In the education department they asked me what “Math” I teach. I said I could teach anything. They repeated “No, what Math are you specialised to teach in class: Algebra, Geometry, Calculus? What?”

That’s when I realised why the Americans use “Math”. Teachers are given one specialised area to teach, and they teach it again and again and again…

In the UK, teachers mix the different “Maths” in the same year group, we try to keep it fresh with constant rotation between the disciplines.

UK wins on that one.

38. Shannon Wentworth says:

I love this! I am also an American living in Birmingham England. There are so many more differences than I had expected.

39. Sally says:

In the UK we do not put the decimal point in the centre.

1. Exactly! I don’t know where they got that from. I was just about to comment about it.

1. I think it’s a generational thing. When I taught in the UK, our textbooks (by Rayner) did the notation that way, and so did my colleagues aged 50+. Colleagues in their 30s/40s seemed to recognize it but considered it old-fashioned. In other words, the UK seems to have moved in the last generation to adopt the US convention.

40. As someone who is doing A Level mathematics in England, I don’t understand how people can get confused by some of these things. First of all the decimal point. I don’t know whether or not you were comparing where the point is placed or whether it is a decimal point or a multiplication sign. I for one have never seen the decimal point in the middle and if you have it is probably just a student with terrible handwritting. We also hardly ever use the dot as a multiplication sign and I’ve only just seen it when my teacher was teaching us the product,chain and quotient rules. We mainly use the x and we don’t get that confused with the variable x because they are written differently (the variable x is like two c s back to back). I have also never in my life heard of BIMDAS or BEDMAS. We learn exponents and indicies. We learn the rules of indicies and continue to call them indicies up until we learn about exponentials and logarithms in A level maths so it depends on what type of problem we’re solving. I have to agree with you on standard form though it just doesn’t make sense but neither does scientific notation as mathematicians and engineers also use it. 🙂

41. Paul says:

I am an American, and I really like the word “cuboid”. I use it all the time now.

1. as an extension to my last, using the letter “x” as an algebraic expression is like cursive handwriting “Tl” to represent pi. It’s just wrong.

As for “indice”, I have absolutely never heard that said. Index singular, indices plural.
– The index of a number says how many times to use the number in a multiplication – that’s the actual mathematical definition of index. So using index/indices is the correct form also, used since the 14th century (origin: latin “indicis”). Far before the USA bastardised the English language.

42. As an Australian scientist with children attending Elementary school in the US what drives me mad is when my children don’t use AND before the tenths place when saying a number out loud. 132 becomes “one hundred thirty two” which it is, but sounds so awkward to my ears. In Australia we would say “One hundred AND thirty two”. Now this is where it gets really terrible. My third grader came home and told me they are not allowed to say AND because that means a decimal point. Seriously? And cannot mean both in addition (ADD) and a decimal point. So they are learning that 132.18 is “one hundrend thirty two AND eighteen”. Really? If they said that number to any reasonable person, they would wonder why they didnt just say 150. In my understanding 132.18 should be described as one hundred and thirty two POINT one eight. The numbers that come after the decimal point are not a whole number and should not be referred to as such. So my kids get taught the American way at school, and then re-taught the far less confusing way at home.

I am still wondering why a decimal point cannot simply be a point.

43. Lisa Bickford says:

I arrived at this post in trying to find out where the UK stands on a difference I just discovered between definitions in Geometry in Costa Rica and US. A circle, as I learned it in the USA, is the set of all points equidistant from a given point, its center. The circumference is a measure of distance around the perimeter of the circle. In Costa Rica, material produced by the University defines a ‘cirfunferencia’ (clearly a cognate for circumference) as the set of all points equidistant from a given point, and a ‘circulo’ (a cognate for circle) as the set of points in a ‘circunferencia’ and all interior points. Does anyone know how the rest of the world falls in these definitions?

44. A UK cabinet minister in the 1960s, IIRC, remarked that Britain was “inching towards metrication”. The country still has a way to go, but each new generation gets more used to the metric and regards the antiquated mess more as a stupidity of the old.

I suspect you’ve misunderstood some of the unfamiliar (to you) usage of the UK, although it’s possible some perverse usages have crept in since I left school, two thirds of my life ago.

(Using ^ to denote superscripts, as in TeX.) If x^y is used to express “x to the power y” (as in your 2^5 = 2*2*2*2*2 picture), I would call y an exponent; but if x^i is used to denote the i-th component of a vector x, then I would call it an index. No exponentiation is involved in the latter; it just happens to use a notation that looks the same. I would also refer to a subscript used for indexing (this is the more usual convention, outside theoretical physics) as an index.

I type most of my numbers these days; and software has followed the USAish habit of putting the decimal point down below, so that’s where I’m used to it. I suspect I used a mid-dot for decimal point when I was a student, though; and would use a low-dot to mean multiplication. In practice, in what I type (where a middot is hard), I use the typed low dot for both jobs; and I take care to separate numbers, e.g. (2).(3) to avoid 2.3. Numbers at the ends of sentences also get tricky.

I would revise for a test *and* revise my work. If I were reviewing my work, that would be when I’m reading it through – which might lead me to revise it, if I found fault with it. In the course of revising for a test, I would review the subject matter to be tested.

I imagine I was taught to use the word “surd” when young, and I may also have met “radical”, but I’d just say “root” normally, with “square” usually being implicit, if not over-ridden, as in “cube root”.

I have no memory of any acronym that was supposed to help me remember to evaluate multiplicative sub-expressions before additive ones. There may have been such a thing when I was young, but the rule was soon enough so natural that I threw away the cumbersome crutch.
Rather like SOHCAHTOA; I recognise it, and can decode it, but never use it; the diagram is there in my head.

Meanwhile, why has USAish lately developed the habit of adding “of” after “outside” and in various other places where I’ve never seen a need for it ? The outside of an object is its outer surface; but objects not within the space it encloses and occupies are simply outside it. The inside of a box is the region it contains; things in that space are inside the box.

1. In the U.S., our grandfathers beat people, our fathers beat up people (or beat people up), and we beat up on people. Hopefully our children will be able to avoid all these activities.