Do the math:

There are actually two answers to this question.

First, “maths” looks plural and is preferred by some because “mathematics” is plural. The problem with that is “mathematics” is no more plural than “physics” or any other compound noun. It is a rational sounding utterly incorrect argument. If we said “mathematics are cool” then there might be a case. But we say “mathematics is cool.”

Second, some people say maths and some people say math, and that’s how language works. That is a valid argument, but if you are walking around in the US saying “maths” instead of “math” be aware that you are demonstrating an anglophile affection, which is fine, as long as you know you are doing it. Please remember to demonstrate other anglophile affections such as referring to “English Muffins” and “Crumpets” and telling your friend “I’ll knock you up in the morning” when you merely intend to come by to walk to work together. Most importantly, if you have switched to “maths” from “math” because of some rational argument you once heard, just know there isn’t a rational argument. It is just a matter of usage. It is arbitrary. There is no readon. And if you are in the US you are using the non-standard usage. If you are in England or somewhere fine, talk funny all you want!

ADDED:

The conversation about “knocking up” has developed here, on Facebook and on Twitter. Interestingly a lot of Brits claim this is simply not a thing Brits say, yet it is. It may simply be patchy in its use, but it really is a British saying. More so than an English Muffin being a Crumpet (I know it is not, but I do love the reaction to the comparison among the Crumpet Sympathizers). Anyway, “I’ll Knock You Up” is defined in many places, and used by many Brits, to mean to rouse, wake up, call on, etc. another person. In American English, it means to make pregnant. In at least some forms of British, when does not “get pregnant” but one “fall’s pregnant” and if one chooses one might have the baby in the hospital, in America, or in hospital, in British-English areas.

Anyway, here’s the Google Ngram for various uses of “knocked”:

Comments

  1. #1 Brainstorms
    August 21, 2014

    Funny, sure, but if I told my female colleague that I’ll “knock her up in the morning”, she’s liable to to slap me or, worse, file a sexual harassment complaint — in America, that is.

    (And it’s “female colleague”, not “woman colleague” — but that’s usage, right? :^)

  2. #2 Sou
    Australia
    August 21, 2014

    20.

    Back decades ago before Americans knew where Australia was, I spent some time in your wonderful country. People used to come up to me, just so they could hear me speak. I figure they liked my accent. Or they could have been quietly laughing at it :) (Some were surprised at how well I understood English.)

    Anyway, math sounds uneducated to my ear, but not so much as it used to back in the 1970s, what with television and later the internet removing cultural barriers.

    I’ll stick with maths.

  3. #3 Brainstorms
    August 21, 2014

    Sou, I doubt they were laughing at you. To an American ear, the Aussie accent sounds beguilingly euphonic. (Just as nice as the people there.) I can’t wait to go back…

  4. #4 Greg Laden
    August 21, 2014

    Brain: You’ll notice that in my construction of knocking up, I used absolutely no reference to gender!

    If I was British I’d say “knock up the old girl” or something like that.

    Sou, do Americans now know where Australia is?

  5. #5 James
    Virginia, USA
    August 21, 2014

    Greg: What is the term you use for the items that I call “English Muffins”? I was unaware that there was any other term.

    I refer, of course, to the fork-split Thomas’ English Muffins I grew up with here in Virginia.

  6. #6 James
    August 21, 2014

    Sou: When my wife was studying abroad in London, people assumed she was Australian. I don’t think it was an accent thing. They just couldn’t believe she was American, as she was too polite. Somehow, that only left Australia.

  7. #7 cosmicomics
    Denmark
    August 21, 2014

    Math or Maths?
    BEST ANSWER
    As is well known, sometimes British and American usage, spelling, and vocabulary differ. This is one of those cases. In British English maths is the accepted term. In American English, math.

    Also, I think it makes sense to distinguish between arithmetic and math. The above example, involving addition, subtraction, and multiplication is arithmetic. I can do that. But show me an equation and I’ll curl up into a ball and cry.

  8. #8 cosmicomics
    Denmark
    August 21, 2014

    James –
    It is “an accent thing.” The difference between British and Australian pronunciation is not subtle.

  9. #9 Michael Kelsey
    SLAC National Accelerator Laboratory
    August 21, 2014

    @Greg: I believe the word you were looking for (twice) is “affectation”. Anglophile affectation is considered quite acceptable behaviour in some parts of this country (as well as in our dear neighbour to the north).

    “Anglophile affection” is almost trivially redundant, in the same way that “The La Brea Tar Pits” is :-)

  10. #10 Greg Laden
    August 21, 2014

    James: Here is a good argument for them being different:

    http://www.thekitchn.com/whats-the-difference-crumpets-113577

    But everything in that blog post can be used as an argument for them being the same, with variation within the category.

  11. #11 Greg Laden
    August 21, 2014

    Michael, affectation is the correct word to use there if one likes, but affection is “the act or process of affecting or being affected” so I use it sometimes. But with affection!

    I suppose I could go for even less ink and just us “affect”

  12. #12 John Russell
    UK
    August 21, 2014

    So an American who says “alloominum” , “nooclear” and “processeese”—for example—has the temerity to say we English talk “funny”? Offence taken.

  13. #13 Brainstorms
    August 21, 2014

    John, I think *we’re* funny for claming to speak English. You might, but over here we speak “American”.

    (I’ve always noted that Hispanics in this hemisphere speak “Spanish”, whereas most residents of Spain speak Castillian… They’re just as different.)

  14. #14 BBD
    August 21, 2014

    Okay, we know that UK usage is maths (I’m a Brit) and we know US usage is math. No problem with that.

    But nobody of my acquaintance (see what I did there?) says ‘I’ll knock you up in the morning’. That would be an affectation and anachronistic to boot.

    ;-)

  15. #15 Greg Laden
    August 21, 2014

    “processeese” is a clear affectation, or mispronunciation, that kinda got out of hand.

  16. #16 DAVID DOMKE
    United States
    August 21, 2014

    20 or320

  17. #17 Richard Simons
    August 21, 2014

    When my mother sampled one she said it was a bit like a stottie cake (Newcastle area) but in 35 years or so in Britain I never came across what is called an ‘English muffin’ in the US and Canada. Any suggestions?

  18. #18 Greg Laden
    August 21, 2014

    It is basically a Crumpet. I’ve eaten them side by side. Pretty darn similar.

  19. #19 jyyh
    Finland
    August 21, 2014

    There are two kinds of maths, says Greg Laden, :-).

    the treatment of infinity divides the two, to one with a discrete boundary value and the second where infinity is not a number. There is one that imagines imaginary number

    There are three kinds of maths:
    There is one that imagines imaginary number and
    There are those who treat the infinity differently from each other. And there is one that believes space is curved so trigonometry transforms to a boundary value problem

    There are four kinds of maths.

    I firmly believe one could add several more here. Maybe one even at the beginning, ‘the math that doesn’t believe in non-existence and negative values’.

  20. #20 Louise
    England
    August 22, 2014

    When my mother was a child (1930s) people in her area employed a Knocker Upper to wake them. He had a very long pole with wires on the end that he would rattle on the windows. This was Oldham, Lancashire and most didn’t own alarm clocks

  21. #21 Nathan Tetlaw
    August 22, 2014

    Wondering about the ‘Maths is plural claim’

    I always thought the word ‘maths’ was a contraction of Mathematics, rather than preserving the plural.

    I am Australian though, so perhaps we see it upside down or something :)

  22. #22 PZis Khan, king of MongoliA+
    August 22, 2014

    Sup tool? Teh maths answer = 20. Nathan Tetlaw wins today: contraction doesn’t imply a plural item. Lurk moar, lardo.

    >OP is american, sarcastically asks if americans know where Australia is
    >implying OP is a retard who can’t read a map

  23. #23 proximity1
    August 22, 2014

    Weren’t both “mathematics” and “physics” first understood as plural nouns? —and didn’t that usage pre-date the advent of the British colonies in North America, let alone anything going by the name of American English language? I thought mathematics referred to arithmetic, alegbra, geometry, trigonometry, and calculus–for example.

    Now, on English language grammar and usage in general, here’s a view that people on “both sides” of the issue can either find comforting or annoying: both in Britain and in the U.S.–not to mention the rest of the Anglophone world–standards of spoken and written English are shitty and getting shittier by the year. In that indictment I include the “educated”, people with what we call “higher education,” just as much as those who’ve never completed a high-school level education; and I don’t exclude those in the professions of editing and publishing and journalism. They, too, with relatively few exceptions, have either never learned anything that even an average educated person of 100 years ago would regard as good standard English speach and writing (which is most of them) or they’ve resigned to using the commonly-seen and heard shitty English all around them–no longer objecting, if they ever did, when they hear shitty grammar.

    The grammar and usage found everyday in The Guardian or the Times or the New York Times –once regarded as models of good grammar–is shitty. Pick any news report from your own idea of the best written magazine or newspaper and I’ll show you examples of what I mean.

    Please–spare me the excuses. I’ve seen and heard them all and they’re pathetic. “Nobody speaks like that anymore!” or, a favorite, “But, but, Shakespeare (or Jane Austen) said, wrote, the same in his day, or the all-time champion excuse, “language is always evolving, there is no point in insisting on one or another example as required for good usage.” Thus, nearly everyone now uses the plural “their” instead of the singular “his”–unless, as on occasion happens, “her” happens to be the correct possessive pronoun.

    Quiz: Complete the following using pronouns rather than proper nouns (hint, do not use the names “Claire” or “Michael” in filling in the blanks.) —

    If your sister Claire is taller than your older brother Michael and you are not as tall as Michael, you should say of Michael,

    “Michael is taller than ___ but Claire is taller than ___.”

    Give your answer and, optionally and for grins, the last completed level of your formal schooling.

    ————

    I calculate the math answer to be 320.

    You’re worried about “maths” versus “math”? Very well. But reflect on the fact–as I contend it–that our entire language is now so debased that nearly everyone, educated people included, speak and write in what I consider a squalid kind of English.

  24. #24 proximity1
    August 22, 2014

    Oh, well, (now for the obligatory corrections)

    …The grammar and usage found everyday in The Guardian or the Times or the New York Times –once regarded as models of good grammar–are shitty. …

    … “But, but, Shakespeare (or Jane Austen) said, wrote, the same in his (or her) day, …

  25. #25 proximity1
    August 22, 2014

    Greg,

    English muffins are made from sourdough and crumpets aren’t. That’s the key distinction. They may look very similar but, if made properly, they should no more taste the the same than good sourdough bread should taste the same as Wonder Bread or than Scottish shortbread should taste the same as Vanilla Wafers.

  26. #26 Greg Laden
    August 22, 2014

    The texture and flavor for the two certainly overlap a lot more than the example you give, at least he crumpets and English Muffins I get at my local store! Dinner rolls with sour dough and dinner rolls made of regular dough are still dinner roles! There are a couple of other differences between crumpets and english muffins as well.

    At the very least an “English Muffin” is a version of a “Crumpet” made with someone different ingredients and a slightly different technique to get similar results, perhaps as an improvement. Or perhaps because they lost the dough culture and didn’t really know how to make them (referring here to the primordial English Muffin makers).

  27. #27 proximity1
    August 22, 2014

    See what I mean? Here’s an example taken right from your own blog—

    “Who is smarter, men or women?”

    Today, whether American or English or Australian or Canadian, whether a man or a woman, and whether one has a bachelor’s or a master’s or a doctor’s degree from Princeton or Po-dunk University or never graduated from any university, this is the way the vast majority of native English-speakers speak and write, rather than the way even an apprentice Nanny in any good home in the late 1800s or early 1900s should have put it: “Who are smarter, men or women?”

  28. #28 Greg Laden
    August 22, 2014

    “Weren’t both “mathematics” and “physics” first understood as plural nouns? —”

    The early use of the of the term for the field of study as a plural noun treated in singular form goes back to the beginning of their use (and is how they are used today) as far as I know. There are earlier field of study that were not treated this way. I don’t think it is an ancient practice. So I think you are part right about the origin of the term, but today we don’t treat the word as a plural form. Do you have examples now or from the past where it is?

  29. #29 Pete A
    UK
    August 22, 2014

    Mathematics and physics are plural nouns. Arithmetic is a branch of mathematics. These nouns are not countable e.g. there is no such thing as a mathematic therefore “Mathematics are cool” doesn’t make sense. Uncountable plural nouns are usually treated as singular nouns hence “Mathematics is cool” is valid.

    Data is also a plural (of datum) uncountable noun (a mass noun). In formal scientific usage, we write “The data are/were…”, but in common usage it’s perfectly acceptable to treat data as a singular: “The data is/was…”

    Data, mathematics, and physics are collections of items that cannot be used with the indefinite article (a or an).

    Although “forest” is a collection of trees, it is a countable noun therefore it has distinct singular and plural versions and it can be used with the indefinite article. We wouldn’t say “A collection of trees are cool” nor “Forest is/are cool”. We can say “A forest is cool” and “Forests are cool”.

    It doesn’t matter whether we use “math” or “maths” because everyone knows that they are short for mathematics. Generally, it’s best to use the term with which we are most familiar rather than to worry about pedants. The same applies to “data are” and “data is” and the usage of “data set” versus “dataset”.

    I’ve never heard the phrase “I’ll knock you up in the morning” — where did you hear this, Greg?

  30. #30 Greg Laden
    August 22, 2014

    OK, now I need a picture of an authentic Knocker Upper, with a caption.

  31. #31 proximity1
    August 22, 2014

    And one more correction of an error I missed (despite having first saw it and then, before adding it, actually failed to find it again) from my post @ 20,

    …everyone, educated people included, speaks and writes in what I consider…

    This helps me make my point about the generality of the decline in standards. None of us is immune (Or is it “None of us are immune” ?) when the general standards of practice fall so broadly. We are constantly bombarded by such poor grammar that, at length, we become insensitive to it and we adopt the common usages even when they are very wrong and, worse, confused and misleading in their consequences.

  32. #32 Greg Laden
    August 22, 2014

    This is actually grammatically correct because I’m asking about group averages not individuals.

  33. #33 Greg Laden
    August 22, 2014

    This is an area of grammar that you may need to bone up on. You’re making a fundamental mistake. It is a mistake very few people make when they speak or write, but when they inspect their own words they think they’ve made, then they typically return each to his or her own respective activities not ever really knowing if they made the mistake. But they didn’t.

  34. #34 proximity1
    August 22, 2014

    @ 28: See, from Online Etymology, this link,

    http://www.etymonline.com/index.php?term=physic&allowed_in_frame=0

    or search “physic” at the site http://www.etymonline.com

    @ 26 : …” At the very least an “English Muffin” is a version of a “Crumpet” made with someone different ingredients and a slightly different technique to get similar results.” ..

    Well, yeah, I can’t argue with that. I believe that you’re somewhere in Michigan, right? And, unless I’m mistaken, there may still be what goes by the abbreviated name of “IHOP” or, even better, a real old-fashioned mom ‘n pop breakfast diner within easy reach of you. If so, sample side by side sourdough pancakes and ordinary pancakes. You ought to be able to tell the difference blind-folded. The same is true with crumpets and english muffins.

  35. #35 proximity1
    August 22, 2014

    @ 29 : “I’ve never heard the phrase “I’ll knock you up in the morning”

    Again, from Online Etymology Dictionary–
    http://www.etymonline.com

    knock up (v.) 1660s in sense of “arouse by knocking at the door,” from knock (v.).

    and, from “Discovering Sherlock Holmes”
    http://sherlockholmes.stanford.edu?issue2.html

    “Very sorry to knock you up, Watson,” said he, “but it’s the common lot this morning. Mrs. Hudson has been knocked up, she retorted upon me, and I on you.”

    Holmes means that Mrs. Hudson woke him up, and now he is waking Watson.

    Elementary, my dear Peter.

  36. #36 symball
    uk
    August 22, 2014

    Knocker upper
    http://2.bp.blogspot.com/_VKnlNvwbGMM/S3PirpTuz9I/AAAAAAAAAis/ZbVZxliEYRk/s400/KU.jpg

    Crumpet
    http://dearloveblog.files.wordpress.com/2010/11/dsc_1301_2.jpg

    Muffin
    http://images.agoramedia.com/everydayhealth/gcms/snacks-under-100-calories-16-pg-full.jpg

    If you can’t tell the difference between a muffin and a crumpet then either you, or your baker, should be indited for crimes against food!

  37. #37 Greg Laden
    August 22, 2014

    Right, like in the pictures, they’re basically the same!

    Great picture of a knocker upper!

  38. #38 Greg Laden
    August 22, 2014

    No, not Michigan.

    Had pancakes this morning, as a mater of fact. But I’m closer to Canada than Detroit and the nearest IHOP is probably 200 miles away. We don’t have sour dough pancakes here, I’m not sure I’ve ever had one.

  39. #39 Pete A
    UK
    August 22, 2014

    @35: I wrote: “I’ve never heard the phrase”. I did not write: “I’ve never heard of the phrase”.
    I meant that I have never heard the phrase, used in practice, during my lifetime in the UK.

  40. #40 bks
    Tellus
    August 22, 2014

    In the lead graphic, what does “failed to answer this” mean: They didn’t answer or they got the wrong answer? –bks

  41. #41 Greg Laden
    August 22, 2014

    Right…. 99% of the people who look at it just never even bother to answer it!

  42. #42 George Montgomery
    August 22, 2014

    As an Australianism, “knocked up” used to mean “physically exhausted” e.g. “I knocked up trying to complete the jetty-to-jetty half-marathon and ended up walking the last kilometre.”
    I once heard an American athletics coach tell a group of Australian women 100m hurdlers to get their ‘fanny’ closer to the hurdle crossbar. He was referring to their backsides or bums, they thought he was being rude and referring to something else. Almost led to an international incident.

  43. #43 Richard Simons
    August 22, 2014

    It is basically a Crumpet. I’ve eaten them side by side. Pretty darn similar.

    The English muffins I’ve had in Canada have a very different appearance and texture from the crumpets I grew up with in Manchester, which had a rather rubbery texture (before they were toasted) and lots of vertical holes to hold the melted butter.

    My mother-in-law, when she first arrived in Canada, asked the hotel clerk to knock her up in the morning. He explained that that has a different meaning here.

    BTW: the answer is 20 unless you forget the correct order of operations (BEDMAS – brackets, exponents, divide, multiply, add, subtract).

  44. #44 Pete A
    August 23, 2014

    @43: Basic electronic calculators rely on the fact that the user understands operator precedence. I’ve noticed that some (many?) of the recent “advanced calculators” include an idiot mode to protect advanced users from their dire lack of this basic knowledge. Such things are frequently called “progress”.

  45. #45 Brainstorms
    August 23, 2014

    Years ago I got rid of any basic calculators that so “lacked progress” that they had no sense of “this basic knowledge” of arithmetic. After all, if I’m expected to know this basic knowledge of arithmetic, why shouldn’t my calculators also know it?

    In fact, every calculator I’ve used in the last 10+ years (advanced and not advanced) must be “progressive”, because they compute correctly. (However, something must be wrong, because I can’t find an “idiot mode” button on any of them!)

    I gather I must be losing out on something edifying because I can no longer lord my superior knowledge of mathematics over a poor, inferior calculator.. Nor will I be able to revel in the smug satisfaction of knowing that my less-educated neighbor will be computing the family budgets incorrectly. (Well, they might if their basic calculator that “lacks progress” also lacks that important “idiot” button.)

    All this raises another curious “maths” question: Do anti-progressives embrace other devices, technologies, and ways of thinking that lead to incorrect outcomes? What percentage will fail to answer this?

  46. #46 John Russell
    UK
    August 23, 2014

    Actually, if you google “knocker upper” and click on ‘images’ you’ll be awash with photographs of them.

    Interesting about ‘processeese’. I’ve never noticed an American say the word ‘processes’ any other way.

  47. #47 Pete A
    UK
    August 24, 2014

    Brainstorms #45 wrote: “In fact, every calculator I’ve used in the last 10+ years (advanced and not advanced) must be ‘progressive’, because they compute correctly.”

    How do you know that they compute correctly? I would guess it’s because you learnt operator precedence therefore you know how to double-check the results. It is the blind acceptance of calculated results combined with the inability to double-check using an alternative method that causes most errors. The alternative method can be as simple as a rough estimate using mental arithmetic, perhaps aided by scribbling on a piece of paper.

    It’s good that calculator technology has progressed; it’s very sad that many users of the technology do not possess the skills to use it assuredly, accurately, and consistently. The fact that 73% people failed to answer the 4’s question heading this article is appalling — it is not a sign of overall progress. Just by inspection, it ought to be completely obvious that the answer is 20. In my humble opinion, I think calculators have inadvertently replaced the need to have a fundamental understanding of arithmetic and simple mathematics.

    Who’s being superior or revelling in smug satisfaction? Certainly not me — I’m deeply saddened by the retrograde I’ve observed in basic education and fundamental knowledge over the decades (maths and science in particular). Jobs place ever increasing demands on applicants therefore having knowledge of the basics is becoming increasingly important.

  48. #48 patricia gaydar
    USA
    August 24, 2014

    i figured out the answer
    4×4=16
    16+4=20
    20×4=80
    80+4=84
    84-4=80
    80×4=320
    AND THATS HOW YOU SLOVE A MATH PROBLEM!
    Math is my favorite subject and im pretty good at it.
    You wanna give me a math problem with adding,multiplying,and subtracting with just 4’s?
    Come on, you can do better than that give me any math problem and i think i can figure it out.
    So people, GIVE ME YOUR BEST SHOT! ;)

  49. #49 Greg Laden
    August 24, 2014

    Patricia, try this one:

    1 + 1 x 3 + 4 – 8

  50. #50 patricia gaydar
    USA
    August 24, 2014

    by the way im 11 years old so if you read my last comment this is what i didnt put in. :b

  51. #51 patricia gaydar
    USA
    August 24, 2014

    ok
    1+1=2
    2×3=6
    6+4=10
    10-8=2
    What do you think i am a first grader? :/

  52. #52 patricia gaydar
    USA
    August 24, 2014

    come on people give me your best shot

  53. #53 Pete A
    UK
    August 24, 2014

    @patricia gaydar,
    Dats d sorta mafs I like, innit :-)

  54. #54 patricia gaydar
    USA
    August 24, 2014

    pete a i have no idea what your saying i mean like what the heck did you say cause i cant read that
    “dats d sorta mafs i like, innit”
    that i cant read you really messed up your words can you try typing that again

  55. #55 Pete A
    UK
    August 24, 2014

    Sorry Patricia, I had assumed that readers are familiar with Catherine Tate’s fictional character “Lauren Cooper” and the stereotypical Essex way of speaking and dealing with life:
    http://en.wikipedia.org/wiki/Lauren_Cooper

    Perhaps I should’ve simply answered Greg’s question with:
    After years of endless debate over “math”, “maths”, and “mafs”, am I bovvered? Do I look bovvered? Are you disrespecting me?

  56. #56 Obstreperous Applesauce
    August 24, 2014

    So to be correct, assuming priority of the motherland, how is it pronounced?
    ‘Marths’ or ‘moths’?

    http://m.wikihow.com/Speak-in-a-British-Accent

  57. #57 sailor
    August 24, 2014

    20. And I’ll knock you up in the morning” was a very common expression when I was young and not at all rude. But recently I have been visited by Brits a few generations younger, and told that Americanism has crept in and that would be considered very rude in this day an age. You might still get away with “I’m going to lay the table”

  58. #58 Brainstorms
    August 24, 2014

    @47:
    Pete, yes, I learned operator precedence at an early age, and that’s what I use to judge the calculators. (I also frequently use quick mental estimations as a “sanity check” for calculations.)

    Other people –provided they know about this– can look up arithmetic precedence rules in many places by various means. (Yes, we both know that they don’t, generally.)

    I fully agree with you about the problem of blind acceptance, lack of having one’s work checked, and the dismal state of education in this country.

    My point was that it’s good that calculator technology has progressed — because it helps to prevent errors (imperfect as it will ever be until the users are properly educated). What I caution against is a mindset that says that we should keep things such as calculators “dumbed down” as a means of forcing people to learn what they need to learn. (Or that we shouldn’t be making things easier in ways that remove the need to learn the how & why details.)

    It is obvious that the answer is 20. The 73% didn’t answer incorrectly (that would be sad); it’s that they refused to answer at all. (And that reveals something different, which is also sad.) So we can’t judge where we are by that figure; we would need a random sample of the population, all of whom would need to answer the question, then look at the right/wrong statistics.

    Perhaps calculators have replaced a lot of need to understand the details of arithmetic. But that doesn’t make them bad. I think a lot of those who rely on machines to generate math answers would still not make the effort to understand mathematics without them. With modern calculators, at least they have a chance to work out their family budgets correctly in any case.

    Making calculators that “don’t help the mathematically illiterate” is not the answer. Just as modern calculators that “do it all for you” are not to blame for the current percentage of math illiterates in society. (And are not increasing that percentage.)

    We need to fix the fundamental problem at its root: Poor standards of education, poor funding of education, poor attitudes towards education and teaching as a profession, and an insufficiency in getting students excited about learning something.

    We also need to recognize that not everyone is cut out to be a math whiz, most won’t need more than basic math understanding in their lives, and we don’t need to have everyone on-board with expertise in intermediate or higher mathematics. Nice if you can get it, but not realistic.

    Still, I’m just as saddened as you at the noticeable difference between what’s accepted today and what was the norm in years past as far as basic education. I think society will continue to stratify, especially as long as there’s a significant income gap (which partially drives all this).

  59. #59 Greg Laden
    August 24, 2014

    Operator precedence isn’t just rote procedure. It is married directly to some very important and deep number theory stuff that allows certain math to work the way it works.

  60. #60 Pete A
    UK
    August 25, 2014

    @58:
    Thanks for the interesting reply, Brainstorms. I agree with you.

    One thing I’d like to point out to readers is that the Windows calculator application changes its behaviour depending on the mode it is in (which can catch out those unaware of it).
    Standard: 1 + 2 x 3 = 9
    Other modes: 1 + 2 x 3 = 7
    http://en.wikipedia.org/wiki/Calculator_(Windows)

  61. #61 Greg Laden
    August 25, 2014

    OK, just so we are clear, 1 + 2 x 3 = 1 + 6 = 7 as long as these numbers are all base ten and we are doing Earthling math.

    However, if you are using a calculator you could be telling the calculator to calcualte 1 + 2 to get 3, then multiplying that by 3. Normal calcualtors that are not broken will give 7 if you enter 1, then a plus sign, then a 2, then a times sign, then a 3.

    RPN calculators use a different method of entering data, but they don’t use different math. So, if your keypresses are 1 ENTER + Enter the answer will be 1 or an error. If you then enter 2 and the “x” you will get 1 times 2 (1 in the stack, 2 in the stack, a times key, enter, multiplies the two) then enter times enter you get an error, enter 3 then = you’ll get 3. So you have to know how to do that.

  62. #62 Pete A
    UK
    August 25, 2014

    “Normal calcualtors that are not broken will give 7 if you enter 1, then a plus sign, then a 2, then a times sign, then a 3.”

    Please read the Wiki article to which I linked. The Windows calculator in Standard mode gives the result 9 using the key entry sequence you stated. The calculator is not broken, it is working in “checkbook calculator” mode (as do some other simple calculators). Note: This applies up to Windows version 7. I don’t know if the Windows 8 calculator still does this.

    Here’s a quote from the link I posted:
    “Standard mode behaves as a simple checkbook calculator; entering the sequence 6 * 4 + 12 / 4 – 4 * 5 gives the answer 25. In scientific mode, order of operations is followed while doing calculations (multiplication and division are done before addition and subtraction), which means 6 * 4 + 12 / 4 – 4 * 5 = 7.”

  63. #63 Greg Laden
    August 25, 2014

    Pete, I’m not suggesting that your characterization of the Windows 7 calculator in standard mode is wrong. I’m sure you are right.

    I am however questioning the wisdom of calling “checkbook mode” standard.

  64. #64 Brainstorms
    August 25, 2014

    Pete has a point: Very simple calculators will give 9, not 7 for “1 + 2 * 3″, and the user needs to know the limitations of the calculator, as well as precedence rules (in order to get the answer that “the math world” has agreed upon: 7).

    Those with simple calculators must do the multiplication first, then the addition. For more complex expressions, this can become prohibitively difficult without writing down intermediate results (unless the calculator is stupid but helpful and has parentheses or memory registers).

    RPN is my preferred method of using a calculator. Having the stack provides memory registers that are more visible, and which combine in evaluating expressions in a straightforward, fluid manner. No parentheses are needed, and complex expressions can be evaluated often without resorting to memory registers (since the stack provides this function); order of evaluation is generally flexible as well. But one *does* need to know precedence to get the “correct” answer!

    Greg, on HP RPN calculators, “1 ENTER +” will result in “2”, not an error. (“1″ in X, ENTER copies X to Y; “+” adds X & Y to get 2. This is a common technique to double a number; subsitute * for + to square a number…) And it’s difficult to generate errors on an RPN calculator (aside from the obvious ones, such as divide by zero).

    So your sequence above will yield (on HP RPN calculators), “2”, then “4”, then (continuing your procedure) “16”, then 16 in both X & Y (no error), then X=3, Y=16, Z=16. Then things break down, as RPN calculators don’t have equal sign keys. (They don’t need them: The “answer” is always present.)

    The key to understanding RPN is that the operators are taken to mean “do this operation on values in X and Y”, where X and Y are values that are already there in the calculator (on the stack, where you can see them).

    With typical calculators, you enter one value, press an operator key, enter a second value, etc., then tell the calculator to resolve all the pending operations in one go. With RPN you resolve each value in step-wise fashion, so you get to see the intermediate results as you go along.

  65. #65 Brainstorms
    August 25, 2014

    For those who want to play with an HP RPN calculator, but don’t want to go out and buy one, here is an amazingly faithful simulation of the HP-15C RPN engineering calculator written in Tcl/Tk by Torsten Manz of Germany. (I still have my 15C; it’s my “checkbook calculator”, actually.)

    Manz’s app implements all the functions, memory, and programmability features of the HP-15C, as well as its appearance.

    http://hp-15c.homepage.t-online.de/

    Works in Windows, Linux, and Mac.

  66. #66 Pete A
    UK
    August 25, 2014

    Greg: I totally agree that it’s silly to call checkbook mode “Standard mode” — even worse, it’s the default mode! This is why I raised the issue. I imagine this could be very confusing for people (especially children) the first time they use the calculator.

    Using it for the 4’s example heading your article it produces the answer 320. In “Scientific mode” it gives the correct answer: 20.

    Apologies for misunderstanding your previous comment, Greg.

  67. #67 Greg Laden
    August 25, 2014

    Brain, right I was doing that RPN in my head, and my head produced an error. An HP calculator probably would have managed it!

    Pete: Now we are going to have to check all the calculators!

  68. #68 proximity1
    August 26, 2014

    I very much agree with Brainstorm’s points @ 58 and with Greg’s point @ 59. Everyone who is called upon to routinely calculate such equations really needs to know the order of precedence because, as Greg writes, it matters, and not just for reasons of conventional consistency. In fact, it’s probably nearly true that ” Everyone who routinely calculates such equations really does know the order of precedence.

    That many people do not–whether they respond to the problem posed or not–tells us both about what people learn in school, what they remember and, not least, what they really need to retain for their lives’ practical purposes. We could feel justifiably proud if 90% or more of the general public could correctly answer the problem without first looking up the correct procedure. I figure among those who couldn’t–and who didn’t first check the correct precedence. But nothing in my routine life requires that I have such knowledge in my working memory.

    On the other hand, what’s worse–if true–should be that many people, faced with a practical problem which posed this series of calculations, could not recognize from the basic facts of the matter the proper order of calculation. Fortunately, I suspect that in such real-life matters, the circumstances themselves often present clear common-sense indications of the order of calculation and it is mainly for this sort of “canned” example above that one must know the operational rules by heart.

    I gather the reasoning behind the order of precedence–what Greg means by ” …very important and deep number theory stuff that allows certain math to work the way it works… ” was neither always obvious nor understood. It had to be discovered like so much of the rest of mathematics. Without looking it up, I couldn’t state these bases in ordinary laymen’s tems and that’s another thing I think we can safely suppose is true of that “73%.”

    BTW,
    The pocket calculator I routinely carry– a simple Casio SL-300VE– operates by checkbook (or, for British readers, chequebook) mode. Thank you, Brainstorm, for the reference to the online HP calculator @ 65. That’s one of the most helpful posts I’ve read in quite a while!

  69. #69 Pete A
    August 26, 2014

    @proximity1: I’m very fortunate to own working working examples of the HP-15C and the amazing HP-16C (which to my knowledge has never been emulated, unfortunately). Just the instruction manuals alone for these machines are highly educational. The manuals contain examples and snippets of information that are still very hard to find in modern textbooks and online in 2014 — more than three decades after the machines were first produced!

    These calculators were designed by engineers who needed to solve real problems; they were not designed-by-consensus by a marketing team :-)

  70. #70 Brainstorms
    August 26, 2014

    As a point of interest, there was enough support & encouragement from the public to motivate HP to bring back the HP-15C; they re-marketed an “anniversary edition” in 2011.

    Also, the HP-12C model has never gone out of production in 30 years! It’s the “financial calculator” version of this line, and became very popular with real estate agents, who’ve been keeping its market alive.

  71. #71 Greg Laden
    August 26, 2014

    I’m holding on to my HP 15C and my HP 42S for the Smithsonian.

  72. #73 Brainstorms
    August 26, 2014

    Did the Twin Cities secede and join Ontario? (Manitoba?)

    Seriously, is there an advantage to virtual shopping in Canada? (I know it can be a pain to virtually sell there…)

  73. #74 Pete A
    August 26, 2014

    Greg, you probably know this being an OS X user, but just in case you don’t: The OS X Calculator has a neat RPN mode, which I don’t use, but I always use this calculator with its Paper Tape window visible (Command-T or Window menu: “Show Paper Tape”) — very handy for backtracking/double-checking a series of calculations.

  74. #75 Greg Laden
    August 26, 2014

    Yes, I believe the iOS version switches to RPN if you do something funny, like shake your iPhone. No, wait, if you tip the phone over.

  75. #76 James Porter
    Los Angeles
    August 27, 2014

    I was just seeing patricia’s comment and they didn’t show P.E.M.D.A.S (Parenthesis, exponents, multiplication, division, addition, subtraction) meaning 1 + 1 x 3 + 4 – 8 is actually 0 because 1 x 3 = 3 and 3 + 1 + 4 + 8 so 8 – 8 equals 0. 4 x 4 + 4 x 4 + 4 – 4 x 4 is actually 30 because 16 + 16 + 4 = 36 and 36 – 16 is 30. By the way I am also 11 and I learned that method a long time ago proving that using that method is the correct way.

  76. #77 Greg Laden
    August 27, 2014

    James, you are correct!

  77. #78 proximity1
    August 28, 2014

    James @76:
    I contend that 36 minus 16 is 20 rather than 30. But that’s just my minority view. It’s a simple error which anyone might commit. Larger points are that you’re trying to apply the correct precedence of calculation and the fact that, at age 11 you may not appreciate just how many of us, now much, much older, also were taught the correct precedence of calculation and at your age could correctly cite it but that, unused, many years later, it is not at unusual to have forgotten it.

    If you remain in pursuits which rely routinely on such math practices, then of course you won’t likely forget.

  78. #79 Pete A
    August 28, 2014

    proximity1 @78:
    I interpret you comment as being sarcastic towards both Greg and James. While reading their comments I exercised the principle of charity and drew the conclusion that James had made a typo rather than making an arithmetic error.

    Notwithstanding, in science, engineering, and medicine, typos often result in catastrophes that cannot be excused by simply writing it off to: Oops, the patient died / the building collapsed / the satellite is in the wrong orbit due to my simple typo or putting a decimal point in the wrong place; all humans make these errors so don’t blame me.

  79. #80 Brainstorms
    August 28, 2014

    Very true that humans (and the computers they program) DO make errors at times.

    This is why the wise engineer ALWAYS has someone check their work! (Sometimes this requires one team to check the output of another team. Management and policy comes into play here, of course.)

  80. #81 proximity1
    August 29, 2014

    Pete A. @ 79:

    “I interpret you comment as being sarcastic towards both Greg and James.”

    Well, that’s your right as a reader. It’s true that there’s some tongue-in-cheek in my post (e.g. “just my minority view”) but there was no malicious intent on my part. I, too, make plenty of typographical errors. I can also make simple mistakes in aritmetic. If you care to have it, here’s my assertion of no offense intended. And note that Greg must have taken it all in stride since he first reads and accepts (what’s called “moderation” ) everything I post here.

    Now, in my capacity as amateur philosopher, and thus, more seriously, I wonder if you’d consider this: there has grown up in English-speaking culture over the past half-century a deep and open hostility to all kinds of critical commentary which dares to point up the mistakes of others–even the most well intentioned of such criticism is very often met with objections in popular discussion blogs that such corrective criticisms, it’s alleged (usually by third parties) are or just might be hurtful and so ought not be made. This often comes in the form people angrily objecting, without the slightest irony, “How dare you be so judgmental! ”

    A blog written in the spirit of science’s quest for knowlege and the elimination of error should welcome corrections and critical commentary–and Greg clearly does that. But I’ve seen other science blogs that are squarely part of the cultural trend which preemptorily denounces practically anything that can be interpreted or misinterpreted as less than sweet, cheerful and benign in tone and apparent intention. I hope that James P., even at age 11 years, is made of sterner stuff and I give him enough credit to imagine that he could read my correction and, even if he blushes a bit, laugh in good humor at what was, after all, an honest and a harmless error. Okay?

  81. #82 Pete A
    August 29, 2014

    proximity1 @ 81:
    If you think your reply was okay then that is your right as a commentator.

    I was unaware that you are an amateur philosopher therefore I apologise for my critical remark.

  82. #83 dean
    August 29, 2014

    I’m holding on to my HP 15C and my HP 42S for the Smithsonian.

    Want a 48G to replace them?

    I have found one other problem with calculator-aided work, a mixture of user-error and (IMO) poor implementation by the manufacturer. Many of the current TI and other graphing calculators allow long calculations to be entered in one line, as you would “write” them, with parentheses as needed.
    BUT
    it is possible for a parenthesis to be opened, with typing following, and the calculation to be completed without the closing parenthesis to be input. No end of “hilarity” can result.

  83. #84 20
    August 29, 2014

    20!

    (not 20 factorial…that is, um, quite large)

  84. #85 maia
    September 3, 2014

    the answer is 20

    4*4+4*4+4-4*4
    =16+4*4+4-4*4
    =16+16+4-4*4
    =16+16+4-16
    =32+4-16
    =36-16
    =20

  85. #86 maia
    September 3, 2014

    by the way i’m 11.

  86. #87 Alphagamma
    Cambridge
    September 4, 2014

    Of course, while people in the UK say maths rather than math, we also say sport rather than sports.

    (Well, both are used. “Football, cricket and rugby are all popular sports” is a valid sentence, but the title of the section of the newspaper you read about them in would be Sport).

  87. #88 Tim
    September 4, 2014

    @#2

    They weren’t laughing *at it*, Sou. Only near it. ;)

  88. #89 Greg Laden
    September 4, 2014

    Alphagamma, good point! Of course, “sport” is wrong because there are multiple sports, and sports is a plural word.

  89. #90 Pete A
    UK
    September 6, 2014

    Sports is obviously a plural word, as is mathematics. However, the singular words sport and math can also be used as mass nouns (uncountable nouns). “I used to play a lot of sport.” cannot logically lead to the deduction that I used to play a lot of one particular sport.

    Compare: “I enjoy math.” cannot logically imply that I enjoy only one branch of mathematics.

    The huge difference between the words sports and mathematics is that the singular of mathematics (mathematic) is not a defined word.

  90. #91 Greg Laden
    September 6, 2014

    It might be an adjective.

  91. #92 Pete A
    UK
    September 6, 2014

    The adjective is mathematical and the adverb is mathematically :-)

    As I stated in comment #29: It doesn’t matter whether we use “math” or “maths” because everyone knows that they are short for mathematics.

    Greg, you have the rare gift of being able to educate people who are willing to learn, which is infinitely more valuable than debating the subtle nuances of syntax.

    As always, I thank you most sincerely for freely sharing your extensive knowledge with us.

  92. #93 somathoholicca
    September 8, 2014

    patricia try this

    5×3=3×5
    What property is named in this statment?

    15-2x if x=7

  93. […] Should it be “math” or “maths”?ScienceBlogsThere are actually two answers to this question. First, “maths” looks plural and is preferred by some because “mathematics” is plural. The problem with that is “mathematics” is no more plural than “physics” or any other compound noun.2014-08-20 23:53:54 […]

  94. #95 Lizzy
    October 15, 2014

    the answer is 20
    -nine year old

Current ye@r *