Math 101

Here in manattan there are various little free newspapers around, supported only by ad revenue. None of them are of very high quality, but one thing they all seem to have in common is a puzzle page. The crossword puzzles aren’t very good (I’m spoiled by The New York Times) but I find the sudoku to be a perfect mindless divertion during subway rides uptown. All I need is a pen in my pocket when I leave home or office, and I’m good to go.

But there is one oddity about the Sudoku page. In many newspapers, it has a little instructions page that reads (and I quote):

How to play:
Fill in the grid so that every row, every column and every 3×3 box contains the digits 1-9. There is no math involved. You solve the puzzle with reasoning and logic.

Today I became curious whether anybody else is bothered by the patently false and absurd claim that “There is no math involved”. So I did a Google search on:

“There is no math involved” sudoku


and found 82 hits (Google gives an estimate of over 900 hits, but they only actually find 82). I went through them all, and found that every page simply repeated the nonsensical statement that there is no math in Sudoku, without thinking to question it.

If I were to start printing some equally absurd statement in newspapers, like “There is no gravity, we just all secrete glue out the bottoms of our feet and shoes,” I suspect somebody might complain. So what’s going on here?

My theory is that math education is so fundamentally broken in our society that people actually grow up believing that “math” is a synonym for “arithmetic”. And there is certainly no arithmetic in Sudoku. But in fact Sudoku is a math puzzle. It consists of nothing but math.

Actual mathematics is, quite precisely, any endeavor in which you start with a set of symbols, together with some rules for combining and manipulating those symbols, and then you set about discovering what symbol combinations are provably true or provably false, according to the rules you started with. Sudoku has nine symbols, and a few elegant rules for how you are allowed to combine those symbols. Most combinations produce a provably false result, and one combination produces a provably true result.

Things don’t get much more mathematical than that.

And so I come to the reluctant conclusion that almost nobody in our society has any inkling of what math is. Which is really strange when you consider that kids are required to take math in high school. For example, if you attended high school in this country, the odds are that your state curriculum required you to study Geometry somewhere along the way. That’s an entire year in which you did math pretty much without arithmetic or numbers. You would have encountered a bit of arithmetic, like summing the occasional pair of angles, but that was pretty incidental to what you were actually studying, which was how to prove theorems from a given set of simple initial rules.

It’s no wonder there is so much math phobia in this country. For one thing, people aren’t even aware of what math is. It’s just that scary thing they are supposed to learn from people who apparently also have no idea what it is.

Imagine how bizarre the system must seem to the average high school student. An entire year is spent taking a math course called “Geometry” which – by common consensus – has nothing whatever to do with what most people mean when they say the word “math”, since most people are under the misapprehension that math is the same as arithmetic.

And yet, ironically, Geometry is the one math subject offered in high school which actually is math, as that word is understood by mathematicians. Algebra and Calculus would be math too, if anybody bothered to show you how and why they really work. But in high school that doesn’t seem to happen. Instead, these courses are generally taught as a set of mysterious formulas: Plug in the right formula and the right answer comes out.

I was completely uninterested in math when I was in middle school – it was all taught as a set of formulas by bored teachers who seemed much more focused on stopping us kids from throwing pencils at the backs of each others’ heads. And because I wasn’t interested in math, I wasn’t particularly good at it.

Then in ninth grade I had my first great math teacher, and everything changed. I was finally shown that math (actual math, not what most people mistake for math) is one of the most beautiful things that a human being can encounter in life.

But that’s enough for now. More tomorrow.

8 Responses to “Math 101”

  1. LastSilmaril says:

    …I don’t know if you grew up in New York State or what the curriculum was when you were growing up, but it has since changed. There was no one year where I focused on one subject exclusively for its entirety; instead it was more or less all jumbled up, a few weeks here, a few weeks there of topic loosely related to each other.

    This became worse when the Power that Be (e.g. “The Idiots In Albany”, as my math teacher at the time, since retired, called them) introduced the Math A/B curriculum to replace Math I/II/III. The two aren’t particularly coherent and are divided each over 1.5 years. It was a PR disaster for the Board of Regents and they’ve since reinstated the old system.

    The few times anyone actually tried to “prove” something, it was either in Discrete Math, which was fun, or in Calculus, though the teacher, a grad student, did a fairly poor job at it, since it was maybe his first or second time teaching. Both of those where summer courses though…but still, few were the times that my hs Calc teacher dove into proving something he’d taught (outside of maybe the fundamental theorem).

    So…I guess you could say I’ve never encountered “actual math” either ;(

    I’ve actually been on-again-off-again trying to see if I could get it. I have this copy of “What is Mathematics” that I bought a whiles back that I keep starting to read, and it’s great for the first 25 pages of the books, where it covers things I already know. Past that, I didn’t really have the time to parse what Courant was saying.


  2. Dagmar says:

    I realised that only a few people can see the beauty in an equation. But I believe you have to see the beauty to solve an equation.

    Most of the people are afraid of math, so if I would want to ‘sell’ SUDOKU I would perhaps do the same, tell the people it has nothing to do with math and let them enjoy it without realising what they really do…

    I remember my time at the university very well, when I gave math courses for the students of business economics. Honestly I would have hardly given a diploma to any of them, if you would have asked me while I corrected their math tests. :-)

    And I remember one time where math let do me something that I didn’t like at school at all (now I love it) translating a Latin text into German, just because I a had a diary from a mediaeval philosopher in front of me, who happened to be a math teacher, too.

    And in the end it was math, that led me to my second love the philosophy, because in the end philosophy is nothing else than pure logic and exact terminology – or pure math.

    And you will find the same structures in music too.

    So just imagine a math teacher, who let his pupils listen to a math rock band like the Battles and then gets to the hard core stuff. :-)
    So maybe it is not a bad idea to call it SUDOKU or rock and let the people have more fun with math.

  3. troy says:

    I can remember, quite clearly, the math teacher/Gym teachers that I had in junior high and Hight School. My Algebra teacher in High School was also the gymnastics coach. I think “math teacher” for him was sort of a side gig.

    When I was in junior high, I had a friend who’s brother was a sysop at Orange Coast College. We would go visit him and look at the huge “computer” that he administered. It took up a room that was air conditioned and had wires everywhere. Other than the jellybean computers on the Jetson’s, this was the only one that I had ever seen. It amazed me that someone knew how to build that thing. It just seemed so huge and complex.

    Brother Bob told me that I needed to be really good in math if I ever wanted to be an engineer that could design and build these things… At that time, this had huge appeal to me. So, I tried really hard in my math classes…

    But, subject to the rank and file of disinterested gym-teacher/reluctant math teachers, I struggled. There’s only so much you can get from a book. At some point, during my high school tenure, I just gave up… Something just wasn’t clicking…

    So, I followed my other passions with theatre, music, and art. I was an art major at College of the Desert, a Musical Theatre major at USIU, a dance major at NYU, and later, briefly an Arts Administration major at NYU… (eternal student). At some point, I said “enough”.

    I had gotten what I wanted out of the arts and my heart wasn’t in it anymore. I went back to NYU as a computer science major, and my first semester I took a calculus class.

    The instructor was a TA that barely spoke english. But, he was very passionate about the subject. After a few classes of refamiliarization with algebra and trigonometry, he explained the Fundamental Theorem of Calculus to us. I remember thinking that limits and sums made sense, but, were obviously tedious… But, The Calculus was so elegant and well crafted and useful and functional… At the time, it was like seeing God for me. It actually worked!

    I know this sounds really stupid, but, it had a profound effect on me and my appreciation of mathematics. I wanted to know more. I was always dreaming up real-world problems that I could find elegant mathematical solutions for. It was an odd, and geeky part of my life. If I had more time, I would have added a math minor to my studies. But, I really enjoyed the Calculus, the wierd quirky applications of discrete mathematics, combinitorics, etc…

    The point being… as a public school student that was very eager to learn, I was done a huge disservice. Dispassionate teachers should be relegated solely to woodshop instruction. It wasn’t until I found a teacher that was genuinely interested in the subject that I started to see the light. And this light shined (shone?) far past the classroom, into my everyday life.

    This was about the time that I ran into this Perlin guy who was taking transforms of matrices and turning them into dancing girls. Wow. Somehow, I’d made a full circle.

    I’ve never attempted a Soduko puzzle, but, for years I’ve been trying to find the blueprint for that time machine in the digits of Pi. Maybe then, I’ll know God. Sagan, you out there?

  4. Dagmar says:

    Perhaps someone has fun with this:

    “What is surf?

    surf is a tool to visualize some real algebraic geometry: plane algebraic curves, algebraic surfaces and hyperplane sections of surfaces. surf is script driven and has (optionally) a nifty GUI using the Gtk widget set.”

    ( I stole this quote from the website.)

    It is just fun to try it and get some beautiful geometry out of a formula you type in.
    It is always sitting on my desktop. :-)

  5. Lisa says:

    I’m glad (in a way) to hear that I wasn’t alone in being mistaught mathematics. I hardly remember anything from those high school classes, other than sitting in the back and never once speaking to any of my teachers, but do know that I barely made it through Algebra II before giving it up and never, ever taking another maths class again. I even considered architecture as a major, but when I learned I’d have to study maths, changed to Humanities.

  6. I used to believe that maths was the same as calculation. At least, that’s how it was taught all the way through primary school and high school. I hated it, and chose other subjects over maths as soon as I got the opportunity.

    It wasn’t until after I started studying linguistics in university that I fully realized that maths isn’t about boring things like numbers; it’s about fun things like axioms and theorems. But by then it was too late to change tracks.

  7. Ben Kanegson says:

    Our 4 to six year old minds are myopic and limited. We have little concept of the “big picture” then, and most information is absorbed in small, self oriented bits. When we begin learning arithmetic at that age we have no idea why we do the exercise.

    Later in grade school, when our minds are ready, we need to be shown what math really is: a language that can be used to describe the world and its dynamics. But most of our grade school teachers themselves never actually get past learning arithmetic, and so the lack of understanding is perpetuated. Ken was lucky to have an exceptional teacher who did an intervention; and some students persevere until they can see this on their own, in geometry or college level science classes. But sadly, after hundreds of years of

  8. Dennis says:

    I think math is just arithmetic till my high school. Then calculus comes into my life after that. Math gets totally different to me. I guess that’s the first time my teacher uses the word “beautiful” to describe an equation.

    To tell someone Sudoku is purely math is like Rubik’s Cube to math or Tetris to math. Most people just don’t get it. But I do think there are people understanding the relation between Sudoku and math. We do have a wiki page about them.

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