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.