Thursday, 5 June 2008

I give up, Math is really not hard

OH GOD, I give up, Math is really not hard (but it really is)…..

A BBC article finally broke the news to the British people, “The British are uniquely happy to admit being bad at maths.” If I didn’t have a calendar in front of me I would swear it was the early eighties and I was reading the same articles that appeared all over America during the years when the National Council of Teachers of Mathematics developed their “agenda for action”..
The article had lines like “Imagine a famous television presenter joking that they couldn't read” and later, a successful “former maths teacher” (for the non-studious, he don’t teach math no more, but that doesn’t mean he won’t tell you what’s wrong with math education…) “John Dunford, general secretary of the Association of School and College Leaders and a former maths teacher(emphasis added), publicly bemoaned the fact there were Lord Mayors who proudly said they couldn't do maths.

"I think people see maths in a different light to English language. They see it as being hard but it's no harder than other subjects”. Okay, that seems reasonable, but wait, the article says that people would never suggest they couldn’t read (because they can) but they admit that they have difficulty understanding math… wait… does that mean that, in fact, Math IS different, mathIS harder???

Ok, one more time… Here is one of many reasons why math is harder than other areas of study. Try to think of a problem in literature, social studies, whatever your favorite field of interest is; but there is a catch. The problem has to be simple enough that any 15 year old could understand it completely, but so difficult that no one on earth can solve it, or maybe someone can solve it, but only about ten people in the world would understand the answer. Wait, let’s add a third rule, the problems has to be one that has been studied for over a century… Got one???? Well math has, lots of them…

In 1900 when David Hilbert, whom many believe was the best mathematician of the era, listed the great unsolved problems for the future of math, several of them could be understood by a typical high school student. Some of those same problems still remain unsolved, and many are understandable, by a 15 year old high school student. How about an easy one from geometry, it was his third problem. Math folk know that if you take any planer closed simple polygon (a rectangle, or pentagon or any of those).. you can cut it up into a finite number of pieces and reassemble the parts into another polygon, ANY other polygon, that has the same area. If the problem is a three dimensional solid, there is no such nice relationship, in fact, it has been proved that there are some solid shapes that you definitely can NOT cut up and reassemble into some other particular shape.. The problem is easy, but the solution is a bear (0K, I was going to say bit**, but trying to keep it clean here).

Wait, there is more. Hilbert’s eighth problem was simple enough for a grade school student to understand, every even integer greater than two can be expressed as the sum of two primes. NO fancy language… 4 = 2+2; 6 = 3 + 3; 8 = 5+3; 10 = 5+5…etc.. Simple, but guess what.. not only was there no proof in 1900, there still wasn’t one in 2000, and my bet is that there won’t be one by 2100. Ok, I know its true, you know its true… John Dunford, (he was the guy earlier who said “math is easy”) knows its true, but he can’t prove it either.

OK, if you haven’t been sleeping under a rock, you’ve heard about Fermat’s Last Theorem. It’s sort of like the Pythagorean theorem (of course you remember, a2 + b2 = c2. It works for non-zero integers; for example 32 + 42 = 52). There a proof that there is at least one set of integers that make it true. Somewhere back about the fourth century AD (about the time the Bible is being put together), a guy named Diaphantus suggested that it couldn’t be done with cubes or fourth powers or anything higher than squares. Jump forward to the seventeenth century, and a guy named Fermat, (the guy in the picture at the top) just an amateur mathematician who proved lots of hard stuff. He owned a copy of Diaphantus book, and next to the problem he wrote something like, “I have a marvelous solution, but it is too large for the margin of this book.” Then he died… ohhhh … very evil.. So now everyone is looking for Fermat’s proof. A hundred years pass, then two hundred; three hundred; four hundred… I’m in high school, I hear the story.. I’m sure I can do it but…. NOPE.. never happened.. then just before the dawn of the 21st century, a guy comes along and proves the thing. Huge press releases.. but they don’t last long. To prove the theorem, he had to piggyback on four hundred years of other peoples efforts and then, solve a theorem in a field so unusual that it was suggested that only eleven people alive in the world could understand the proof.

Let me break it down one more time… MATH IS HARD.. Harder than almost anything else you will try.. harder than skipping rope.. Harder than juggling (but just), and at least as hard as riding a unicycle (I can’t do that yet, so I’m thinking it may be VERY hard).

That’s why people who think it is no big deal to read or write or run big companies will say… I’m not very good at math. You can be pretty bright and still struggle with math… maybe the guys who want to tell people how easy it is should do some of those tough things that other people can do who find math a bit challenging… Try walking across Michigan on Stilts, for instance.

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