My high school math teacher used to give us extra classes that weren't directly connected to the curriculum. They were always about structure, elegance, and beauty. Quite a lot of time was also spent on history: who was studying what, when, and why. (Also there was a cult of Leonard Euler, which maybe is not so surprising if you did high school math.)<p>I found it to be the most important glue in my math education. In fact, all the natural science ought to be taught in this way. Kinda like Bill Bryson's Brief History of Everything, plus actual calculations.<p>We won a math contest in my last year. I was expecting it to stay interesting.<p>Unfortunately when I got to university math (and the rest of engineering) was taught in a very utilitarian way. There was very little context, just a lot of similar looking derivations.<p>I blame the exam culture. In a way it's good because it motivates you to learn something, but it's bad because you end up learning it in a way that isn't useful. At the end of your college days, you are unlikely to remember just how Stoke's theorem works or the coefficients in Runge-Kutta. That's just because the size of the curriculum is huge. But if you had a context, a set of stories about when and why something was studied, you'd have a much better chance of being able to recall that it even exists.
Having earned an undergraduate degree in math I've often had similar thoughts about US elementary math education's emphasis on rules and mechanical calculation and memorization rather than more abstract concepts like pattern matching.<p>Turns out there was a thing called "New Math" (<a href="https://en.wikipedia.org/wiki/New_Math" rel="nofollow">https://en.wikipedia.org/wiki/New_Math</a>) in the 1960s where public elementary schools tried to teach concepts from set theory and abstract algebra. Basically everyone hated it.<p>Perhaps there was just a curriculum failure, or perhaps teachers weren't well-equipped enough to teach the material. But we can't ignore the attempt and need to come up with an answer for why New Math failed before we can try it again.
That problem is actually very easy to solve. If you number the cells in binary, patterns fall out enough that it's easy to convert back and forth from the original numbering to the final numbering.<p>If he wants to just work it out by hand, well, maybe he doesn't understand math as well as he thinks. If you want to use math to "build hammers", it help to know what a nail is first.
Totally agree with the author. In high-school, I was interested in physics more than math and whenever I took interest in math it was because it would help me understand some specific aspect of the physics better. As I got into engineering, my interest in math again were only in areas where it was directly useful to me (like signal/image processing, operations research etc.) As a CS engineer, I've used very little math I was forced to learn by rote to write exams. Only use that came of it I think is training my brain muscles to do pattern recognition and fast memory recall.
First off cool blog.<p>But is there a reason why the maintainer of this blog hasn't shared his or her identity? I am very interested in your background. It looks like some of your earlier entries were made when you were in high school. In any case I am very impressed. Sent a few of your articles to my younger siblings to read.