At the previously mentioned Christmas party I spent most of the time chatting with a pharmacy grad student about math education. He felt ripped off by the educational system because it did not make math interesting enough and now he doesn't readily have the mathematical tools at hand to most effectively do his work. So we mostly ended up talking about what we wished we had different about our math education. One of the things that struck me was that nearly all of the exciting things that happened in my pre-college math education were from my own investigation/curiosity and if it involved a teacher it was in a group of three or less.

I've talked to Rebekah before about how neither of us can remember where we learned many core math concepts that we do not struggle understanding, but we can clearly see the way that math we learned later built upon that foundation. From my perspective now if I see someone struggling to understand addition or multiplication I revert in my head to an axiomatic basis for the natural numbers that asserts the number one and successor that is also a number. Should schools teach math and numbers at that level until the kids get it then move on to higher concepts like addition and multiplication? After that the concept of inverses so that division and subtraction come for free? Really shouldn't students understand our place value number writing system inside and out as soon as they dare to count passed nine? Can this be avoided with such tactics?

One thing that I think helped Rebekah and I was an ability to have negligible regard for math application in the course of learning. Neither of us needed justification to study math beyond obtaining a deeper knowledge of math. Word problems only become annoying in that they bother to contrive a situation that must be abstracted out to get to the real problem. Maybe we were motivated at times in the thrill of solving a puzzle, but what makes a puzzle interesting is the beauty or wit of the solution.

So how was I inspired to recognize and appreciate the beauty and wit of mathematics? Sadly I don't remember.