When I first began setting up study subjects for HomeworkCentral.com in 1997, the arrangement for most of them was obvious. Science could be broken down into physics, chemistry, biology and most other sciences fit fairly well under those, if sometimes redundantly. History I realized had to be set-up two ways, chronologically and geographically. But mathematics was a puzzle. I asked some scholars and they shied away from giving me an answer.
My mathematician brother gave me, as is his nature, an insightful answer. He said that when he was learning math in the mid-20th century it was taught so that “lightbulbs went on in your head” as you progressed, for example, from algebra I to algebra II to calculus in a set order. But, he reflected, when his sons were learning the new math a couple of decades later more advanced topics were taught to them early on. In a manner most uncharacteristic for him he said he did not know which was best.
He turned out to be, as he always is on intellectual stuff, correct. He did not know which way was best because many ways to look at math are instructive. Mathematics is a network where linear progression does not mesh. That is why a large website where every idea is connected to every other idea is perfect for learning mathematics. Mathworld fits that description and is a terrific example of how to use interconnectivity to express a web of ideas. Having done that well, Mathworld mirrors, in a primitive way, how mathematics becomes a web of ideas in our mind.
How the best knowledge gets to everybody to learn
