While doing a good job of warming people up to math there was still a little bit too much “math is hard” or “math is impenetrable” discussion in the opening here. We need to get away from continuing the myth that math is “hard”. The stories we tell are crucially important here. I do like the fact that Alan Alda talks about how he’s been fascinated with it and has never given up. I’m also intrigued at Strogatz’ discussion of puzzling things out as a means of teaching math–a viewpoint I’ve always felt was important. It’s this sense of exploration that has driven math discovery for centuries and not the theorem-proof, theorem-proof structure of math text books that moves us forward.
I’ve always thought that Euler and Cauchy have their names on so many theorems simply because they did a lot of simple, basic exploration at a time when there was a lot of low hanging mathematical fruit to be gathered. Too many math books and teachers mythologize these men for what seems like magic, yet when taught to explore the same way even young children can figure out many of these same theorems for themselves.
If we could only teach the “how to do math” while children are young and then only move to the theorem-proof business later on as a means of quickly advancing through a lot of history and background so that students can get to the frontiers of math to begin doing their own explorations on their own again we would be far better off. Though along that path we should always have at least some emphasis on the doing of math and discovery to keep it at the fore.
Jason McIntosh