In a surprise, this book arrived in the mail for me today (I had pre ordered it the moment Paul Solomon told me about it. But it came today, on the perfect day just as I’m trying to wrap up the first few weeks of planning for my Algebra II class. Now I can’t put it down.
Let me share two quotes:
I want to talk about a different sort of place. I’m going to call it “mathematical reality.” In my mind’s eye, there is a universe where beautiful shapes and patterns float by and do curious and surprising things that keep me amused and entertained. It’s an amazing place and I really love it.
But I won’t lie to you: this is going to be very hard work. Mathematical reality is an infinite jungle full of enchanting mysteries, but the jungle does not give up its secrets easily. Be prepared to struggle, both intellectually and creatively. The truth is, I don’t know of any human activity as demanding of one’s imagination, intuition and ingenuity. But I do it anyway. I do it because I love it and I can’t help it. Once you’ve been to the jungle, you can never really leave. It haunts your waking dreams.
So I invite you to go on an amazing adventure! And of course, I want you to love the jungle and to fall under its spell.
From there, Lockhart goes on to introduce you to a the idea of a mathematical problem, and as an example, he points out the curious fact that when you connect each corner of a triangle to the middle of the opposite side, the three lines meet at a point, and this seems to work for every triangle. But you have to wonder if it the lines are really meeting, and if this really works for every triangle. To answer this question requires a very special type of argument, one that doesn’t involve drawing triangles on paper, but instead involves imagining triangles in our mind.
I’m sold. I can’t wait to read and savor this book, and I want others to join me in this adventure. What I imagine is a virtual reading/discusison group about this book. I would love to study this book with my many friends in the mathtwitterblogosphere, as well my awesome colleagues in my math department, I’m even thinking of getting up at school meeting and inviting interested students and other faculty outside the math department to join this adventure. Who’s in?