I come to you by way of your computational complexity blog. I get that there is some really good stuff there, but frankly don’t understand about 99% of it. What I do understand is that math can be fascinating and that knowing how to ask the right questions can fill a lifetime with wonder. I am now homeschooling one of my children. He has a good grasp of basic math of the elementary and junior high level, but I just don’t have the experience to pose the questions that don’t have clear answers and that can keep a young mind engaged on a deeper level.
I am writing in the hope that you can share with me, or even poll your readers on, the questions that inspired you and them to further your own investigations and advancement in the worlds of math. Ideally, I would be interested in creating some structure that I could share with the homeschooling community so that an unsophisticated mathematical mind could enjoy this journey with its homeschooled child.
You might try some of the books I enjoyed as a child, Flatland, Gödel, Escher, Bach and the puzzles of Raymond Smullyan.
Everybody's story is different. While I did well in math growing up, I didn't really consider taking a career in a math-related field until college when I discovered my need to know why. But what did fascinate me as a child was process, for example what happens to my letter from when the mailman picked it up until it got delivered. Once I started having access to computers as a teen I started thinking about what they could and couldn't do. For example, I remember asking myself whether our school's computer with its fixed amount of memory could eventually print all the digits of π (no it can't). Not until late in my college career did I find out there was a whole field of study devoted to the mathematical understanding of the possibilities and limits of computation. And I was hooked.