<p>I have a great many books on math that I have given my kids at various points in their education to encourage thinking about math as more of a language underlying reality than simply a collection of tricks and exercises with numbers. Don’t know the ability of the kid discussed here, but I have found a few books to be particularly useful in helping my kids begin this journey.</p>
<p>I recommend the du Sautoy book already mentioned here, and I think I recommend it first. Du Sautoy has a winsome personality, at least his book does. You just like the guy. You like what he says and the way he says it. I am not good at math. But I read this book and was able to understand a fair amount of it. More important to my purpose was that I could see that through this book any math kid would learn of the fascination inherent in math.</p>
<p>I also recommend Dan Rockmore’s book “Stalking the Riemann Hypothesis” mostly because it includes a nice general introduction of non-Euclidian Geometry that has gripped each of my kids and changed them forever when it comes to thinking of math as language underlying our reality. I also think Rockmore comes right out and calls himself “a number” in that book, an idea I had pushed for ages here at home. I have this thing I do here where I put a pencil on a table and continually ask the kids to describe it. Eventually they come to understand that there is more information about the pencil that mere words cannot describe. There is not just one “yellow”, for example. So we need a highly specific way to nail down the “yellow” of the pencil. And it is not just sitting on the table. It is sitting there in a very specific way, relative to everything else, and at a very specific time that changes continually. So much information that is lost with mere words, and this idea tends to make them uncomfortable. Eventually, their descriptions become ever more specific and mathematical until they exhaust their knowledge. Then they see how all things are ultimately reducible to this concept of “number” and the search is on. Rockmore was useful here. My experience has been that when kids begin to see “numbers” rather than, say, cars flowing in traffic, then math and learning math (and life in general) become compelling.</p>
<p>I also recommend the Derbyshire book mentioned here because it seems to be a nice history lesson surrounding the whole Riemann thing. There are so many others I could recommend, but I have found that after I have introduced these few books, my kids have pretty much taken off on their own separate paths.</p>
<p>I should say almost all of them have found themselves reading Penrose’s “Road to Reality”, so I recommend it too (maybe later?), though I haven’t read it myself.</p>