<p><pre><code>  The second moment occurred soon after he turned twelve, when he
  was given “a little book dealing with Euclidean plane
  geometry.” The book’s “lucidity,” he wrote—the idea that a
  mathematical assertion could “be proved with such certainty
  that any doubt appeared to be out of the question”—provoked
  “wonder of a totally different nature.”
</code></pre>
Mathematical proofs, first really introduced in Geometry classes for most US students around 9th or 10th grade, are what really hooked me on math. I understood everything up to that point (and after), but it was a structural understanding (the rules and syntax, essentially). Once we arrived at logic, I (as a very bored precocious student) spent most of my class time proving everything from the axioms we were given (for algebra or geometry) that I could.<p>Giving students the tools to play and explore freely (we had proof assignments, of course, but I took it far beyond that) is what really hooks them on a subject. Mandate that they <i>must</i> read these books, they&#x27;ll hate it. Require them to read a book and a few excerpts of others, and give them access to a large library, and they&#x27;ll read forever. Same with every other subject. That&#x27;s where many of the real geniuses[0] of a field come from.<p>[0] Whether technically geniuses by IQ or just acknowledged as such for their understanding and creations.