<p>Thanks johnshade, I hope it is somewhat welcoming =]</p>
<p>The Rubik’s cube looks like it’d be really fun and exciting! I think I even have a principle, aside from any specific examples, of how to get someone excited about math. It’s by showing that it’s POWERFUL. I.e., I think you could walk someone through the proof of Fermat’s Little Theorem (OR my problem about the Euler-phi function, listed on another thread) using group theory and the theorems, without actually proving the theorems themselves. </p>
<p>You could prove the Brouer (YIKES, no idea how to spell) Fixed Point Theorem in all dimensions using homology groups, but without actually showing how to compute the homology groups or the fundamental group. </p>
<p>The general principle of mine is to forget the technical details and show how a natural flow of logic can yield unobvious conclusions. It’s had some success with people I talked to at least!</p>