Mathematics should not be boring

<p>This is the text of a lecture before the mathematics teachers of the Catholic Schools in the Diocese of Pittsburgh. First, I make the distinction between arithmetic and true mathematics, starting with geometry and algebra. For the latter, rote memorization is deadly while conceptual understanding and problem solving ability are essential. I illustrate this insight by a section entitled <em>The art of avoiding unnecessary calculation </em>and a section on <em>The Theorem of Pythagoras.</em></p>