> Lockhart missed the point a bit. I think it's fairer to say that his point may not have been what you expected it to be. As a teacher myself, trust me, if a

> Lockhart missed the point a bit. I think it's fairer to say that his point may not have been what you expected it to be. As a teacher myself, trust me, if a student comes to you and says "I came up with a proof!" and you say "no, you see, what you have is an intuitive explanation that can possibly be turned into a proof," then all that will happen is that that student will not be interested any more in exploring, or at least will not be interested any more in sharing their explorations with you. At that point, you have both lost. Lockhart is well aware of the standard of mathematical proof, and knows that, all else aside, this theorem is not in want of proof. His focus is on the fact that, if we want mathematics to remain a live profession, then we must improve our pedagogy, and help to train students who enjoy and want to pursue mathematics—even if it means occasionally accepting less than maximally rigorous mathematics from a seventh grader.