When we lived in Canada I was a member of the Education Committee of the school my children attended. My responsibilities included interviewing candidates for teaching positions and over the years I must have met dozens of teachers. I developed a standard question that I asked of them all. It had a double virtue: it was one for which no one seemed to have a canned answer, hence it allowed committee members to see the candidate thinking on his/her feet. Second, the way the candidate framed the answer told us a good deal about that person, much more than the reply to usual questions. My question was: tell me about your successes and your failures, with special emphasis on the failures, rather than the successes.

In this chapter I want to take up the challenge of answering my own question. At conferences and in published papers we rarely present our failures, only what we believe to be our successes (how we feel after the discussion of our paper is another matter). And yet, our failures have a lot to teach us. Why do we consider certain ideas successes and others failures? What distinguishes a success from a failure? What, if anything, can we learn from our failures?