Mathematical and Computational Mistakes and Failures as a Source of Creativity

Mistakes are generally considered a negative phenomenon. There is however a positive face of mistakes, essential in learning, in teaching, in scientific research and in any creative work. We discuss the reason of this fact, we give several such examples and we show how various historical failures in some respect became important successes in another respect. In a second part of this paper, three types of mistakes are distinguished: syntactic, semantic and pragmatic. Each type has its chance to lead to great successes. Keywords-syntactic mistakes, semantic mistakes, pragmatic mistakes, creativity.