"Induction is the process of discovering general laws by the observation and combination of particular instances. It is used in all sciences, even in mathematics. ...Induction tries to find regularity and coherence behind the observations. Its most conspicuous instruments are generalization, specialization, analogy. Tentative generalization starts from an effort to understand the observed facts; it is based on analogy, and tested by further facts. ...many mathematical results are found by induction first and proved later. Mathematics presented with rigor is a systematic deductive science but mathematics in the making is an experimental inductive science. ...In the physical sciences, there is no higher authority than observation and induction but in mathematics there is such an authority: rigorous proof."