I am aware of two major modes of reasoning: [deductive][1] and [inductive][2]. Whereas physics relies on induction, mathematics seems to rely exclusively on deductive inference, which ensures the soundness of its conclusions. Is that correct? Are there other modes of inference used in mathematics?


  [1]: https://en.wikipedia.org/wiki/Deductive_reasoning
  [2]: https://en.wikipedia.org/wiki/Inductive_reasoning