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? 

Also, to be precise, what I am after here are the admissible modes of inference used for justification in the _final product_ of mathematics, not the types of inferences mathematicians use in their daily work to generate mathematics. 

(if there is nothing in mathematics but deduction, mathematics is an extension of logic, and there is no other way to see the situation)


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