I am aware of two major modes of reasoning: deductive and inductive. 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.

For inductive reasoning, what I have in mind here is what is explaining in this entry of the SEP.

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

I am aware of two major modes of reasoning used for justification of belief: deductive and inductive. 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.

For inductive reasoning, what I have in mind here is what is explaining in this entry of the SEP.

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

I am aware of two major modes of reasoning: deductive and inductive. 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)

I am aware of two major modes of reasoning: deductive and inductive. 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.

For inductive reasoning, what I have in mind here is what is explaining in this entry of the SEP.

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

I am aware of two major modes of reasoning: deductive and inductive. 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?

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

I am aware of two major modes of reasoning: deductive and inductive. 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)