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I have a curiosity about mathematical proofs and I don't know how to research it properly. I apologize to the admins in advance, but it's a genuine question.

Given a proposition P, are there other demonstration methods that allow me to prove that P is true, other than the usual/classic ones (direct proof, contradiction, contraposition and induction)?

Gleberson Antunes
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  • Some others are listed here. For some types of proposition, we can go further. For example, there are many ways to prove "this integral has this value". – J.G. Feb 28 '23 at 09:46
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    There are a few books on this topic. I have heard "How to Prove it" by Velleman is good. – Porky Feb 28 '23 at 10:02
  • In a sense, there is only one way to prove anything: the direct proof: a list of statements that are either axioms, or a statement $A$ which is preceeded in the list by statements $B$ and $B \implies A$. All other methods of proof are essentially metamathematical demonstrations that a direct proof exists. – Paul Sinclair Mar 01 '23 at 03:14

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