I am looking for a taxonomy of proof methods in mathematics.

For basic proof methods I would think of proof by contradiction, mathematical induction, structural induction (yes I am a computer scientist), proof by symmetry, proof by duality

for advanced proof methods, forcing comes to my mind.

For a starter, I have found

TAPTICS: A Taxonomy of Proof Techniques In Computer Science

Proof Techniques

But is there a book or a survey journal paper devoted to this?

  • 3
    $\begingroup$ This definitely seems like a worthwhile question to ask, except that it seems way too broad to have any chance at an answer—especially if one doesn't specify a discipline, each discipline having its own specific collection of interesting proof techniques. $\endgroup$ – LSpice 2 days ago
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    $\begingroup$ An early classic whose aim was to be pedagogic, rather than encyclopedic, is How to Solve It (1945) by G. Pólya. $\endgroup$ – Igor Khavkine 2 days ago
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    $\begingroup$ There is also the Tricki, which is a Wiki-style site of proof techniques: tricki.org $\endgroup$ – Tony Huynh 2 days ago
  • $\begingroup$ Perhaps the question could be reframed to a narrower scope, asking how one might go about classifying the proof methods. I.e. what are the highest level distinctions we can make between types of proofs, and how would you go about categorising those at the lower levels of the taxonomy. I could imagine seeing how different people organise these ideas in their head would be insightful. $\endgroup$ – PolymorphismPrince 9 hours ago