5 ms·

A proof only requires a valid transformation from axioms to conclusion. No person required.

• leeoniya 11y ago
  until an automated theorem prover can be made to certify these transformations as valid, a person has to do this work manually. this is particularly true in this specific instance since an enormous, alien framework has been erected to set up what defines a valid transformation within it. on point [1], though i suppose mathematical proofs don't quite align with this characterization. [1] https://www.quora.com/Is-it-possible-to-have-a-world-without-an-observer https://www.quora.com/Is-it-possible-to-have-a-world-without...
• eru 11y ago
  Depends on your notion of proof. That is one notion. There's the human version, that the other commentors talk about. There's also https://en.wikipedia.org/wiki/Interactive_proof_system https://en.wikipedia.org/wiki/Interactive_proof_system for an interesting formal version that is not `transforming axioms'.
  • jsprogrammer 11y ago
    In this case, the proof should be formal since it is a statement about the natural numbers. (as far as I can tell)
    • eru 11y ago
      Doesn't really matter too much what the proof is about, does it? You can still choose different notions of proof.
• hyperpape 11y ago
  This is a simplified picture of mathematical practice. Not everything is formal in the sense of an logical derivation, and there are phrases like "trivially..." that show that the proof relies on being read by a competent mathematician. The standards of what makes a good proof are also malleable. Here is a paper that discusses some of these issues in passing: https://dl.dropboxusercontent.com/u/10561191/Published/ProbProofs.pdf https://dl.dropboxusercontent.com/u/10561191/Published/ProbP...
  • jsprogrammer 11y ago
    "Trivially" should be reserved for conclusions that follow directly from a simple transformation of an axiom or proved theorem.