3 ms·

^ Exhibit A why using "believe" is a bad choice of words. Mathematical poofs are either correct or false. There is no middle ground.

• karmakurtisaani 2y ago
  Well.. there is. Middle ground being a very complex, but somehow convincing argument that no one can reasonably check. There was one of these cases in number theory some years ago, can't remember the details. Proofs can be only true or false, but accepting proofs is in the end a social process.
  • unclad5968 2y ago
    A convincing argument that cannot be checked is not a proof. If you want to extend the definition of proofs you're welcome to do that, but for academic mathematics the meaning of proof doesn't contain a middle ground.
    • valenterry 2y ago
      Why would it not be a proof? What is your criteria of "can be checked then"? If a proof for "sqrt(2) is not a rational number" can't be checked by a 5yo, it's still a proof no?
  • nhatcher 2y ago
    A couple come to mind * The proof of the classification of simple groups[0] * The work on topological four manifolds by M. Freedman [1] [0]: https://en.m.wikipedia.org/wiki/Classification_of_finite_simple_groups https://en.m.wikipedia.org/wiki/Classification_of_finite_sim... [1]: https://news.ycombinator.com/item?id=28471159 https://news.ycombinator.com/item?id=28471159
  • konschubert 2y ago
    > Proofs can be only true or false Yes. The fact that we don't know the truth doesn't mean there isn't one.