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Sure, it is certainly possible that mathematics can be automated, but mathematics is also over 2000 years old. We are not much closer to automating it than the
by c_lebesgue 11y ago
Sure, it is certainly possible that mathematics can be automated, but mathematics is also over 2000 years old. We are not much closer to automating it than the Greeks were. P=NP does not only break the Complexity theory (which is a relatively new invention), it also has profound consequences to all of human reasoning.
- TheOtherHobbes 11y agoWe already have commoditised math solvers for any number of (relatively) trivial problems. What we haven't automated is mathematical creativity, which is a completely different class of problem.
- foobar2020 11y agoThe whole difficulty of the hard complexity questions such as "Is P=NP?" hides in the non-trivial, "corner" cases. Sure, we have SAT solvers that are by many practical standards really good. P=NP would imply that we can relatively easily find polynomially long proofs to many hard propositions, such as the P=NP problem itself! Or many other open mathematical problems. Creativity is an anthropomorphic, abstract concept, a way of describing human ways to find solutions. What really matters is the proofs.