Post #2920366

But this has always seemed contradictory to the notion of "pure" mathematics, since it is motivated primarily by "the love of wisdom" for lack of a better term. One may object that this invites all kinds of 'crankery'. I.e. that the previous structure was primarily geared towards knowing immediately the difference between 'crankery' and 'non crankery', and that this became necessary because of the internet. But for a pragmatic rebuttal, this problem is potentially solved by lean formalized proofs becoming cheaper. One can now look at a result being proved and see that it was truly proved in the paper. Since that is no longer the bottle neck, the way in which the result should be interpreted by humans, and the way in which it enhances our understanding of interesting philosophical questions, is the most valuable part of the paper. The peer review process becomes more about looking at the lean formalized result being proved, and reading the philosophical interpretation/discussion, and deciding if that interpretation is actually correct, or if there are serious rebuttals to it. For example, the formalized theorem may be 'the wrong theorem', or perhaps some of the philosophical discussion is not actually philosophical, and can be settled entirely formally. These are both situations that would warrant rejection of the paper. This means that this philosophical discussion still requires the mathematician to know and utilize classic formal reasoning, but it is just that it must be used in an entirely different way. (9/n)