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He doesn't mention this (I guess it goes without saying among mathematicians), but part of the problem is that in mathematics one fact doesn't generally seem to

• JadeNB 16y ago
  > He doesn't mention this (I guess it goes without saying among mathematicians), but part of the problem is that in mathematics one fact doesn't generally seem to cause another: certainly there's no adequate causality that can trivially be verified by intuition or common sense. However, there is a sense (albeit informal) in which mathematicians recognise causality, and he alludes to that when he says that probably no one would say that the Riemann hypothesis implies Fermat's last theorem. I think that all mathematicians (or at least those who learned from Herstein!) would agree that Sylow's theorem on the existence of p-subgroups of all possible orders is equivalent to the weaker statement about the existence of p-Sylow subgroups; but no mathematician would mean by that merely that both are true.