As far as I can see people always radically exaggerate the effect of the incompleteness theorems. It seems interesting that any nontrivial axiomatic system has statements which are true but unprovable but to say that derails Hilbert’s project seems just obviously untrue when you can for example join math postgrad programs now which are focused on formalisation. [1] So formalisation is very much still going on, probably more so now than ever given advances in theorem provers.
Yes there are undecidable statements (eg the continuum hypothesis) but that doesn’t change the fact that the vast vast majority of statements in any axiomatic system are going to be decidable, and most undecidable statements are going to have “niche” significance like that.
Yes there are undecidable statements (eg the continuum hypothesis) but that doesn’t change the fact that the vast vast majority of statements in any axiomatic system are going to be decidable, and most undecidable statements are going to have “niche” significance like that.
[1] eg https://www.imperial.ac.uk/study/courses/postgraduate-taught...