Nevertheless, there are large parts of mathematics that are catagorical. Not only are all theorems provable, there is a proof scheme for these theorems. Euclidean (and consequently, all the non-Euclidean) geometry is one such. First order logic is another as is Pressburger arithemetic.
Nevertheless, there are large parts of mathematics that are catagorical. Not only are all theorems provable, there is a proof scheme for these theorems. Euclidean (and consequently, all the non-Euclidean) geometry is one such. First order logic is another as is Pressburger arithemetic.
Always good to be reminded that things aren't totally hopeless.
I recommend Huber-Dyson's book, DS, even though it has a surfeit of typos. The book is one of those 'camera-ready copy' jobs, and she should've had a good proof reader go over it, but didn't.
The other thing to keep in mind is that the limitation imposed by Gödel's Incompleteness theorems has little if any practical effect on most Mathematicians. Since the only sort of theorem used by Mathematicians to prove other theorems are theorems which have already been proven, Gödel's Theorems never come into play. IOW, that which we can prove, we can prove.
It's only the meta-Mathematicians, the Russells, the Whiteheads, et al., whose lofty goals were trashed forever by Gödel's results. Life for mortal Mathematicians goes on as before, they hardly even feel a bump when the pass over Gödel's Theorems.