> However, Godel shattered these aspirations in 1931 by proving the existence of true but unprovable mathematical formulas.
Godel sentences are unprovable, but they are not "true". They are independent, i.e. true in some models and false in others. The godel sentence happens to be true in the standard model - some people take liberties with this and extend to calling it true, but that's not accurate, or at the very least misleading.
> However, Godel shattered these aspirations in 1931 by proving the existence of true but unprovable mathematical formulas.
Godel sentences are unprovable, but they are not "true". They are independent, i.e. true in some models and false in others. The godel sentence happens to be true in the standard model - some people take liberties with this and extend to calling it true, but that's not accurate, or at the very least misleading.