I am new here and, although I have considerable knowledge in general science, I am definitely not an expert at maths.
Correct me if I am wrong but; two of the implications of the proven Godel's theorem is that:
1, there must be some mathematical theorems that can be made that are unprovable and yet are nevertheless true.
2, we cannot ever know exactly which mathematical theorems are the ones that are both unprovable and yet are nevertheless true.
But my main question which is my thirds question is this;
3, Is there is an infinite number of possible mathematical theorems that are BOTH true AND unprovable AND which can NOT be proven to be unprovable?
4, IF the answer to question 3, is 'yes', can this be deduced from Godel's theorem alone or is understanding of some extra deduction required to deduce that the answer to 3, is 'yes'?