Calculus works on functions that we may consider as curves. The derivative of the derivative (and etc.) of some curves always end up at the line y=0. That means that at the heart of every derivative lies a line for these curves. However, to construct a curve with many lines makes points on the curve where the point is not differentiable.

Because the curve may have many possible derivatives at certain points, is it possible that Godel's Theorem may be understanding that these specific curves are both differentiable (by popular belief) and not differentiable? Could this be altering other equations in the Incompleteness Theorem?

If so, I would suggest re-writing the calculus theorems used in creating the other of Godel's Theorems in hopes that incompleteness would be solved.

I’m thinking of getting a tattoo of the first theorem as it would be represented in his numbering system but I can’t seem to find the answer anywhere. I understand the theorem is long but maybe just the final line. Thanks