How can we rank and compare the difficulty of theorems in different fields?
Why would one need to?
Don't know but one might find it interesting to do so and wonders how?
The answer is that every actively researched field has theorems of any desired difficulty i.e. for all fields of research F and for all levels of difficulty D there is at least one theorem T in F such that the difficulty of F is greater then D.
Separate names with a comma.