Since most posts don’t get many comments, I thought I would make one the required audience participation. The subject is “fundamental” theorems in the various subjects. What I am going for is hard to actually describe, but encapsulates a theorem being fundamental, its utility, its depth. It is the result in the subject that would hurt the most not to have, but does not have to be the putative “fundamental theorem of X”
For example, my votes for a few subjects:
Calculus: Mean Value Theorem.
Probability: Linearity of expected value.
Model Theory: The compactness theorem.