One might say that coming up with the right definitions/theorems is subjective and hence un-examinable, but it’s certainly true that some definitions and theorems are more interesting and fruitful than others. It’s quasi-objective. One often gets the feeling of the “right definition“, say, in category theory.
Perhaps one example of a definition-formulating or theorem-formulating question in an exam would be this:
(E.g.1) … (E.g. 2)… (E.g. 3) …(E.g. 4) … Come up with a theorem which encapsulates E.g. 1 – 3 and with an additional criterion, E.g. 4.
One could say that coming up with the right definitions/theorems is even more difficult and insightful than simply theorem-proving/problem-solving since it requires greater creativity.