Inadmissible theorems in research One of my engineering friends told me how e once had to take a make-up calculus I exam due to being hospitalised and so self-studied a lot of the missed topics. For the make-up exam, e used L'Hôpital's rule, although we weren't taught that until 1 or 2 exams later. My friend told me that the professor wrote

'You are not yet allowed to use L'Hôpital's rule.'

So, I like to say that L'Hôpital's rule was inadmissible in that exam.
Now, it absolutely makes sense that if you're the student that you're not allowed to use propositions, theorems, etc from future topics, all the more for future classes and especially for something as basic as calculus I. It also makes sense to adjust for majors: Certainly maths majors shouldn't be allowed to use topics in discrete mathematics or linear algebra to have an edge over their business, environmental science or engineering (who take linear algebra later than maths majors in my university) classmates in calculus I or II.
But after bachelor's and master's and maths PhD coursework, you're the researcher and not merely the student (this is supposed to link to a star wars video): Say, you're doing your maths PhD dissertation or even after you've finished the PhD.
Does maths research have anything inadmissible?
I can't imagine you have something to prove and then you find some paper that helps you prove something and then you go to your advisor who would then tell you, 'You are not yet allowed to use Poincaré theorem' or for something proven true more than 12 years ago: 'You are not yet allowed to use Cauchy's differentiation formula'.
Actually what about outside maths, say, physics or computer science?
Does maths research have anything inadmissible?


No, but trying to prove X without using Y is still a very useful concept even in research, because it can lead to interesting generalizations, or new proof techniques that can be applied to a larger set of problems. 

For instance, in some sense the Lebesgue integral is "just" trying to prove the properties of integrals without using the continuity of f, or the theory of matroids is "just" trying to prove the properties of linearly independent vectors without using a lot of properties from the vector space structure.

So this is far from being a pointless exercise, if that's what you had in mind.