When is it appropriate to add a title to a theorem?

Question

I am writing a paper and I have proved a couple of theorems and three propositions. Is it appropriate to add titles to these theorems and propositions for more clarity? For instance, say

Theorem 2. (Convergence of X) ....

Proposition 1. (Unbiasedness of Y) ....

Answer 1

Usually when the theorem is important, and you would like to refer to it repeatedly in the future calling it something more distinctive than "Theorem 2.6". This adds clarity because when readers read your article, they immediately know the theorem is important, and when referenced in the future, they will not need to jump between pages to remember the theorem. Alternatively, if it's something that has a common name in the literature, or if it's something that can be stated simply and be understood, you should name the theorem as well.

For example, suppose you had proven the twin prime conjecture. You wouldn't want to just let it be Theorem X.Y, and you would want to instead label it Theorem X.Y (Twin Prime). But if you had proven something trivial, like that $(x+y)^2=x^2+xy+yx+y^2$ in any ring, you can safely not give it a name.

Answer 2

It seems to me that the comments could be put just before the statements. For instance:

The theorem below establishes the convergence of $X$.

Theorem 2. Let ...