If one uses a classically rigorous definition of a tautology, the answer is yes. Classically, a tautology is a statement that is necessarily true by the classical laws of logic (identity, non-contradiction, excluded middle). So, statements such as “if the grass is green then the grass is green” and “all bachelors are unmarried men” are both tautologies as is “all men are mortal, Socrates is a man, therefore Socrates is mortal” —- in fact, all valid deductive reasoning would be a tautology in classical logic. Mathematical theorems are derived by valid deductive reasoning from assumed axioms thus they are all tautologies.


Problem is that it is common these days to play with words including the word “tautology” so as to avoid classically rigorous definitions that do not give the answer desired. The common technique is to split tautologies into semantics (logical truths) and syntax (analytic truths). Though this was originally done for heuristic purposes, ontologically and for philosophy of logic and even metaphysics purposes syntax and semantics are now often severed as if they are not necessarily dependent on each other — being used as abstractly severed aspects of a holistic conceptual wordgame.


So, if one defines logical truths as merely logical syntax, then of course created differences in semantics can be used to argue mathematical theorems or anything else are not tautologies. “If it is green then it is green” is not a tautology because “it” may have different meanings.


Same with a concept of analytic truths in which semantics is used solely as a basis to define a tautology. “All bachelors are unmarried men” is not a tautology if we are speaking Swahili.


Using the above semantic/syntax distinctions in a sophisticated sleight-of-hand combining of semantics and syntax as logicians and mathematicians often do can also be used to define away “tautology” by pointing out that some axioms and theorems derived from them are necessary truths in a given model but not in other models — that is that not all necessary truths can necessarily be proven to be “true” with truth taken to mean true in all possible worlds (which is what Godel proved through his Incompleteness Theorem which may itself be a tautology). The fact that some mathematical theorems may be true without proof that they are “true” does not disprove that any which we can prove as “true” are tautologies. The only way to have a known necessarily true mathematical theorem is by having it validly and deductively follow from the assumed axioms, at which point it is a tautology in the wordgame of those axioms.


This does not mean that mathematical theorems or tautologies are trivial. They tell us truths about our language and our use of it in describing reality irrespective of whether or not they say anything about reality. Language may be its own reality just as numbers may be, an abstract reality of numbers and their theorems may be as real as any of the objects of the senses.