Complex sentence: While the meaning has not always been defined precisely, the term is commonly used in mathematical jargon An elementary proof is not necessarily simple, in the sense of being easy to understand: some elementary proofs can be quite complicated.
Split into simpler sentences: While the meaning has not always been defined precisely, the term is commonly used in mathematical parlance. It should be noted that an elementary proof is not necessarily simple, in the sense of being easy to understand: some elementary proofs can be quite complicated.