Yes, to an extent. When you actually study history of mathematics, you find many ideas swept under the rug as they are for whatever reason making some people uncomfortable. Simple example is a material implication, precisely handling false antecedents in binary logic (90% of population finds it weird as it doesn't correspond to their thought processes). The problem of its adoption was solved by waiting for logicians that didn't accept it to die. Arguably, this very logical connective is the cause of Goedel's incompleteness problem and some logics that reject it such as Relevance logic get to almost complete systems but are way more complicated (though also way more logical to lay persons and arguably more similar to how humans think). There is a reason why medicine doesn't use mathematical logic and rather is based on counter-factuals.

So you can compare current mathematics to be like a certain programming language. Let's say it's like FORTRAN. There might be C++ for the same concepts, there might be Python, Smalltalk, Prolog or Haskell for the same concepts, but everything you read is in FORTRAN. And very few people like or are capable reading FORTRAN.