That is why scientific papers have so much "let x be ..."
What is a pitfall however to declare these variables implicitly and rely on them too long. As a writer it is very easy to forget this because of course you know what topic you are writing about. As a reader however you have to do some work to get into the same (or similar) world of thinking as the one the writer created for you.
Same is true for speaking. Of course I know what I mean when I say something, but the other person might not even know what language I am speaking in and would have to decipher that first. In a similar way people have to decipher abstract topics you might be talking about