The sort of mathematics which was heavily based on calculation had its heyday with Leonhard Euler in the 18th century. Of Euler it has been written: “Euler calculated without apparent effort, as men breathe, or as eagles sustain themselves in the air”.
In his writings you are more likely to find long passages of algebraic working, with few words of explanation, than in more modern mathematics.
But Euler, too, was keen to use good notation, and words to explain notation to make clear what he was doing in the algebra and convince his readers about concepts. Here is an excerpt from his book on differential calculus.