As an example, I dislike how overloaded symbols like 'dx' are, which are sometimes purely syntactic sugar (specifying the variable of integration), sometimes ar

As an example, I dislike how overloaded symbols like 'dx' are, which are sometimes purely syntactic sugar (specifying the variable of integration), sometimes are just a part of another indivisible symbol (dy/dx), sometimes are treated as things that can be manipulated on their own but don't actually have a value or any rigorous meaning (physicists...), sometimes represent entire entities such as differential forms, and sometimes the 'd' is actually a fully qualified, completely rigorously defined operator (the exterior derivative, or the boundary map in a chain complex, especially for de Rham cohomology). I wouldn't be surprised at all if I'm missing other ways in which this exact same symbol occurs with different meanings. To the experienced eye, all these usages overlap in subtle ways, so that it all feels reasonable and even justified. But to newcomers, I think the notation just feels like a complete mess.