I think in some part you had it right that it differs a bit by specialty, but I think the bigger part of it is that the syntax doesn't mean much without the concepts behind it. Notation is a way to compress concepts that are already understood in elaboration.
Being able to recognize notation without the conceptual underpinning might be useful in directing you towards what you need to learn for a particular task, but it's going to be difficult to learn without anything to hang it on. That said, maybe what you actually want is a math notation OCR that can direct you to documentation for possible interpretations.
