I agree that the notation can be a problem, but it has to serve a number of different uses: 1. Communication between mathematicians. Like coding (or legal com

I agree that the notation can be a problem, but it has to serve a number of different uses: 1. Communication between mathematicians. Like coding (or legal communication), the notation needs to be precise and unambiguous or you can cause misunderstandings the derail the point you are trying to make. This does not always make for easy to understand notation. 2. A shorthand for key concepts and relations to other math users. This is something of a problem that is caused by the fact that mathematicians are often the people who teach the non-mathematicians. Who then in turn use the math or teach it to novices. It's a large hurdle, but then you're left with people who learned one notation as a novice, and are then forced to relearn how to communicate these concepts if you want to participate in the academic conversation. 3. A method of communication between non-mathematicians (like physicists or engineers). There is actually a fairly large difference between how physicists communicate a key concept in their field, and how a mathematician might communicate the same idea. This isn't a large problem at the start, but then you're left with trying to move the ideas down the chain to novices and you have possibly several competing notations that eventually have to be sorted out. Which is why some notation is carried down and others eventually gets "weeded out".