As the name indicates, Reverse Polish Notation, or Direct Polish
notation, are notations. They are syntax for representing something,
and actually efficient syntax if you consider memory requirements.
What they represent are rooted trees, which can be formulae, abstract
syntax trees (AST), and other kinds of entities, that anyone has a
constitutional right to consider absolutely useless.
Occasionally, one has to store such entities on file. For example
there are systems that may edit or transform programs as AST, and
may need to store such representations. Polish Form is convenient.
It has limited readability for humans, especially for large trees, but
it is a very convenient representation for machines.
Another aspect of it is that I believe the study of trees and their
elementary uses and representation, as well as associated devices
(stacks), to be pedagogically useful as an introduction to future
studies of more advanced concepts (syntax, parsing, logic,
It has also the advantage of being conceptually rather simple, and
easy to experiment on paper. It is also a nice occasion to discuss syntax and the fact that syntax is representation, and that representations may vary, while representing the same thing, and that different representations may be used depending on the need to be met (space optimization, easy modification, human readability, computer readability, ...).
But I am surprised that this question, and its answers, are
considering only RPN, and none considers direct polish notation.
It is certainly excellent that students ask. But answering such
question always has diverse aspects. Is it useful for the knowledge itself?
I think it is. Is it useful as pedagogical exercise? I think it is,
but that depends much on the intended audience, and only the teacher
can assess what it is able to understand. Is it useful to understand some conceptual issues? I think it is, but again it depends on the teacher's assessment of what concepts can be explained to their students.