Radio is currently the only realistic means of interstellar communication at our disposal, so we listen for (and sometimes send [1]) radio waves. In other word

Radio is currently the only realistic means of interstellar communication at our disposal, so we listen for (and sometimes send [1]) radio waves. In other words, we look for aliens equipped with radio telescopes, because they are the only kind we can hope to find. The choice of language follows from that. To have technology at the level of radio telescopes, you need to understand physics at mid-20th century level (or higher). To understand physics at that level, you need math at the level of calculus and differential equations. So we look for, and sometimes send, messages which start with simple mathematical relations and then build up to physical quantities. [1] https://en.wikipedia.org/wiki/Arecibo_message https://en.wikipedia.org/wiki/Arecibo_message