Also, the assumption that math is universal so sharing vocabulary in math is helpful for bootstrapping language understanding is a fascinating assumption to que

Also, the assumption that math is universal so sharing vocabulary in math is helpful for bootstrapping language understanding is a fascinating assumption to question. Even if you can explain Pi and prove that you can mutually understand trigonometry that might give you some small portion of engineering insight, but it can't yield most of the rest of engineering such as design or aesthetics (or emotions) or any number of other things that make for useful project communication. It's something I've often thought about in the way that the Voyager record was built and Sagan's Cosmos novel assumes it and many others. Even recently, the novel Project Hail Mary borrowed that assumption that math is enough shared language to bootstrap understanding. I think the movie Arrival did some of the best work of showing why that wouldn't necessarily work, but also had the language in question designed by a mathematician and still fell into some parts of the assumption/trope. I'm not saying any of these examples are bad for doing this, I certainly love them all. It's still a small something worth criticizing. It's certainly not a bad thing to want to communicate math, and to hope that things like Pi are "constant enough" to provide bootstraps to other communications, but it's also such a fascinating thing how much science fiction thinking (and real world scientific thinking such as the Voyage Record) think that you can just sort of "yada yada yada" your way from "so we established communications of basic mathematical constants and concepts" directly as a straight line of some sort to "now we can communicate all sorts of other things".