It is, in a way, the idea behind Borge's “Analytical Language of John Wilkins”: https://www.alamut.com/subj/artiface/language/johnWilkins.ht...

It is a neat idea!

This is very close to how Godel numbering (https://en.wikipedia.org/wiki/G%C3%B6del_numbering) works, to give every possible mathematical formula in a fixed language its own unique number.

Lol, that's a great story; if only that sort of thing was practical, how much more fun life would be :-) I actually had the opportunity to do something similar not too long ago. I'm a beginner learning to program and I had a little puzzle that I got from my grandma ~15 years ago. You have a tower of blocks with symbols on them, and have to arrange the blocks so that all of the symbols on each side are distinct [1]. The problem was small enough that I could just model each symbol as a prime and check uniqueness by seeing of the product was equal to 2 * 3 * 5 * 7 * 11 * 13.

[1] https://imgur.com/vTZotGC

Whether or not it's incredibly stupid, you're in good company: it occurred to Leibniz, too. Search for 'prime' at https://pron.github.io/posts/computation-logic-algebra-pt1 (though for him the unique IDs were for concepts rather than individuals).

You've rediscovered one-hot binary encoding with prime numbers :)

species complex, hybrids, mimicry, evolutive convergence, chimaeras... Life is too complicated and exhuberant to reduce it to a math formula

No it's not. It is likely too complicated to reduce to a formula that you can evaluate in reasonable time, or too complicated to measure with sufficient accuracy to even know what numbers to put into that formula, but life still follows the laws of physics and to the best of our knowledge they can be expressed in mathematical language.