Tbf, half the linguistics discipline thought that language's grammar was somehow hardcoded into our brain, which is clearly ridiculous if you look at how LLMs work, so you're not the only one who had misconceptions.

Perhaps you can turn your idea around slightly into finding a language that finds a balance between formality and universality, rather than computers and humans. Because even though computers now speak our language they do not use it in a logical way at all (arguably because we humans don't).

And while mathematics is very formal it has a lot of trouble expressing ideas from different branches that aren't as formal. Things like fuzzy logics have been created and many things like that but they are still very much on the formal side.

Perhaps you could even derive an academic language for a specific field, perhaps standardizing between synonymous constructions. You could even use LLMs to accelerate the process. Maybe LLMs are a good thing that makes your work easier!