

I didn’t read more than what’s in OP’s post, but I think the reason the researchers can be so sure is because there are ways to mathematically prove that something cannot be calculated by an algorithm (this is related to how we can mathematically prove that some things cannot be proven).
One classic, simple example of this is the halting problem. It boils down to the fact that we can prove that there is no algorithm that can take any algorithm as an input and determine if that algorithm will finish (halt) after finite time.


This one isn’t super well known, but for small projects I really like raylib, and raygui. It gets impractical for complex GUIs, but it does make it really easy to quickly start something from scratch.