Universality and unreachability in physics, mathematics, computer science and slightly beyond

Certain statistical physics models are universal (arXiv: 2407.13428) in a similar way to universal Turing machines and the universal approximation theorem for machine learning models. I will share our work to understand the relation between these forms of universality by direct comparison (arXiv:2006.03529, arxiv:2507.07669) and via a categorical framework (arXiv: 2307.06851). I will also talk about their relation to forms of unreachability such as uncomputability or undecidability, which are instances of Lawvere’s fixed point theorem.