what is a model of computation, mathematically? Where can I find a mathematical definition for "model of computation"? https://en.m.wikipedia.org/wiki/Model_of_computation doesn't provide a precise definition for "model of computation"--it doesn't treat it as a maths object, it states it in English. Contrast this to clear maths definition for formal language: subset of finite set of symbols together with Kleene star
I think that different mathematical models of computation capture different aspects of physical reality. Similar to models of solid state physics (say), these mathematical models may be largely incomparable. Think of analog computers, where the model may not even be described with discrete math. When it comes to automata and formal languages (of finite words over a finite alphabet), an early attempt of an overarching mathematical definition was the abstract family of acceptors, which encompasses Turing machines, finite automata,  stack automata,  pushdown automata and similar notions: Ginsburg, Seymour; Greibach, Sheila (1967). "Abstract Families of Languages". Conference Record of 1967 Eighth Annual Symposium on Switching and Automata Theory, 18–20 October 1967, Austin, Texas, USA. IEEE. pp. 128–139. Needless to say, that notion does not describe L-systems, nonuniform circuit families, quantum devices, probabilistic models, membrane computing etc.