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by Grothendieck 4587 days ago
There's good evidence that Turing machines do capture the right notion of computability. You can enhance a Turing machine in many ways without changing what it can compute. Further, Turing machines, the lambda calculus, recursive functions, cellular automata, and register machines all give the same notion. Even a quantum computer can be simulated by a Turing machine.

https://en.wikipedia.org/wiki/Church-turing_thesis