Mathematics
The Church-Turing Thesis and Effective Computability
Quick fact
The Church-Turing thesis asserts that any function that can be computed by a human following a finite, step-by-step algorithm can also be computed by a Turing machine. Despite being unprovable, it is universally accepted because every proposed model of computation—lambda calculus, Turing machines, recursive functions—has been shown to define the same class of functions.
Why this is interesting
Imagine you are asked to write a recipe for a cake. But what if the recipe must work for any ingredient list, even one that includes 'a unicorn's tooth'? This is the kind of wild question that led to the Church-Turing thesis—a cornerstone of everything we know about what computers can and cannot do.