Turing's Computability Hypothesis

The Church-Turing thesis posits that any effectively calculable function can be computed by a Turing machine, highlighting the machine's ability to perform calculations based solely on its current state and the symbols it encounters. Although often mistaken for a theorem, this hypothesis remains unprovable due to the elusive nature of what constitutes "effectively calculable." Turing's intuitive concept suggests that with enough time and resources, a mathematician could compute any function through a series of logical operations, even if it takes eons to do so.