That’s why the machines were central to Turing’s paper. To show there were algorithms that Turing machines would run indefinitely and inconclusively was a way of showing Hilbert was mistaken.

Britain’s Alan Turing published a paper entitled “On Computable Numbers with an Application to the Entscheidungs-problem” on November 12, 1937, that would form the basic theory of computability for ...

Alan Turing: still casting a long shadow over mathematics One hundred and fifty years of mathematics will be proved wrong if a new computer program stops running. Thankfully, it’s unlikely to ...