„We may compare a man in the process of computing a real number to a machine which is only capable of a finite number of conditions q1, q2, …, qK which will be called ” m-configurations .”“

— Alan Turing
„It remains to discuss briefly what general requirements may be justly laid down for the solution of a mathematical problem. I should say first of all, this: that it shall be possible to establish the correctness of the solution by means of a finite number of steps based upon a finite number of hypotheses which are implied in the statement of the problem and which must always be exactly formulated. This requirement of logical deduction by means of a finite number of processes is simply the requirement of rigor in reasoning.“
— David Hilbert
„[T]he m-configuration may be changed.“
— Alan Turing
„If an ɑ-machine prints two kinds of symbols, of which the first kind (called figures) consists entirely of 0 and 1 (the others being called symbols of the second kind), then the machine will be called a computing machine.“
— Alan Turing
„To each computable sequence there corresponds at least one description number, while to no description number does there correspond more than one computable sequence. The computable sequences and numbers are therefore enumerable.“
— Alan Turing
„The idea behind digital computers may be explained by saying that these machines are intended to carry out any operations which could be done by a human computer.“
— Alan Turing
„In some of the configurations in which the scanned square is blank... the machine writes down a new symbol on the scanned square: in other configurations it erases the scanned symbol.“
— Alan Turing