[T]hese operations include all those which are used in the computation... - Alan Turing

The isolated man does not develop any intellectual power. It is necessary for him to be immersed in an environment of other men, whose techniques he absorbs during the first twenty years of his life. He may then perhaps do a little research of his own and make a very few discoveries which are passed on to other men. From this point of view the search for new techniques must be regarded as carried out by the human community as a whole, rather than by individuals.

The "computable" numbers may be described briefly as the real numbers whose expressions as a decimal are calculable by finite means. ...According to my definition, a number is computable if its decimal can be written down by a machine. ...I show that certain large classes of numbers are computable. They include, for instance, the real parts of all s, the real parts of the zeros of the Bessel functions, the numbers π, e, etc. The computable numbers do not, however, include all definable numbers. ...[C]onclusions are reached which are superficially similar to those of Gödel. ...[I]t is shown ...that the Hilbertian can have no solution. In a recent paper ... reaches similar conclusions...

Sometimes it is the people no one imagines anything of, who do the things that no one can imagine