Quite often a branch of mathematics is discovered before it is appreciated that it is of use in the real world. This happened with the computer.

In August 1900, in Paris, at the start of a new century, David Hilbert, one of the world’s leading mathematicians, listed 23 outstanding problems in mathematics. These included questions regarding the foundations of mathematics and whether specific  problems were soluble. In 1928 he made one of his questions more specific: to determine whether there was some definite system that, in principle, could decide the truth of any mathematical assertion.

In April 1936, at Cambridge, a student named Alan Turing handed to his lecturer, Max Newman, a paper: On Computable Numbers. This answered Hilbert’s question in the negative: no such all embracing system exists.

But in the process of this abstract mathematical proof, Turing analysed the concepts of computing and showed that what could be calculated by a human computer could also be calculated by a machine. His theoretical machine - the Turing Machine - turned out to be uncannily similar to the computer which evolved by 1949. In fact Turing was formalising many of the ideas put forward by Babbage and others in the previous century, though Turing himself seems to have been unaware of, and therefore not influenced by, Babbage's work.

This moment may be considered to have launched   AGE OF THE COMPUTER!

David Hilbert