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If you read a history of computing published before 1974 you will discover that the first programmable electronic digital computer was ENIAC (Electronic Numerical Integrator And Calculator) which was designed and built by Presper Eckhert and John W Mauchly at the University of Pennsylvania and announced to the world in 1946. The real first computer, Colossus, was actually completed three years earlier but it was destroyed in order to protect the secret work it had been involved in. The story involves theoretical mathematics, codes & cyphers and the pressures of war. The secrecy was so intense that, even today, the true story is not generally known (the Pennsylvania University ENIAC Museum website makes no mention of Colossus).

Although there is some argument about what constitutes the "first computer", it can be stated without question that Colossus was (a) programmable; (b) electronic; (c) digital; and (d) a computer of sorts. And so was ENIAC. That Eckhert and Mauchly "...only had the comparable ENIAC fully working in 1946, by which time its design was obsolete" [AH-WHOI], shows that the two machines were both computers of some sort and that Colossus was first.

The origin of Alan Turing's contribution to the development computers in general, and the creation of Colossus in particular, lay with some peculiar discoveries in the abstract realms of pure mathematics in the early part of the 20th century. Mathematicians at the time were trying to put the very foundations of mathematics on a firm, logical footing. Amongst the leading proponents of such a scheme was German mathematician, David Hilbert who, famously, collected 23 (then) unsolved mathematical problems for an address to the 2nd International Congress of Mathematics in Paris in 1900. Many of those problems have been solved, but they are all fundamental to the core of pure mathematics. This was followed, between 1910 and 1913, by the Principia Mathematica by Alfred North Whitehead and Betrand Russell. This attempted to put one part of mathematics on a secure footing: number theory. In particular it provided what seemed to be a consistent method of demonstrating the correctness of the propositions it contained and, most importantly, of demonstrating the correctness of the method used to prove those propositions.

As a result of this, David Hilbert returns to the story again, in the early 1920s, with the notion of decidability: "Could there exist, at least in principle, a definite method or process by which

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