He was in some respects a quintessential British amateur, dipping his intellect into different areas. He achieved a high level of competence in pure mathematics, and used that as his professional base. His contributions in traditional mathematics were certainly perfectly respectable, though not spectacular. But in every area he touched, there was a certain crispness to the ideas he developed–even if their technical implementation was sometimes shrouded in arcane notation and masses of detail.
In some ways he was fortunate to live when he did. For he was at the right time to be able take the formalism of mathematics as it had been developed, and to combine it with the emerging engineering of his day, to see for the first time the general concept of computation.
It is perhaps a shame that he died 25 years before computer experiments became widely feasible. I certainly wonder what he would have discovered tinkering with Mathematica. I don’t doubt that he would have pushed it to its limits, writing code that would horrify me. But I fully expect that long before I did, he would have discovered the main elements of NKS, and begun to understand their significance.
More on Alan Turing here.
(Via Jennifer Peterson of Wolfram Research.)