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Might he have missed something in his informal reasoning about what an algorithm is?
In 1985, the English physicist David Deutsch suggested a deeper approach to the problem of defining what is meant by an algorithm.
In his paper, published in 1936, Turing wasn’t trying to invent a clever gadget or to create an industry.
Rather, he was attacking a problem about the nature of mathematics posed by the German mathematician David Hilbert in 1928.
Turing was arguing that a single, fixed device could imitate algorithmic process whatsoever, provided the right program was supplied.
It was an amazing leap of imagination, and the foundation of modern computing.
But Turing’s argument was convincing enough that later mathematicians and scientists have for the most part been willing to accept it.
Turing’s machine became the gold standard: an algorithm was what we could perform on a Turing machine.
Today we’re used to the idea that computers can be programmed to do many different things.
In Turing’s day, however, the idea of a universal programmable computer was remarkable.