Computable Numbers, 80 Years on..

There’s been rather a lot of sad news conveyed via this blog recently, so I thought that today I’d mark a happier event. Eighty years ago today (i.e. on 28th May 1936), a paper by Alan Turing arrived at the London Mathematical Society. Entitled “On Computable Numbers, with an Application to the Enstscheidungsproblem“, this was not only enormously influential but also a truly beautiful piece of work. Turing was only 23 when he wrote it. It was delivered to the London Mathematical Society about 6 months after it was submitted,  i.e. in November 1936..

Here’s the first page:


The full reference is

Proc. London Math. Soc. (1937) s2-42 (1): 230-265. doi: 10.1112/plms/s2-42.1.230

You can find the full paper here. I heartily recommend reading it, it’s wonderful.


4 Responses to “Computable Numbers, 80 Years on..”

  1. Is there an open access version? This link gives me a paywall. Copyright must have expired though.

  2. Anton Garrett Says:

    Are numbers which are representable only as an infinite series computable? I don’t quite get the category. Or the point, in fact, for the pure maths of computation theory looks more contrived than elegant to me, and as for application I don’t know if it has been applied to help anybody design a better computer. I am willing to believe that the problem is with me (and my scepticism is not aimed against Turing, who deserved high national honour), but I’d love an explanation from somebody having a theoretical-physics background.

  3. “Are numbers which are representable only as an infinite series computable?”

    He explicitly mentions pi and e.

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