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Turing Machine Controversy *November 13, 2007*

*Posted by Andre Vellino in Epistemology, Logic.*

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In a previous post, I noted that Alex Smith had won a 25,000 prize for finding the smallest Universal Turing Machine. When I saw that the Prize Committee included Martin Davis, Marvin Minsky and Dana Scott, I figured there wasn’t much question about the correctness of the proof.

But it didn’t take long after this prize was “won” for some respectable academics on the FOM (Foundations of Mathematics) mailing list, notably Vaughn Pratt, to start poking holes in the proof. The current state of the debate is summarized in this post and it looks like Alex Smith is losing the argument.

Furthermore, there’s some question about who exactly on this committee checked the proof. The argument seems to have spilled over to the SciAm blog.

You’d think there wouldn’t be anything controversial about a mathematical proof. But where there are strong personalities, self interest and money involved, perhaps it’s inevitable that even truths in mathematics are disputable.

I seem to remember a similar controversy over a proof of Hilbert’s 16th a few years ago. There’s an article on it here, but I don’t know whether it was eventually resolved. There’s also an interesting set of mathematical mistakes here (scroll down about half way). At one point I’d talked about this sort of thing in my thesis, but ended up cutting it out, since I wasn’t saying much more than “hey, when things get complicated, everyone makes mistakes”…