A paper recently made available on Arxiv claims to have found a contradiction in Gödel's proof of his most famous theorem, that the metamathematical system of Whitehead and Russel is incomplete (ie, there exist sentences that can neither be proven true nor proven false.)
I haven't read the paper, and I've got to admit that it seems very unlikely. But it's interesting to consider it at least.
A Junior Magistrate’s Education
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