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THIS PROGRAM WAS FIRST AIRED ON 20 FEBRUARY 2010.Kurt Gödel was one of the foremost mathematicians and logicians of the 20th century, best known for his famous incompleteness theorem, which tells us that there are mathematical 'blind spots': parts of mathematics that traditional methods of proof cannot access. The theorem has far-reaching consequences for computing and even for our understanding of the nature of the human mind. This week, Mark Colyvan from the University of Sydney introduces us to this strange and paradoxical result.