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Documentary about infinite and its implications in mathematics (BBC)
http://www.youtube.com/watch?v=Cw-zNRNcF90

As usual, Gregory Chaitin on the history of logic
http://www.youtube.com/watch?v=HLPO-RTFU2o

Another one about logic and artificial intelligence
http://www.youtube.com/watch?v=nA3m9jgMp3U