Girdles in Completeness

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mathematics is about taking axioms. This is where we all begin, the fundamental truths we think about and then use proof to see the logical consequences of that. But Girdle says that's a hopeless task - there will always be things missing. So maybe I've been working on this conjecture for 15 years but it isn't true. And you know, one thought is, well, if it is true, why not just add it as an axiom? And Girdle's incompleteness theorem, everything will still remain incomplete. There's no way to complete the thing by adding another axiom.

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How can we have System-2-type reflection but with System-1-type speed? How can math be considered to be a "fast" way of solving problems? Is math discovered or invented? How can we use math to think better in everyday life? How can math education be improved? Do mathematicians have a snobbish preference for "pure" maths over applied maths? How can math be used to tell stories?

Marcus du Sautoy is the Simonyi Professor for the Public Understanding of Science and Professor of Mathematics at the University of Oxford. He is author of seven books including his most recent book, Thinking Better: the Art of the Shortcut. He has also published a play, I is a Strange Loop, which was performed at the Barbican in London in which he was also lead actor. He has presented numerous radio and TV series including a four-part landmark TV series for the BBC called The Story of Maths. He works extensively with a range of arts organisations bringing science alive for the public from The Royal Opera House to the Glastonbury Festival. He received an OBE for services to science in the 2010 New Year's Honours List and was made a Fellow of the Royal Society in 2016. Follow him on Twitter at @MarcusduSautoy or find out more about him at www.simonyi.ox.ac.uk.

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