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Godel's Incompleteness Theorems

45 minutes
First broadcast:
Thursday 09 October 2008

Melvyn Bragg and guests discuss an iconic piece of 20th century maths - Gödel’s Incompleteness Theorems. In 1900, in Paris, the International Congress of Mathematicians gathered in a mood of hope and fear. The edifice of maths was grand and ornate but its foundations, called axioms, had been shaken. They were deemed to be inconsistent and possibly paradoxical. At the conference, a young man called David Hilbert set out a plan to rebuild the foundations of maths – to make them consistent, all encompassing and without any hint of a paradox.

Hilbert was one of the greatest mathematicians that ever lived, but his plan failed spectacularly because of Kurt Gödel. Gödel proved that there were some problems in maths that were impossible to solve, that the bright clear plain of mathematics was in fact a labyrinth filled with potential paradox. In doing so Gödel changed the way we understand what mathematics is and the implications of his work in physics and philosophy take us to the very edge of what we can know.

With Marcus du Sautoy, Professor of Mathematics at Wadham College, University of Oxford; John Barrow, Professor of Mathematical Sciences at the University of Cambridge and Gresham Professor of Geometry and Philip Welch, Professor of Mathematical Logic at the University of Bristol.

  • Further Reading

    The Music of the Primes: Why an Unsolved Problem in Mathematics Matters by Marcus du Sautoy (HarperPerennial; New Ed edition, Sep 2004)

    The Emperor's New Mind: Concerning Computers, Minds and the Laws of Physics by Roger Penrose (Oxford Paperbacks; New Ed edition, March 1999)

    Gödel's Proof by Ernest Nagel and James R. Newman (Routledge; New Ed edition, June 1971)

    Gödel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter (Penguin; 20Anniversary Ed edition, March 2000)

    Kurt Gödel: The Album Editors: K. Sigmund, J. Dawson, K. Muehlberger (Amer Mathematical Society, 2006)

    Forever Undecided: A Puzzle Guide to Gödel by Raymond Smullyan (Alfred a Knopf, 1987)

    Gödel's Proof by Nagel and Newman (NYU Press; Revised edition, 2001)

    Gödel's Incompleteness Theorems: an Incomplete guide to their use and abuse by T. Franzen (AK Peters, 2005)

    Inexhaustibility: a non-exhaustive treatment by T. Franzen (AK Peters, 2004)

    Incompleteness in the Land of Sets by M. Fitting

    A Logical Journey by Hao Wang (the MIT Press, 1997)

    What is Mathematical Logic by C. J. Ash, J. N. Crossley, C. J. Brickhill, J. C. Stillwell, N. H. Williams (Dover Publications, 1990)

    Incompleteness: The Proof and Paradox of Kurt Gödel by Rebecca Goldstein (W. W. Norton & Company; 2005)

    Logical Dilemmas: The Life and work of Kurt Gödel by J. Dawson (AK Peters, 1996)

  • Radio 4 Mathematics Collection

    Radio 4 Mathematics Collection

    Listen to more maths programmes


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