The Bridges to Fermat's Last Theorem
Ken Ribet - a key player in the solution to Fermat's Last Theorem - gives a taste of how real mathematics is done... piece by piece and by human beings.
More Fermat (with Simon Singh): http://youtu.be/qiNcEguuFSA
Even more Fermat (with Simon and Homer Simpson): http://youtu.be/ReOQ300AcSU
Simon Singh's brilliant documentary on BBC iPlayer (UK only): http://bit.ly/TheProofDoco
And his Fermat book: http://amzn.to/1jWqMTa