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 links & stuff in full description below ↓↓↓

More Fermat (with Simon Singh):    • Fermat's Last Theorem - Numberphile  
Even more Fermat (with Simon and Homer Simpson):    • Homer Simpson vs Pierre de Fermat - N...  

Simon Singh's brilliant documentary on BBC iPlayer (UK only): http://bit.ly/TheProofDoco
And his Fermat book: http://amzn.to/1jWqMTa

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