NOVA's The Proof

One can appreciate great works of literature, music and art without being a writer, composer, or artist. Similarly, you can appreciate the highlights and great works of mathematicians. Read through the sheet, and take notes while you are watching the video. To help you identify the mathematicians in the video:
Andrew Wiles: Appears first
John Conway: M.C. Escher shirt
Peter Sarnak: Maroon polo with grey collar and later a green polo
Nick Katz: Mustache, light blue button down / helped review the proof
Ken Ribet: Peach sweater with blue collar / cafe / Epsilon conjecture
John Coates: Suit jacket and tie / Wiles' adviser
Barry Mazur: Patterned dark button down
Goro Shimura: White button down / Taniyama-Shimura

What are the analogies or metaphors (including verbal descriptions and visual images) that people in the video present to describe the process of doing mathematics and/or mathematical research? List them all.

How do people in the video describe what a proof is?

What practices do mathematicians employ in order to encourage the flashes of insight they need for research?

Some people view mathematics as a solitary profession. What community aspects are portrayed? List them all.

Global Perspectives: What countries from abroad play a part? List them all.