Here is the biggest (?) unsolved problem in maths... The Riemann Hypothesis.
Prime Number Theorem: http://youtu.be/l8ezziaEeNE
Fermat's Last Theorem: http://youtu.be/qiNcEguuFSA
Prof Edward Frenkel's book Love and Math: http://amzn.to/1g6XP6j
Professor Frenkel is a mathematics professor at the University of California, Berkeley - http://edwardfrenkel.com
The Millennium Prize at the Clay Mathematics Institute: http://www.claymath.org
Number Line: http://youtu.be/JmyLeESQWGw
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Videos by Brady Haran
A run-down of Brady's channels: http://bit.ly/bradychannels
CORRECTION: At 7:20 the zeta function of 2 should be (Pi^2)/6 as correctly stated earlier in the video (Basel Problem)