I think I maybe should point out that there is a difference in 'vacuum' and 'nothing'.
Edit: Watching the video now.
Edit: Hmm... Only three geometical systems, open, spherical or flat... I thought there were more. Interesting.
Edit: Ok, due to general relativity
Edit: Ok, now I understand a bit of how they concluded the dark matter.
Edit: Quantum fluctuations can produce the universe...
Edit: Whooo! Triangles
Edit: So the conclusion he presents, of a flat universe, is based upon computer simulations. Cool
Edit: Cosmic natural selection
Edit: "The humility that we don't understand everything." I like that.
Edit: "General relativity unfortunately give people the wrong idea about science."
Edit: Mathematics is the language of nature, yay!
Edit: He even covers the agrument about impossibility in odds.
All in all, a rewarding video
it really made me interested in mathematics again (summer breaks notoriously dulls interests).