One Geometry

Perelman's proof of the Poincare conjecture to the tune of Snoop Dogg and Pharrell William's "Drop it Like it's Hot"
Lyrics: http://cs.fairfield.edu/~sawin/Rap/pe...
videography:Lisa Sawin
sound engineer:Oliver Sawin
Artist/Author:Steve Sawin

• Category

  Science & Technology

[Headkiller]

what does he mean with there is no topology?

[Stephen Sawin]

I mean that if every loop contracts it is the simplest manifold, which is the sphere. Informally, because it is the simplest shape, I say it has no topology.

[boobah1067]

I have a question: entropy comes from taking these point-spheres of Poincare-Perelman and turning them into a true zero, not anymore a point still existing as a mini sphere (point)?

[Stephen Sawin]

Here is my best shot at an answer, with the caveat that you are going beyond my comfort zone. The Ricci curvature equation can be thought very loosely as changing the geometry of the shape slowly the way blowing up a balloon changes its geometry. Very, very loosely, the appearance of singularities corresponds to a region being stretched so much it bursts. If this happens only finitely many times, you can finish the proof.

[Stephen Sawin]

continuing! Because you can reconstruct the original manifold. Entropy just allows you to control that. It increases (or decreases?) during the blowing up and the replacing, and I believe you can show if it is big (small?) enough these singularities cannot arise, so you get finitely many. Perelman also controls what kind of singularities can occur and how.

[feministbabe]

rapping + mathematic proofs = best thing ever

[AndrewMarcell]

I laughed out loud :)

Rock on with your bad self! When your Ricci flow stops at one geometry, one geometry, one geometry... if every loop contracts there's no topology, no topology, no topology!

Good times :)

I still don't get the Poincare conjecture though.

[Lolly Paige]

How could anyone in the Universe give this a thumbs down?

[Gustavo Fernandez]

So let me get this. You are a white dude mathematician who is trying to rap about Poincare..wtf

This world is upside down.

[Maxime Bergeron]

This needs a higher res version with animations in the background. Throw in a couple of dancing bitches or something.

[Maxime Bergeron]

WHATTTT

[Gagerivas]

Gay shit

[snow carlson]

i got here by the annoying orange and it said it wouldent disapoint me...THATS A LIE!

[yellowlght]

If you only knew how tough Ricci equations are even for the fully initiated mathematicians u wouldn't be rapping like that - Perelman is a genius as are his colleagues at the institute were he works. Not even the best mathematicians in the US tackle & solve the problems these Russians do -