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/perelman.pdf
videography:Lisa Sawin
sound engineer:Oliver Sawin
Artist/Author:Steve Sawin

Category:

Science & Technology

Tags:

• math
• topology
• geometry
• rap
• perelman
• poincare
• snoop
• dogg
• Pharrell

[Headkiller]

what does he mean with there is no topology?

[mathrapper]

@Headkiller 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)?

[mathrapper]

@boobah1067 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.

[mathrapper]

@boobah1067 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

[brownbug007]

I'm dying !!!

[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 -

[nightowl8936]

come on man ... topology, one of the most amazing and fascinating of the pure math subjects ... combined with black assed crack baby music? please don't do this again ... i can't stay for this ... this is is painful ... my ears are bleeding.

I doubt any black person on the planet will ever contribute to the pure maths, they are too god damnably stupid.

[GuidoSenden]

That is just amazing.

[Kingportable]

I think now that you've passed the hype of filming and writing this, you feel like a fool =)

[ybaol1]

what the hell ,sucks,you bitch!

[boobah1067]

@mathrapper Hm. Thanks! So the idea is a) that any "ring" of a surface is, of course, its own boundary (mini sphere). But it has to "pop", as in, express space in a specific way and "end" to be considered a finite bound, and a "singularity", and if so, it is not a replicative sphere of the original, but rather is "countable" and "dies" at some stage. If so, then it demonstrates something about the original sphere's limit per segment?