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When your Ricci flow stops at one geometry, one geometry, one
geometry If every loop contracts there's no topology,
no topology, no topology
So Poincare's correct in dimension three, in dimension three, in
dimension three He's just an unemployed don who's living with
his mom But his name is Perelman and he's got it going
on. Poincare's a nice dude, wit some nice dreams
Invent topology for all his math schemes Three-body problem can't solve in closed form
Find the features of the shape which still remain when you deform.
A loop around a doughnut never will contract; You can try it if you doubt me and you'll
see that I'm correct. It has to be a sphere, if every loop is naught
Like that million dollar Farberge egg I just bought!
Two dimension's alright but we're living in three here
If circles all bound disks does it have to be a three-sphere?
P. tried to see if it was true using all of that mathy ***
He tried to prove that *** He da man! still he coudn't seem to manage
it You should think about it. Take a second...
Matter fact, you could take a century And think before you mess with little Henry
P! When your Ricci flow stops at one geometry,
one geometry, one geometry
If every loop contracts there's no topology, no topology, no
topology So Poincar\'e's correct in dimension three,
in dimension three, in dimension three
He's just an unemployed don who's living with his mom
But his name is Perelman and he's got it going on.
Well I'm a math geek. You all knew that. Ask me a theorem, yeah I know who proved that.
It was proven by Steve Smale in five or more D
Friedman did the tricky D, yeah I mean four-D. There's only one dimension where it ain't
decided You guessed the one where Poincare first tried
it! (scratch) Two-nuh-nuh-five-Yep-three!
P -o-i-n-c-a-r-e. Thurston was bursting his thoughts they were
twisting See he specialized in making all the three-folds
listen. He said every three-fold has a best geometry
To maximize its group of global symmetry. Don't know how the proof should gizzo
But I've surely got to trizzle Cause every math geek wants to earn a Clay
Prizzle. It's worth a Fields Medal, fo' shizzle, Profizzle
Implies Poincar\'e, so ladies here we gizzo! When your Ricci flow stops at one geometry,
one geometry, one geometry
If every loop contracts there's no topology, no topology, no
topology So Poincare's correct in dimension three,
in dimension three, in dimension three
He's just an unemployed don who's living with his mom
But his name is Perelman and he's got it going on.
Ricci flow's bad, one of them diffEQ's Take your geometry, and cause it to diffuse.
If it plays out smooth, through the end of time
It's one of Thurston's ten, and everything is fine.
That was Hamilton's plan, waiting for the man
With the proof, Dogg, and that was Perelman Oh you wanna form some singularity?
Ricci flow with surgery, now try and stop me!
Excise the ***, its like some black hole Spawns another, we're playing wack-a-mole.
We need an entropy, yeah Grisha found it. Must I remind you I only have to bound it
Hound it to zero, pound til it's ground up Then dance to the music that QED sounds of.
Subscribe fool, and know what the nerds know Baby get close, come and here how the proof
goes! When your Ricci flow stops at one geometry,
one geometry, one geometry
If every loop contracts there's no topology, no topology, no
topology So Poincare's correct in dimension three,
in dimension three, in dimension three
He's just an unemployed don who's living with his mom
But his name is Perelman and he's got it going on.
Grisha... Grisha...