Math Poetry

Modern math
-----------
A perverse scheme of sheaves
chews on a stalk of stacks.
Is it etale or crystal?
We are all chained to a ringed
topos in Serres saga of gaga.

Mathematicians
--------------
Dieudonne wrote
Grothendieck thought
Fermat guessed
Euler knew
Pythagoras believed
Hilbert conjectured
and Witten said

Pop stars
------------
Elvis rule
Gaga cohomology
Eminem estimate
Elton multiplier
Sade  spectrum
Snoop conjecture
Sting principle
Dylan theorem
Miley number

Under drugs
-----------
Holy sheaves of schemes!
What stacks of etale crystals
did Grothendieck smoke
in Deligne's secret garden?
Poor Baki! Mon Dieu Donnee!

Number one
-----------
e^(ix)=cosx+i sinx
sum n^-2=pi^2/6
exp(iPi)+1=0
v-e+f=chi
Euler=
No1

Acronyms (2014)
---------------
ODE
PDE
KdV
3-D
P=NP
QED

Conjectures  (2014)
-------------------
Hilbert's tent
Navier stakes
Even perfect
Hodge fudge
Dry Swinnerton
Riemann hype
Sexy twins
Goldbach flow

Genius
-------
Galois   Cigar
Cantor   Panter
Goedel   Knoedel
Nash     Flash
Noether  Otter
Perelman Peril
Bourbaki Souvlaki

Pro Memoria
-----------
0=1+e^i pi
----------
It is naughty,
if one more fly
eats up my pie!

Row reduction
--------------
Row Row Row Reduce
Redundant columns we produce
swap and scale the rows we must
subtracting rows is lust and frust

Determinants
------------
Laplace, Row Reduce, 
Partitions, Triangular, 
Eigenvectors, Eigenvalues, 
Patterns you can use! 

Sarrus rule
-----------
a e s
o i u
d t m 

Mia Deo Sot
Tuo Dis Emo

What does the matrix say?
-------------------------

Rotation goes woof, 
Translation goes meow.
Reflections goes tweet, 
and ShearKernel goes moo. 
Image goes croak, 
and the Row reduce goes toot.
Columns say quack 
and Rows go blurb, 
and Basis goes ow, ow, ow.
But there's one sound, 
that no one knows ...
What does the Matrix say?

O PDE !
--------

"Oh PDE, Oh PDE, solved easily with Fouriee!
For heat use ee to the minus n2 tee.
For wave, pick coosine n of tee.
Oh PDE, Oh PDE, solved easilee with Fouriee!
With velocitee, sin n of tee you see.
Mix X and tee and you will have to pee ...
Oh PDE, Oh PDE, solved painfully with penalty.
Oh PDE, Oh PDE, solved easilee with Fouriee"!

Fibonacci Rabbits
-----------------

In the wonderful month of Mai 
Two rabbits went to play 
A third rabbit saw the day 
Then five and eight - yuhei! 

In the wonderful month of June 
Thirteen rabbits grew to 21 soon 
They sang and jumped and had more sex 
Now, they all have an Oedipus complex!

Hieroglyphs      2010
-----------------

The priest     1000000
holds a frog    100000
in his finger.   10000
The flower fears  1000
that the monkey    100
is bending          10
its stem.            1

Obscenities (2014)
-----------
It is well known
It is trivial
Obviously
Left to the reader
Screw you

Pedagogical disqualification  (Jan 2017)
-----------------------------

This talk is accessible to a general audience:
"Let X be an Artin stack on an Etal site"

Conclusions   (2014)
--------------------

If A implies B
and B implies A
then A implies A
Ergo
If A does not imply B
and B does not imply A
then A does not imply A
Bingo

Locaux
------

The folloing text is by Luc Illusie,
It just has been discovered as poetry
by Oliver Knill:

"Les schemas strictement locaux
les spectres d'anneaux locaux
strictement henseliens
sont en effet les objets locaux
de la topologie etale
de meme que les schemas locaux
les spectres d'anneaux locaux
sont les objets locaux
de la topologie de Zariski
Ils se comportent topologiquement
comme des 'boules de Milnor'"

Hip Hop Review (PDE's, Extremization, Chain rule, integration) 2017
-------------------------------------------------------------------

PDE rich. You can't stuck with me, if you wanted to:
These expensive, these is rare Laplace, these is bloody heat
Hit the wave, I can get them both, I don't wanna choose
and I'm quick, cut a function off, so don't get comfortable, look!
I don't derive now, I make money moves.

If you'r a saddle, you get popped, you are maxim, you are opt.
Don't you Nabla around my way, you can't Lagrange around my block.
And I just checked my accounts, turns out, I'm max, I'm sad, I'm min.
I put my hand around my D, I bet your D, his D, her D.

I say I let the chain rule go, this hit is hot like a stove.
My regions glitter as gold, tell the order play her role.
I just drove along a curve, I just came up in a nerve.
I need to fill up my x, no I need to fill up my y.

I need to let everybody know that none of their shapes is safe.
I go to polar and break, only the r can relate.
I used to live one D, now it's a crib with a square.
Regions got charms, like butterfly farms.
Had to let the functions go, just in case those cos forgot.
I just run and switch around another integration bound.

Twenty one!

Working for the exam at night, making myself crazy
Out of my mind, out of my mind!
Row reduced and worked it out, hoping it would save me
Too many times, too many times
My column, it makes me feel like nobody else, nobody else
But my row it does not love me, so I tell myself

----------------  REFRAIN  ---------------------------
One: Don't take the leading ones
Zero's only calling because it is alone
Two: if you don't scale it in
You have to kick it back again
Three: don't subtract more than one
You will wake up with a zero in the morning
And If you are done with it, YOU ain't getting over it
I love to row reduce (x 6)
------------------------------------------------------

I keep pushing forwards, but it keeps pulling me backwards
Nowhere to turn, Nowhere to turn
Now, I'm stepping back from it, I finally see the pattern!
I never learn, I never learn
But the row, it does not love me, so I tell myself
I do, I do, I do

----------------  REFRAIN  ---------------------------

Practice makes perfect
I'm still try to learn it by heart
Eat, sleep, and breathe it
Rehearse and repeat it, all night

----------------  REFRAIN  ---------------------------

You will get over it!

QR Dream 
---------
(See this clip 
for second review in Math 21b.)

Last night, I had this dream about QR
In this dream, I'm dancing right beside you
There is nothing wrong with just a little bit of fun
We were Gram Schmidting all night long
Oh, I don't know what to do
Because this might need a clue
I hope that this product comes true

No Shears to try!
-----------------
(See this clip
for final review in Math 21b) modified from the most recent Ariana
Grande hit:  

21 B, is all right!
Right now, I want to find a way
to find a basis for Fourier
I ain't got no shears left to try
So I'm rotating it up, 
reflecting it up

Can't stop now, can't find 
those roots somehow
Shut them out.

Right now, I want a determinate
I want to row reduce all the time.
I got no patters left to try.
So I'm crossing it up, 
partition it up
Laplace it up, yea, 
and transpose it up.

Alexander Hamilton -> William Hamilton 
---------------------------------------

And every day, while thinking about multiplying triplets
Over the years, he struggled but kept his spirit up
Inside, he was longing for something bigger
Almost ready to give up and call it a day ...

Then the inspiration came and happiness reigned.
Our man saw his future rise, becoming a man of fame
Put a pencil to his temple, connected to his brain
And wrote his rules, a testament to his pain.

Well, the word got around, they said, this kid is insane, man
Took up a challenge just for the fun of it
Got his education, did not forget whence he came from
And the world is gonna know his name
What is his name, man?

William Hamilton
His name is William Hamilton

And there are a million things I haven't done
But just you wait, just you wait.

From a Math table talk on 
October 23, 2018:

----------------------------------------
The Landau problems 
----------------------------------------
Goldbach:   Every   integer  2n>2      
            is      a        sum    
            of      two      primes.
Twin prime: There   are      infinitely  
            many    primes   p,   
            p+2,    prime    twins.
Legendre:   Between two      consecutive 
            perfect squares, there 
            is      a        prime.
Landau:     There   are      infinitely  
            many    primes   of   
            the     form     n^2+1.
----------------------------------------

From an exam given on July 25, 2019: a
poem featuring some partial differential equations which one has to know
Burgers, Heat, Wave, Transport and Laplace equation: 



Who ever eats
Hamburgers during
Heat Waves is 
Transported to 
La La place


 

(* Energy Theorem  *) 

Generate[A_]:=Delete[Union[Sort[Flatten[Map[Subsets,A],1]]],1];
R[n_,m_]:=Module[{A={},X=Range[n],k},Do[k:=1+Random[Integer,n-1];
  A=Append[A,Union[RandomChoice[X,k]]],{m}];Generate[A]];
G=R[6,9];n=Length[G]; G=Sort[G];   w[x_]:=-(-1)^Length[x];
star[x_]:=Module[{u={}},Do[v=G[[k]];If[SubsetQ[v,x],u=Append[u,v]],{k,n}];u];
core[x_]:=Module[{u={}},Do[v=G[[k]];If[SubsetQ[x,v],u=Append[u,v]],{k,n}];u];
Wminus=Table[Intersection[core[G[[k]]],core[G[[l]]]],{k,n},{l,n}];
Wplus =Table[Intersection[star[G[[k]]],star[G[[l]]]],{k,n},{l,n}];
K =Table[                    Length[Wminus[[k,l]]],{k,n},{l,n}];
KI=Table[w[G[[k]]]*w[G[[l]]]*Length[Wplus[[k,l]]] ,{k,n},{l,n}];
EV=Sort[Eigenvalues[1.0*K]]; Clear[s]; ZetaFunction=Total[EV^(-s)];
CharPol=CoefficientList[CharacteristicPolynomial[K,s],s];
Print["Green Star formula: ",Simplify[K.KI==IdentityMatrix[n]]];
Print["Energy Theorem:     ",Total[Flatten[KI]]==Length[G]];
Print["Spectral Symmetry:  ",CharPol==(-1)^n*Reverse[CharPol]];

There was a finite set of sets
which was proud to be a simplicial complex
Wanting to grow and being excentric
It started to reproduce Barycentric

Before the  Storm
----------------------------------
Za'u oe ftu iknimaya
Niftxavang ting mikyun, ting nari
Tompayae kato, tsawkeyae kato
Si'ekong te'lanae oeru teya si

Fubini was a silly fellow
loved to integrate upside down
Clairaut also sends his hello
will visit once he is in town

Archimedes was a hero
ice cream cones he loved so much
Lagrange thought he lost a zero
Discriminants he would not touch

Za'u oe ftu iknimaya
Niftxavang ting mikyun, ting nari
Tompayae kato, tsawkeyae kato
Si'ekong te'lanae oeru teya si

I found a light inside me
I want to keep it glow
Keep shining right beside me
follow, where I go

So when the thunder becomes 
The storm becomes the night
I guide you through the lightning
Stay close by my side

Up in math21a I found my voice
Up past the clouds and broken noise
I will not fall, because I do belong
Take the exam, the sweet exam  and win it all