Math Poetry

Oliver Knill
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.
Remarks: Perverse sheaves exist, but they are neither perverse, nor sheaves. Stalks of sheaves exist, stacks are sheafes taking values in categories, stalk of stacks is a word creation, a ringed topos is a topos equipped with a choice of ring. "Gaga" refers to "Géometrie Algébrique et Géométrie Analytique" = "Algebraic geometry and analytic geometry", of Jean-Pierre Serre.
Dieudonne wrote
Grothendieck thought
Fermat guessed
Euler knew
Pythagoras believed
Hilbert conjectured
and Witten said
Remarks: Dieudonne wrote huge amount of mathematics ranging over huge amount of math, Grothendieck probably thought about math like nobody else before, Fermat guessed and conjectured, sometimes wrong. Pythagoras believed in natural numbers, Hilbert conjectured or posed lots of problems. And the phrase "Witten said ..." is a golden phrase, especially among string theorists.
Pop stars
Elvis rule
Gaga cohomology
Eminem estimate
Elton multiplier
Sade  spectrum
Snoop conjecture
Sting principle
Dylan theorem
Miley number
Remarks. Cohomology is a bit strange at first, like Gaga, Miley knows to pull some numbers..
Under drugs
Holy sheaves of schemes!
What stacks of etale crystals
did Grothendieck smoke
in Deligne's secret garden?
Poor Baki! Mon Dieu Donnee!
Remarks. Grothendieck was one of the most creative mathematicians ever. Some of his creations appear so strange at first that they appear to have been created with crystal meth involved (for which however there is no evidence). But there is crystalline cohomology and etale cohomology... Pierre Deligne is a student of Grothendieck. "Poor Baki" refers to Bourbaki (an anonymous group of Mathematicians) Dieu Donnee to Jean Dieudonne, "Dieu" is "god" in French so that Mon Dieu Donnee means "my Dieudonne" or "my god,... ". The phrase "Deligne's secret garden" is from an article of Luc Illusie who reports that Deligne loves gardening.
Number one
e^(ix)=cosx+i sinx
sum n^-2=pi^2/6
Remarks. The first four formulas are all due to Euler and belong to the most famous formulas in mathematics Making Euler the number one mathematician who ever lived.
Acronyms (2014)
Remark. ODE=Ordinary differential equation, PDE=Partial differential equation, KdV=Korteveg de Vries equation, QED= Quod erad demonstrandum.
Conjectures  (2014)
Hilbert's tent
Navier stakes
Even perfect
Hodge fudge
Dry Swinnerton
Riemann hype
Sexy twins
Goldbach flow
Remark: these are all open conjectures. Hilbert's tenth is still open over the rationals, the Navier Stokes, Hodge, Birch Swinnerton-Dyer, Riemann problems are Millenium problems. The Goldbach conjecture and the question about even perfect numbers or existence of prime twins or sexy primes are open too. Goldbach refers to the German "Bach", meaning creek.
Galois   Cigar
Cantor   Panter
Goedel   Knoedel
Nash     Flash
Noether  Otter
Perelman Peril
Bourbaki Souvlaki
Remark: more like associations like Galois Gauloise cigarettes or rimes.
Pro Memoria
0=1+e^i pi
It is naughty,
if one more fly
eats up my pie!
Remark: this identity is always considered the most important identity in mathematics as it combines 0,1,e,i, Pi.
Row reduction
Row Row Row Reduce
Redundant columns we produce
swap and scale the rows we must
subtracting rows is lust and frust
Remark: summarizes, what Row reduction is. Made for a review. Song. Of course, heavily leaning on Row, Row, row your boat!.
Laplace, Row Reduce, 
Partitions, Triangular, 
Eigenvectors, Eigenvalues, 
Patterns you can use! 
Remark: summarizes all the methods which can be used to find determinants. For a 21b review: Song
Sarrus rule
a e s
o i u
d t m 

Mia Deo Sot
Tuo Dis Emo
Remark: to remember a rule for computing determinants of 3x3 matrices. Found using computer search. Song (part 2)
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?
Remark: this was a modification of the iconic "What does the fox say?" song by Ylvis..

"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"!
Remarks: A piano performance or part of a slide show. The melody starts like O Tannenbaum a Christmas song which is based on a folk song from the area of Schlesien (now mostly Poland). In that song, the evergreen fir tree is praised as "faithful", contrasting to other trees associated to faithless lovers. This is fitting, as Fourier theory is an "evergreen".
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!
Remarks.See The song. was part of a review for Math 21b.
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
This is a memnonic to learn the Egyptian number system. See Lecture 2: around 10:30
Obscenities (2014)
It is well known
It is trivial
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
If A does not imply B
and B does not imply A
then A does not imply A

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.
See the Video: I'm Boss, I make body moves, or the extended version.
I Love to row reduce (spring 2018) ---------------------------------- See Youtube for first review in Math 21b).
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
Remark. This was for an exam review and was Modified from part of "Daft Punk by Pentatonix:
Last night, I had this dream about you
In this dream, I'm dancing right beside you
There is nothing wrong with just a little bit of fun
We were dancing all night long
Oh, I don't know what to do
About this dream and you
I hope this dream 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.

March 20, 2019: this had been planned for a review in Math 22b but I did not have the time to sing this adaptation of the Hamilton Musical. We had a bit of obsession in this course on Quaternions:
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
July 22, 2019: In our time it is possible to program poetically. Forty years ago: (TI 57 and then TI59), programs, (stored on magnetic cards), were essentially assembler, where numbers had to be stored in storage registers. A conversion program from decimal to hex program was longer the following Mathematica code which appears on this blog entry about this paper. It is an example of modern programming poetry possible in advanced languages:
(* Energy Theorem  *) 

G=R[6,9];n=Length[G]; G=Sort[G];   w[x_]:=-(-1)^Length[x];
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)];
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]];
For a final review on August 6, 2019 Harvard Summer school: posted August 4 on Youtube. It is an adaptation of the lyrics for ``tough love" from Avicii in the Album TIM.
Tough Math (Harvard)

Weight is on me, weight is on you
We scream and we fight like there's nothing to lose
End of the day, come and take out math
There's no place I'd rather be than in this school.

Weight is on you, weight is on me
Sometimes things do not work how I want it to be
God knows I try, we stumble and we fall
There's no place I'd rather be than in this school.

Tough math and a lessons to learn
Some tough math, is what I deserve
Sweet tough math, you're my pretty luck charm
There's no place I'd rather be than in this school.

Weight is on you, weight is on me
Sometimes I'm not who you want me to be
God knows I try, we stumble and we fall
There's no place I'd rather be than in this school.

Tough math and a lessons to learn
Some tough math, is what I deserve
Sweet tough math, you're my pretty luck charm
There's no place I'd rather be than in this school.

For a review on September 29, 2019 Math 21a, on Youtube. It is an adaptation of the lyrics for ``Shape of my Heart" from Sting.
The shape of my heart

He deals with planes as a medication
And those he draws he never detects
He doesn't play for the forms he learns
He does not compute for respect

She deals with planes to find the answer
The sacred geometry of chance
The hidden law of a probable outcome
The numbers lead a dance

I know that the circles are the swords of a geometer
I know that the numbers are weapons of math
I know that coordinates mean all in this part
But that's not the shape of my art

I may play the sphere of diamonds
I may lay the cone of spades
I may conceal a surface in my hand
While the memory of it fades

I know that the circles are the swords of a geometer
I know that the numbers are weapons of math
I know that coordinates mean all in this part
But that's not the shape of my art

That's not the shape, The shape of my heart.

For a review on November 2, 2019 Math 21a, on Youtube. It is of a NCS release song by Janji (featuring Johnning) Youtube.

Exam fight Song

I'm walking alone, Hall C is empty
The only thing I can see is my own silhouette
I'm getting stronger, step by step
The clock is ticking but there is no time for regrets
I've been flying from page to page
From problem one to problem nine
I've been all around the exam
Trying to detect its charm.
We are heroes tonight.
We will fly above the sky.
We are heroes to - night yeah.
We are heroes tonight.
We will fly above the sky.
We are heroes to  -  night, yeah
For a review on December 9, 2019, Math 21a, on youtube: it is based on the iconic Stairways to Heaven piece by Led Zeppelin:

Stokes is a stairway to heaven

There is a theorem  for sure
All it glitters and is gold
And it is known to be a stairway to heaven
When we get it and we know
And if the curves are all closed
With a curl we can get what we came for
Uuuh, Uuuuh and we are on a stairway to heaven.

There is a sign on the wall
But we wants to be sure
because you know sometimes flux can have two meanings
On a curve in the book
There is the wrong field which stings
Sometimes all or our thoughts are forgiven
Uhhhh, it makes me wonder
Uhhh, it makes me wonder

There is a feeling I get
When I look at the rest
And my spirit is crying for leaving
In my thoughts I have seen
Thinks like Stokes through the trees
And the voices of those who stand looking
Uuuh, it makes me wonder
Uuuh, it really makes me wonder

Quotient rule song

For a 1A lecture on February 14, 2020: there is the well known song: "Low Di High, Take High Di Low, Cross the line, and Square the low". See youtube: Here is the finance advise variant:
Buy low, sell high
Take high, not low
Avoid the fine
And take the dough!

Math 1a song

Good Bye, math 1a,
we reach the end of the season.
Good times, I have to say,
we have had all for a reason.
You are wiser now,
having got fed all this brain food.
Go in peace now,
use it for working on doing good.
And here is the Poetry which produces the music
s1=Sound[{"Flute", SN/@rise[a1]},{0T,1T}];
s3=Sound[{"Viola", SN/@rise[a1]},{1T,2T}];
s4=Sound[{"Harp",  SN/@down[a2]},{1T,2T}];
s6=Sound[{"Piano", SN/@down[b2]},{2T,3T}];
s7=Sound[{"Viola", SN/@rise[b1]},{3T,4T}];
s8=Sound[{"Cello", SN/@down[b2]},{3T,4T}];
This this page from the Math 1a course from the spring of 2020 and especially the Youtube version.

Multigraph limerick

May 2020:
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
Remark: there is quite a bit of wisdom in this limerick because as Dieudonne has pointed out, Barycentric refinements are one of the three fundamental pillars of combinatorial topology, incidence matrices and duality being the others. Also interesting is that the structure of finite sets of non-empty sets is actually amazingly rich. The Barycentric refinement of such a structure is already a simplicial complex (as it is always the Whitney complex of a graph). When reproducing with Barycentric subdivision, one reaches a universal, only dimension-dependent limit.

The 360 storm

For This video. The song composed by Fat Rat and Masy Kay has lyrics in the Na'vi Language of Pandara which is an actual language.
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

Its my first exam in 1A

For a Motivation song in Math 1a, Spring 2021.
Its my first exam in 1A
Do it right and get an A
Let me have ingenuity play with me
I wanna be your math girl!

Just give me enough time to be ready
Do my limits, bath me in extremes
Quick true/false, won't take long
Differentiate, just sing this song:

Low D high take high D low
draw the line and square the low
Derive with the chain rule it will be fine
I can call continuous what you call divine.

Olli Rocky Docky

For a second midterm of Summer 2022 song:
Second midterm coming up and second midterm is so near.
Gradients, Max/Min Lagrange, integration is us all so dear
True/false problems get us trembling, matching gradients is our fear.
We are happy, parametrized surfaces will not appear!

This Ole guy Olli Rocky Docky has taught this stuff so much.
No wonder, that we tremble, no wonder we learn so much!
This ole guy Olli Rocky Docky has seen fear, pain and such.
He enjoys in every summer, to write exams with a harder touch!

Calculus you wonder sparkle

For a final review Summer 2022
Calculus you wonder sparkle
Daughter Of Elysium.
We learned so much fire drunken
Heavenly reaching Ecstasium.

Your Magic has taught us lessons
Which even Gods aren't able to preach.
All this knowledge comes from heaven
We have seen what angles teach.

I'm not afraid of tough math!

A condensed pyknotic amoeba schemes in the anima of a crystal.
It has as topos an etale site, wearing an ideal sheaf of Adele.
Oh prismatic perfectoid! Are you conifold, orbifold or amplituhedron?
You are an Aleph Sha stack! Homotop to a very ample syzygy.
All these words do appear in mathematics: Condensed mathematics, Crystalline cohomology, Topos, Site (category with Grothendieck topology), Ideal sheaf, Adele ring, Prismatic cohomology, Perfectoid space, conifold, orbifold, Amplituhedron, Aleph number, Sha (TS for Tate-Shafarevich was dismissed), Stack, Homotopic, Ample line bundle, Syzygy.
While some notions are older like Syzygy (Hilbert), others like condensed mathematics which is only a few years old. See this post from 2020 called "Liquid tensor experiment". There are parts of that post one can understand like Condensed mathematics claims that topological spaces are the wrong definition, and that one should replace them with the slightly different notion of condensed sets. But already the definition (by Scholze,Bhatt from 2013) of Condensed sets are sheaves on the pro-etale site of a point is harder to swallow. About the origin: Scholze writes: This definition (without the name) is already in my 2013 paper with Bhatt. But I never tried to thoroughly understand this notion. I knew that there is a functor from topological spaces to condensed sets (up to set-theoretic problems): Given a topological space T, one can send any profinite set S to the continuous maps from S to T. What I did not understand is that this functor is fully faithful on a very large class of topological spaces, and that condensed sets are actually an improvement over topological spaces. This is what Clausen quickly convinced me of when he arrived in Bonn in 2018 as a PostDoc. See this thread about Pyknoticity an other construction, bornological topos is mentioned aiming to make "functional analysis" look like "linear algebra" or "commutative algebra" or "analytic geometry" into "algebraic geometry". There are some set theoretical issues with all this.


Press releases these days must contain important buzzwords. What is not better than to combine wormholes, teleportation, multiverses and quantum computers. otivated by November 2022, or November 30, 2022, a short poem about this:
A quantum computer has just created
Holographic wormhole entangled in superstrings
producing shortcuts between multi-verses.
We hear the cosmic symphony of the megaverse
while nibbling at energies that contain
black holes and strings. A negative energy      
shock wave travels backwards in time and produces
wormhold teleportation.