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? -------------------------Rotationgoes woof,Translationgoes meow.Reflectionsgoes tweet, andShearKernelgoes moo.Imagegoes croak, and theRowreduce goes toot.Columnssay quack andRowsgo blurb, andBasisgoes ow, ow, ow. But there's one sound, that no one knows ... What does theMatrixsay?

O PDE ! -------- "Oh PDE, Oh PDE, solved easily with Fouriee! For heat use ee to the minus n^{2}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

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.

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]];

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.

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, yeahFor a review on December 9, 2019, Math 21a, on youtube: it is based on the iconic Stairways to Heaven piece by Led Zeppelin:

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

Buy low, sell high Take high, not low Avoid the fine And take the dough!

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

rise[x_]:=Table[{x[[k,1]]+12,x[[k,2]]},{k,Length[x]}]; down[x_]:=Table[{x[[k,1]]-12,x[[k,2]]},{k,Length[x]}]; SN[{x_,t_}]:=SoundNote[x,t];T=6; d={1,5,8};g={1,6,10};a={0,3,8};h={-2,1,5};e={3,6,10}; a1={{{1},4},{{8},4},{{10},1},{{8},1},{{6},2},{{8},4},{{6},1}, {{5},1},{{3},2},{{5},2},{{3},1},{{1},1},{{3},3},{{},1},{{3},4}}; b1={{{1},4},{{1},4},{{3},4},{{-4},4},{{1},2},{{0},1},{{-2},1}, {{-2},2},{{-4},1},{{-6},1},{{-4},3},{{},1},{{-4},4}}; a2={{d,4},{d,4},{g,4},{d,4},{a,4},{d,4},{a,4},{a,4}}; b2={{g,4},{h,4},{e,4},{a,4},{d,4},{g,4},{a,4},{a,4}}; s1=Sound[{"Flute", SN/@rise[a1]},{0T,1T}]; s2=Sound[{"Guitar",SN/@down[a2]},{0T,1T}]; s3=Sound[{"Viola", SN/@rise[a1]},{1T,2T}]; s4=Sound[{"Harp", SN/@down[a2]},{1T,2T}]; s5=Sound[{"Violin",SN/@rise[b1]},{2T,3T}]; s6=Sound[{"Piano", SN/@down[b2]},{2T,3T}]; s7=Sound[{"Viola", SN/@rise[b1]},{3T,4T}]; s8=Sound[{"Cello", SN/@down[b2]},{3T,4T}]; S=Sound[{s1,s2,s3,s4,s5,s6,s7,s8}]This this page from the Math 1a course from the spring of 2020 and especially the Youtube version.

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

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.

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 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.

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.

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

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.