Script of skit performed at the Yale Math Department Christmas Party in 1974 by the second year graduate students:

Chico Miraglia, Craig Huneke, Paul Blanchard, Bob Bix, Richard Foote, Alex Feingold, Monica Baratieri, Dan Coro, John Elton (Piano!), John M(?).

Introduction and Openning Monologue

Ed McMath: Hi folks, I'm Ed McMath. This is the Tonight Show with Johnny Cosine. And, now, h-e-r-e's Johnny! (He points the wrong way while Johnny enters. The recording of the theme music is played while someone holds up an Applause sign, and Johnny swings a golf club and points to the band leader occassionally while Ed makes his usual obnoxious noises.)

Johnny: Did you hear that Mr. Kakutani was named the friendliest analyst at Yale? They gave him the title ``Fourier Jolly Good Fellow".

The Times said that the Yale Math Department is going to close down next semester -- Mrs. Stevens is going on leave!

Gossip has it that there's going to be a divorce at Gracie Mansion; Mayor Vietoris is having trouble with his wife. The story is that he's nilpotent and hasn't functor in ages.

Ed: (Holds up a sign saying ``That's FUNCTOR".) Hey, Johnny, a little ergotic humor there.

Johnny: I read that two analysts proved the same theorem at the same time and challenged each other to a fight.

Ed: Where?

Johnny: In a dual space! Did you hear about the group theorist who thought he'd discovered a new simple group?
He flushed it down the toilet when he found out it was p-soluble.

Ed: Whoa!

Johnny: We asked a series of questions to Yale graduate students in mathematics and here are some of their answers.

Why did you come to Yale? Because I wanted to stay in New Haven and they wouldn't let me in to Southern Connecticut.

Why are you in graduate school in math? Because I don't like honest work.

What's the funniest thing that happened to you at Yale? I passed my orals.

Why do you go to classes? It's warmer than my apartment.

What's the most important thing your thesis advisor should be able to do for you? Sign his name.

What bothers you the most at Yale? The bathroom's on the bottom floor.

Prove the Spectral Theorem. (Johnny throws that question away and shrugs.)

What is the Spectral Theorem? (Johnny throws that question away and looks around.)

What is a Spectral Measure? Who wrote this? (Throws all his cards away, and Ed chases after them while Johnny continues.)

Johnny: But, seriously, folks, we have a really great show tonight. We have the Yale Math Department Glee Club, interviews with worthy professors, and we have the former Cy Young Award winner for the Polish girls softball league of Finchburg, Massachusetts. But, first, a word from our sponsors!

Rickart Commercial

Ed: Excision Headache Number 23. The ``I used to be able to prove it" headache. Mr. Charles Rickart.

Rickart: (Walks over to the blackboard.) Now, class, I'd like to do the following theorem, which I first proved in 1957. You just, ... Well, ... (Pause while Rickart thinks.) At least I think I proved it in 1957. Or was it 58 ? (Pause) Or was it a Proposition? (Pause, Rickart looks upset.) Boy, have I got a headache.

Ed: So when you get a headache or your chalk just allergy acts up, take excision. It works three times faster than the Mayer-Vietoris sequence.


Johnny: Our first guests tonight are making their network television premier. So, here they are, the Chorus D'Analyse, or, as they are otherwise known, the Chorus Locaux.



Johnny: We have to take a break now, and we'll be right back!

Commercial: Analysis Acres

Ed: Friends, have you been getting tensor? Need a change? Move into Analysis Acres! (Holds up sign) Just give us a ring, torsion-free, and we'll make it your domain.

Come out to Topological Towers and inspect our manifold advantages; dense carpeting spans the interior. The kitchenette has a complete spectrum of modern appliances, including a compact range and cold dynkin water. Kids a bother? You can always split upstairs!

Here we have a typical person before he came to Analysis Acres, and here he is afterwards. (Holds up pictures) Of course, we have an open neighborhood, we practice integration. So call our local operators today. Think Homological Haven is for you? Just put your Ext here and we'll give you a Hom.

Jacobson Interview

Johnny: Now, please welcome our next guest, the current President of Categories Anonymous, Mr. Nathan Jacobson. (He enters) Mr. Jacobson, just what does Categories Anonymous do?

Jacobson: Johnny, our organization was founded to lead the fight against Categories. This dreaded disease can strike any mathematician, regardless of age, sex, sponsoring institution, or expected area of concentration. Categories is now the Number One Killer of Mathematics. Johnny, did you know that Categories has destroyed more mathematics than co- and homology combined?

Johnny: No.

Jacobson: Did you know that algebraic geometry used to make some sense?

Johnny: I didn't know that.

Jacobson: Now all our rings have units. Where did we go rng? I'm sorry, Johnny, but when something this terrible strikes so close to home --

Johnny: I understand. But tell me, is  there a cure for categories?

Jacobson: Not yet. But if diagnosed early enough, categories can be controlled; the patient is forced to factor integers into primes and multiply matrices out until his insanity passes.

Johnny: Can a person examine himself for categories? (Ed looks himself over)

Jacobson: I'm glad you asked me that. Remember that categories can strike anyone, any time, any place. So learn the Early Warning Signs for Categories:

  1. Have you stopped caring whether you understand what you're doing?
  2. Do you like your theorems general but vacuous?
  3. Do you consider yourself a social arrow-chaser?
  4. Do you think of everything as a universal object?


(Lepowsky enters and walks to the middle of the stage, facing the audience, and holding up his hand to stop the show.)

Johnny: Who is that man?

Jacobson: It's Lepowsky.

Lepowsky: (In a condescending sing-song voice) Well, what do we do now? (Ed begins sneeking up on him holding a whipped cream pie.) Hasn't anyone out there read the script? What do we do next? (As he says ``next", he turns his head to the side and Ed hits him with the pie in the face, SPLAT!!!) That's not what I meant! (Lepowsky exits.)

Johnny: What happens next? A commercial.

Commercial for LOM Manor

Ed: Friends, Ed McMath here, and have I got a deal for you. Right now, Mother Yale needs quick money. So, for this recession only, you can lease an apartment on the second floor of Leet Oliver Memorial Hall, or, as we call it, Math Manor. Yes, friends, you can make your home in one of these luxurious offices, fully equipped with file cabinets and chalk. Or take our emperor's suite across the hall -- it's perfect for parties -- 40 seats all facing the same direction. And you'll get all the modern conveniences -- bathrooms just two floors down and plenty of heat every day until winter. If your children need help with their math homework, within a week they may be able to find a graduate student capable of helping them. Are you looking for a stable neighborhood? Nothing ever changes around here. There's plenty of excitement here, too: Thrill to people conjecturing on your very doorstep, wave to the trucks shaking the building as they go by, or race up to the top floor and fight your way to the cookies. And if you want peace and tranquility, you can't get more perfect rest than in some of the classes around here. So take it from Honest Ed and start living in Math Manor.

Tamagawi Interview

Johnny: And here's our next guest, the guru of the valuation army, Tamagawi. (Tamagawi enters in a white robe, with a ``p" around his neck and carrying Artin and Tate. He exchanges bows with Johnny, etc. He walks to the middle of the stage and addresses the audience.)

Tamagawi: Beloved children, come into our ideal group. It is a prime spot to learn your place in the cocyle of life. Study the ramifications of the word of the master Zeta, from whom you can learn the prime function and become complete.

Tamagawi: (He switches to a hellfire-and brimstone delivery.) Brothers and sisters, you set your norms too low. Throw off your residues of inertia and adjoin yourself to the one! Abandon your roots in the base field, and lift yourself up, up through the algebraic extensions, all the way up to the algebraic closure, and beyond -- to transcendental fields! Will you be a distinguished element on that great day when the groups are split, and when the towers fall, and the world decomposes? Do you believe in the existence, in the uniqueness, and the constructibility of the prophet Hilbert's class field? Brothers, do you know the norm residue symbol? Do you feel it, do you touch it, do you love it like I do? Hallelujah! Do you believe? Does Abel leave? So let me hear it from your hearts! Sing now, all together, brothers and sisters! Everyone sing ``Bringing in the Sheaves". (Everyone onstage and backstage, and hopefully the congregation sing as Tamagawi exits on the last line.)

All: Bringing in the sheaves, bringing in the sheaves, we'll all go rejoicing, bringing in the sheaves.


Johnny: Inspired by your singing, here they are again, the Yale Lie Club. (The chorus slinks out, snapping their fingers to the ``West Side Story" music, then gathers together, waving knives and chains.)

Tough Guy 1: How much longer do we have to wait?

Tough Guy 2: They'll be out any second now.

Tough Guy 3: They won't get past us.

Tough Guy 4: No one can get by us, we're the greatest.

Tough Guy 5: Shut up. Here they come. (All freeze into menacing positions,  Tough Guy 5 pantomimes stopping someone and threatening him.)
Well, did he pass his orals? (The chorus puts their knives away and begins marching like Mounties.)


Chorus Sings: POOR POLLY

Howe Commercial

Johnny: We'll be right back after this message.

Ed: Excision Headache Number 45. The ``Why isn't my child normal?" headache. (Mrs. Howe enters.)

Mrs. Howe: I'm Mrs. Howe, and there's something strange about my son,  Roger. His teachers say that he'll flunk kindergarten if he doesn't start paying more attention. I don't know what gets into his head. We offered to get him a cycle for Christmas, but he said that he'd already studied the symmetric group. Have I got a headache! And when I have a headache, I take excision. (Roger skips up to her dressed in shorts, a torn sweatshirt, and a beanie.)

Roger Howe: Mommy, Mommie, I've solved the four-color problem!

Mrs. Howe: That's nice, Roger. Did you lose your other eight crayons? (She smiles and shrugs, and they exit.)

Paul Interview -- Teaching Skits

Johnny: Now, I'd like to bring out the author of that new bestseller, ``My Adventures at Yale". Here he is, that singular Pole, essential to the Math Department -- Paul Lukasiewicz.

Paul: Before we get started, Johnny, I'd like to make an announcement: The following twentyfive books have not yet been stolen from the Math Department Library: (He reads)

Johnny: Thank you, Paul. Could you tell us about some of the wildlife you've seen in the Yale Math Department?

Paul: Better than that, Johnny. We've made movies of some typical Math classes, and I've brought them here tonight to show you. First we have a look at one of our rising (lifts eyebrows) young topologists. (Name deliberately omitted??)

(Quinn and Seligman enter, Seligman standing off to one side, gesturing and nodding.)

Quinn: (Toke) Today we're going to talk about things, we're going to have one ... thing on the bottom, and lots more all above it, that look just the same. (Toke; he passes the ? to Johnny.)

Stooge: Question, Sir. Doesn't the space have to be semi-locally simply connected?

Quinn: (Shakes head slowly ``No") Oh, Mr. Bix, this is beauty, art, poetry, topology; we don't worry about details, or anything. (Exits)

Johnny: Oh, boy, Paul, that's pretty heavy. By the way, what's thay guy doing over there? Is he decorating the department Christmas tree?

Paul: No, Johnny, that's Professor Seligman preparing tomorrow's lecture. (Seligman exits)

Johnny: I should have guessed. Who's next?

Paul: Our second film shows a professor who has inspired generations of Yale students with the efficiency of his notation. Roll Tamagawa, please.

(Tamagawa enters and goes over to the blackboard. Lang starts peeking in of all the scenes, with long nose made of a cone of paper having ``Le Nose" written on it.)

Tamagawa: (Confidently) Begin with two distinct prime ideals in an algebraic number field, say p and p. Go to a Galois extension and select primes lying over these, call them p and p. Applying an automorphism in the Galois group, we get two new primes, say p and p. Finally, taking norms, we get primes down below, call them p and p. Since these are visibly equal, we're done!

Paul: Our third film is of Professor Mostow. (Mostow enters)

Mostow: Today, class, I'm going to assume that you know upper semi-continuous Borel right quasi-regular functions, which are commonly denoted by f. (Mostow looks at board, scratches his head, looks around, furtively erases the ``Do Not Erase" sign, looks at the audience and smiles, and then boldly erases the rest of the board.) Such functions naturally lead us to our first theorem -- (Writes) THEOREM K (πMNOP) is constant. Since the proof is very instructive, I will give a detailed ... (Has second thoughts) sketch. (Smiles. He writes ``Proof" on the board and starts talking, but he is immediately drowned out by the tape recording of a truck while he continues to pantomime a proof. As soon as the recording ends, he says) -- and so we're done.

Paul: Our next film is the most interesting one that we edited. It shows a certain well-known professor giving advice to a student concerning his orals.

Nixon Skit: Thompson Lines (I don't seem to have this skit in my script. If anyone has it, please send it to me! AF)

Paul: Finally, we have a typical class of Larry Corwin's. (Corwin starts speaking normally at the blackboard while Lang comes peeking conspicuously around the corner.)

Corwin: Let x-dot equal A x be a linear hyperbolic equation -- (He looks at Lang, slowly looks back, then grabs a water pistol and jumps into a gunfighter stance.) Draw! There isn't room enough on this hyperplane for the both of us! (Corwin and Lang have a water pistol dual, and Corwin drives Lang offstage.)

(There was a longer Lang skit planned for here, but it was removed by those with good taste.)

Johnny: Let's break for a commercial.

Commmercial -- Brewster's Shoppe

Ed: Hi, folks, Ed McMath speaking for ``Brewster's BA, MA, and Ph.D. Shoppe -- where the BS is free! You say you've spent 17 years and 17 grand in schools and you've managed to avoid learning a single useful fact? You say that you aspire to a position of academic distinction and solvency but you're too lazy to get out of the sack before noon? You say that you can't compute integrals and don't know what a differential equation looks like? Friends, the Yale Math Department is designed with you in mind.

We offer you unbounded educational opportunities and first-order instruction from a faculty which is active and interested in students -- whoops, that's the secretary! But most importantly, our faculty goes to the essence of contemporary mathematical research -- that you need an ample supply of the right kind of paper. (Brings out a roll of toilet paper) Yes, friends, the Yale Math Department does its utmost to promote vigorous research -- why just last week we put in an order for a ping pong table -- next year we may even get a blackboard -- and our library has the Math Monthly dating way back to 1966. More than this, for every Colloquium we have cookies and all the hot water you can drink.

How do you get to Yale, you ask. (Takes out a map and stick) You just take this commuter's diagram and solve its universal mapping problem. Take the free-way to the first non-trivial intersection and turn right along Mobius strip. If you're unoriented, chase the arrows to the complex root 5 and follow it to the rotating neon dunce cap. But remember guys, women still have measure zero around here, so you may have to come by yourselves.

Now get out paper and pencils because for the first two applicants we have -- just in time for Christmas -- the amazing Shizuo Kakutani doll -- short but cute -- it Feits, it Thompsons, and for easy storage, contracts to a point.

Final Songs

Johnny: And here, ever hopeful, is the Yale Mathematics Chorus.




Links back to:
Alex Feingold's Webpage,
Department of Mathematical Sciences,
Binghamton University.