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: (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.

Chorus Sings: WHAT DO
COLLOQUIA DO?

Chorus Sings: SPECTRAL
THEOREM

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

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.

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:

- Have you stopped caring whether you understand what you're doing?
- Do you like your theorems general but vacuous?
- Do you consider yourself a social arrow-chaser?
- 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.

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.

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: WHEN A FRIEND
TAKES ORALS

Chorus Sings: POOR POLLY

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.)

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)

- Lang -- Algebra
- Lang -- Algebraic Geometry
- Lang -- Abelian Varieties
- Lang -- Diophantine Approximations
- Lang -- My Life as a Track Star

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.

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.

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

Chorus Sings: WHEN I WAS A
MATH STUDENT

Links back to:

Alex Feingold's
Webpage,

Department of Mathematical
Sciences,

Binghamton University.