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Mathematics Goes to the Movies
by Burkard Polster and Marty Ross
It’s My Turn (1980)
Kate proves the Snake Lemma from homological algebra.
KATE: Let me just show you how to construct the map s, which is the fun of the lemma anyhow, okay? (in the diagram this map corresponds to the long curved arrow.)
So you assume you have an element in the kernel of \gamma, that is, an element in C, such that \gamma takes you to 0 in C’. You pull it back to B, via map g, which is surjective,
COOPERMAN (a student): Hold it, hold it. That’s … that’s not unique.
KATE: Yes, it is unique, Mr. Cooperman, up to an element in the image of f, all right? So we’ve pulled it back to a fixed b here and then you take \beta of b, which takes you to 0 in C’, by the commutivity (should be commutativity) of the diagram. It is therefore in the kernel of the map g’, hence is an image of f’ by the exactness of the lower sequence…
KATE: … so we can pull it back to an element in A’…
COOPERMAN: It’s not well-defined.
KATE: …which it turns out is well-defined modulo the image of \alpha, and thus defines an element in the cokernel of \alpha, (at this point she draws the long curved arrow on the blackboard) and that’s the snake. And on Monday we’ll address ourselves to the cohomology of groups (Cooperman raises his hand) and Mr. Cooperman’s next objections.
COOPERMAN: This stuff is just garbage. That’s another diagram chase. When are we going to move on to something interesting, like your new group. Any progress with the 2-fusion.
KATE: No, still stuck.
COOPERMAN: Maybe you have gone as far as you can with it Dr. G.
KATE: That’s possible.
COOPERMAN: I’ve started looking at it with a whole new angle. KATE: Oh.
COOPERMAN: If it works, I’ll be famous.
KATE: Oh, that would be terrific. I can relax. I’ll be famous for having taught you.
There are a couple more blackboards visible in this scene. To the left of the one that Kate is working on we see
The writing on a second one to the right looks something like
0 -> A -> B -> C -> 0 is exact, then
0 -> Hom(Q,A) -> Hom(Q,B) -> Hom(Q,C) -> 0
How to construct, compute (??) this sequence (???).”
Working on an envelope in bed.
KATE: I’d like to kill that little Cooperman. Now, he is working on the 2-fusion.
KATE: You know what I’d like?
KATE: If I could just solve this problem. You understand, I would be in a class with Euclid and Newton, really, I would be … except for Newton made his breakthrough when he was 22.17:00
Conversation with the people who interviewed her.
PROFESSOR1: Jeremy Grant at Yale. He is a great fan of your thesis. Have you done any new work on your group yet?
KATE: No, not yet.
PROFESSOR1: I broke my back on group theory. It has moved way past me now. You younger minds have to take over.
PROFESSOR2: Has your work come to a standstill, Dr. Gunzinger?
KATE: I certainly hope not.
Dinner with her father, his future wife and some of the future wife’s family members.
KATE’S FATHER: How did the interview go?
KATE: I should have kept my mouth shut. I don’t think I am going to get it.
KATE’S FATHER: That does not sound like you. This is the girl who got one hundred on every math exam (??) except for 98 on plain geometry. Her thesis was on sporadic groups.
OTHER GUEST: Tell me, what did you get wrong in plain geometry.
KATE: The problem was to compute the area of a patio around a pool. I applied the right method, but I put the patio inside the pool.
KATE meets Homer and his two kids.
KID: A prime number is one that cannot be expressed as a product of two smaller numbers.
KATE: Is 2 a prime number?
KATE: Is 3?
KATE: Is 4?
KID: 2 times 2.
HOMER: Smart? Smart kid. You are a graduate of Harvard?
KID: No, I went to Yale.
Back on her home campus Kate runs into Cooperman.
COOPERMAN: Did you make any progress?
KATE: Well, I tell you I have been thinking. I think, I have been looking in the wrong place. I have some new ideas about the 2-fusion.
COOPERMAN: What? Why? Do you mean dot o to dot g.
KATE: Right, just in its simplest case, though.
COOPERMAN: But that might be the hinge of the whole problem. Yeah, right away that’s going to give you the quotient, that’s immediate.
KATE: It’s just a beginning, though.
COOPERMAN: Show me what you are talking about.
KATE: I can’t do it now.
COOPERMAN: Show me.
KATE: I’m going to be here for a while.
COOPERMAN: The classification might even drop right out. This is incredible. If this works, we could be famous.
KATE: Listen, it’s just the beginning. The tough part is working it out.