The Granville Screenplay

The Granville Screenplay Overall Reaction: I think that this is an ambitious and original play. The play presents some really cool and beautiful mathematics. However, I didn’t especially enjoy the story and I have some doubts that it would appeal to a non-mathematician.

Summary of the Play: This play conveys serious and beautiful mathematical ideas and results through a whimsical story about forensic investigators/ mathematicians. Along the way, the play indulges in a lot of inside mathematical humor. The main characters investigate a double (and finally triple) homicide. Each of the murder victims represents a different mathematical object. One of the bodies represents an integer, another represents a permutation, and the third (entering in only at the end) represents a polynomial defined over a finite field.

Many of the elements in the story serve as metaphors for mathematical objects or ideas. The anatomy of the murder victims metaphorically stands for the structural properties of the corresponding mathematical objects. The forensic investigation of the bodies is a metaphor for the mathematical investigation of the properties of the objects for which they stand. As the investigation proceeds, the characters gradually piece together clues about the murders, simultaneously explaining the underlying mathematics.

There are 3 main characters in the story. One main character is the authoritative, famous, and (of course) brilliant inspector Gauss. The other main characters are students Emmy Germain, a cross between Sophie Germain and Emmy Noether, and Sergei Langer, a thinly disguised Serge Lang. The two students compete with each other through the investigation. The student who solves the case first gets to be Gauss’s assistant. In the end, the modest, likeable (and, of course, brilliant) Emmy wins while the smug and annoying (but, actually, sort of brilliant in a pedantic way) Sergei turns out to be the murderer. (The word “brilliant” comes up rather frequently in the text.)

The story has several supporting characters as well. There is a practical and hard-boiled inspector Von Neumann, who serves as a kind of foil for the more theoretical trio of main characters, and there is a reporter/videographer, Barry, who tags along and records some of the action – especially as it pertains to Emmy. Barry serves as a device for introducing elementary definitions to an audience who might not have much mathematical background. There seems to be some kind of budding romance, or at least romantic tension, between Emmy and Barry, but this theme isn’t really developed.

The central point of the play is the the victims, though superficially quite different, are actually “twins ” in a deeper underlying sense. The corresponding mathematical result is that certain statistical properties of the prime factors of a random integer correlate exacty with analogous statistical properties of the cycles in the cycle decomposition of a random permutation. The mathematics behind the play is absolutely beautiful.

A Mathematicial Perspective: As a mathematician – though not an expert in this particular field – I found the discussion of the mathematical results fascinating. Prior to reading the play, I had some general idea that there was an analogy between factoring a number into primes and decomposing a permutation into cycles, but I hadn’t appreciated the depth of the analogy. The play does an extremely good job of conveying (to a mathematician from a different field) the surprise and beauty of these connections. Learning about the mathematics was actually rather exhilarating, and I could easily imagine myself looking up the actual math and trying to learn more. So, in terms of getting mathematicians excited about a particular area of math, the play really succeeds. I must say, however, that I wonder how a lay person would understand what is going on. The work starts out slowly, with e.g. a definition of a prime number. But, rather quickly, the mathematical exposition turns to things like Poisson point processes, Gaussian distributions, and some exotic transcendental functions. I seriously doubt that a lay person would get much out of this stuff, beyond the general sense that there is some weird connection between integers and permutations.

As a mathematician, I also enjoyed some of the inside jokes – e.g. about Serge Lange’s famous “files”. However, I imagine that someone outside the mathematical community, even a very competent non-academic mathematician, would completely miss these references. So, some of the fun of the play would be lost on someone who wasn’t an insider.

A Non-Mathematicial Perspective: As a person reading the play for sheer enjoyment, I have to say that I did not like it at all. Even though I like the analogy between detectives and mathematicians, anatomy and structure theorems, etc., I found the setup rather contrived and the transitions between police work and mathematics somewhat uneasy. Sometimes the characters seem sort of like detectives and then they suddenly shift out of these roles and deliver hard-core mathematicial speeches – especially Langer. Somehow these abrupt transitions reminded me of a musical, where some part of the story is suddenly interrupted by a song and dance.

I found the characters to be fairly one-dimensional, and not especially interesting from a human perspective. Having gone to graduate school (and studied with an extremely famous advisor) I know something about the experience of being in awe of my advisor. However, I can’t really relate to this idea of competing with a fellow student to win favor with the guy. I don’t remember any of my classmates acting this way either. Both Emmy and Sergei seemed like “apple-polishers”, though of course in very different ways. I guess I didn’t really like the central plot device of students competing for favor with their professor. I found Sergei Langer to be an incredibly annoying character. I understand that this guy is supposed to be Serge Lang, a person who by many accounts was incredibly annoying, but still I cringed every time he said something. He was just relentlessly unpleasant. I kept thinking about the Jar-Jar Binks character who ruined one of the Star Wars movies for me because he was so annoying. (Jar-Jar Binks was annoying in a different way than Sergei Langer.) It is only at the end, where we see that Langer killed for the sake of knowledge, that he reveals any depth at all. Basically, Langer seemed like the stereotype of everything that can possibly go wrong with an academic.

Speaking of Langer, I felt uncomfortable reading a play in which a recently living mathematician is so totally lampooned. I didn’t know Lang personally, and everything I heard about him secondhand made me think that I would not have liked him, but the play gives me the same feeling I get when one person leaves as party and then the other people make fun of him in his absence. I wasn’t a huge fan of the name choices of the characters. While could perceive the playfulness in names like Permu-Ta-Tion and Joe Ten-Dick (for Grothendeick) I just found them kind of corny. I was reminded of the names Slick Tracy and Breathtest Nobeera, two characters in the anti-alcohol propaganda comic strip that my daughter used to bring home from school last year. Generally, I just didn’t like the idea of naming fictional characters after famous people. For me, it sort of froze them into stereotypes right from the start. What can I say? I guess I don’t really like that kind of wordplay. Finally, I didn’t really like the device of having the reporter adding another layer of narrative to the story. It made the story seem too self-referential, with the characters watching themselves as we watch them.