a list compiled by Alex Kasman (College of Charleston)
|In this graphic novel, the surprising coincidences between complete factorizations of integers, permutations, and polynomials is presented as if it were the discovery of a forensic team investigating seemingly unconnected murders.
Murder victims Arnie Int (a mobster with the Integer crime family) and Daisy Permutation (a ballet dancer) both had strange incisions on their chests. Moreover, during the forensic examination it was found that both had strange undecomposed (or, perhaps a better word would be indecomposable) things in their bodies. In the case of Int, they were prime numbers and in the case of Permutation they were cycles, but the investigative team of Professor Gauss and his two student assistants Emmy Germain and Sergei Langer seek a deeper theory to explain the coincidences.
Of course, the idea that similar physical objects were found in the victims of two murders with similar "MOs" (isn't that what they say in crime dramas?) is just a metaphor for a real mathematical coincidence that number theorist Andrew Granville and his sister Jennifer are hoping to convey to the reader through this art form. Indeed, just as one can factor a positive integer into primes, one can also factor a permutation (which is a rearrangement of a set of objects) into cycles (a rearrangement of objects arranged on a circle that just rotates each object to the next location), and polynomials can be factored into a product of irreducible polynomials. The mere fact that these things can each be factored into these elementary objects is not in itself much of a coincidence, but the amazing similarity in the way they are distributed (such as in answering the question of how many such factors above a certain minimum size a randomly chosen example would have) is quite surprising. To a mathematician, this raises the fascinating question of whether there is some deeper connection between these different objects, but a non-mathematician would probably have trouble understanding the question let alone caring about the answer. And, that's presumably where Granville got the idea of presenting it in the format of the popular TV show "CSI".
How well it achieves that goal may depend on the audience. Someone who already knows mathematics very well can certainly get a lot out reading this book. If nothing else, there are tons of inside jokes and "Easter eggs" hidden on nearly every page for them to get. (There are cameo appearances by famous mathematicians, punny names, math-themed parody advertisements, etc.) Someone who already knows the algebraic structure under which permutations form a group will also be at an advantage in grasping the main idea. I do wonder whether this book would work at all for someone who did not already have that background. The comic book portion, for example, does use billiard balls to explain what a cycle is but it says nothing about what it means to multiply two of them together to produce a permutation which is not itself a cycle. This sort of mathematical detail is quickly explained in the text at the end, but just as I do not think the mathematical in-jokes would be entertaining to someone who had to search the internet for an explanation, I wonder whether consulting the end notes will really allow a previously mathematically naive reader to get anything out of this work. (Really, I do wonder. It is very difficult for me to judge because I coincidentally used the factorization of permutations into cycles in my last research paper. I would be very interested in hearing from any non-mathematicians who have read this book!)
I hope this does not seem like name-dropping, but I have actually known about this project as a work-in-progress for a long time! Andrew Granville first wrote to me about it in 2007 when he was just starting to think of writing a play on this subject. He wrote again in 2008 with a draft of a script called "MSI: Mathematical Sciences Investigation". By 2009, that play (now renamed "Mathematical Sciences Investigation (MSI): The Anatomy of Integers and Permutations") was performed in a reading at the Institute for Advanced Study. And, ten years later, it has finally been released in the form of a graphic novel by Princeton University Press. I like the new title and think it works well in the comic book format, although the piece of music that was written to accompany the live performance seems out of place in the book. (It is not only that most people will not be able to get out of the printed musical notation anything like they would have gotten from listening to the music being played; it is also that retrieving the song from the heads of the victims and the way it is used as evidence in the murder mystery both seem very weird to me.)
But, it is not only these specific mathematical ideas from algebra and number theory that the authors wanted to convey in this work of mathematical fiction. According to the end notes, there were three other goals. Let me address each of those separately:
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(Maintained by Alex Kasman, College of Charleston)