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Prime Suspects: The Anatomy of Integers and Permutations (2019)
Andrew Granville / Jennifer Granville / Robert J. Lewis (Illustrator)

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:

  • "How research is done, particularly the roles of student and adviser (sic)". The characters are driven by curiosity, act on intuition, build on the work of predecessors, and look for proof. In that way, this may give the reader an idea of what research is like. However, the proof shown in the book is not the logical proof that one generally associates with mathematics. At least, it was not clear to me that they were actually proving theorems rather than simply proceeding purely empirically. Also, the relationship between Professor Gauss and his students may say something about how advisors interact with PhD students. They collaborate and all contribute, although he is in a position of power. I suppose in reality students are competing with each other for advisors and thesis problems, but I hope most professors do not pit individual students against each other in a contest for who will get to be their advisee as Gauss does here.
  • "The role of women in mathematics today." I'm not sure what they mean by that. The character of Emmy Germain is clearly an allusion to two historical female mathematicians. (Not only her name, but also some of her life story is a reference to Sophie Germain's biography.) However, that's obviously not "today". A billboard showing statistics about women in mathematics does appear in the background of one frame. (It says "in the USA 32% of math profs are women, in the UK 16% of math profs are women, in Mexico 65% of math profs are women".) But, I do not see how that sign together with having one female mathematician in a book with many male mathematicians says much about "the role of women in mathematics today". (Or, if it does, what it says is a bit sad.)
  • "The influence and conflict of deep and rigid abstraction". In murder mysteries there are always "good guys" and "bad guys". In math, that is not usually the case. But, the authors of "Prime Suspect" do not shy away from expressing their opinions, which includes critical portrayals of some famous mathematicians (like Lang and Grothendieck) and their mathematical philosophies.
Like "Who Killed Professor X?", this is a graphic novel that represents real mathematical developments in the form of a murder mystery. However, "Prime Suspect" is both more serious and more ambitious. Despite having more than a few jokes squeezed between its covers, this work aspires to be a serious work of art about an obscure but intriguing mathematical mystery that also says something deep about the ways mathematics is practiced. That is certainly admirable. However, if its goal was to reach people who do not already know about its subject, then I fear it may have been overly-ambitious. (Of course, I would be happy to be proven wrong about that!)

Contributed by Aidan Tompkins

You asked for opinions from non-mathematicians, and Prime Suspects was the coolest thing I've read this year! I couldn't resist looking through all the tiny details, and it was fun to read the appendix to see the jokes I missed.

Funny story: I found Prime Suspects on Wikipedia and tried to search it up on MathFiction, but nothing showed up because the title is incorrect. [Oops. I had incorrectly entered it as "Prime Suspect", singular. Thanks for the correction! - ak] It was all for the better though because I'm always trying to discover new Math Fiction, so I read the graphic novel immediately and drafted an email about it. At least I wasn't disappointed, and I'm not too surprised you knew about it already!

It's great to know that you had a connection to Granville and factoring permutations, and that the MSI play was also mentioned. I enjoyed learning about the background as I read the appendix, even though the second half of technical explanations admittedly went over my head. Thank you for making MathFiction!

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Works Similar to Prime Suspects: The Anatomy of Integers and Permutations
According to my `secret formula', the following works of mathematical fiction are similar to this one:
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  10. L.A. Math: Romance, Crime and Mathematics in the City of Angels by James D. Stein
Ratings for Prime Suspects: The Anatomy of Integers and Permutations:
RatingsHave you seen/read this work of mathematical fiction? Then click here to enter your own votes on its mathematical content and literary quality or send me comments to post on this Webpage.
Mathematical Content:
5/5 (1 votes)
Literary Quality:
3/5 (1 votes)

GenreMystery, Fantasy, Didactic,
MotifEvil mathematicians, Cool/Heroic Mathematicians, Academia, Proving Theorems, Female Mathematicians, Sherlock Holmes,
TopicAlgebra/Arithmetic/Number Theory, Real Mathematics,
MediumGraphic Novel/Comic Book/Manga,

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Exciting News: The 1,600th entry was recently added to this database of mathematical fiction! Also, for those of you interested in non-fictional math books let me (shamelessly) plug the recent release of the second edition of my soliton theory textbook.

(Maintained by Alex Kasman, College of Charleston)