In addition to the three corpses in the story, the title refers to the famous mathematical problem which attempts to describe the motion of three or more masses subject to the laws of physics (and especially gravitational attraction) developed by Isaac Newton. In fact, it was Newton's mathematical proof that a stable elliptical orbit was one of the possible consequences of the ``inverse square law of gravity'' in the case of two bodies which convincingly demonstrated the role of gravity in governing the motion of celestial objects as well as smaller objects falling to Earth. However, all attempts to provide similar results in the case of three or more objects had failed, making the ``n-body problem'' (where n here is considered to be an arbitrary positive integer representing the number of objects under consideration) a significant goal of mathematicians from the time of Newton until the late 19th Century.

In 1888, the King of Sweden offered a significant prize for the solution of this problem. The prize was claimed by Henri Poincare who showed not only that no general solution was possible, but moreover identified the ``sensitive dependence upon initial conditions'' which limits the usefulness of any solution which one could find based on imprecise measurements. With hindsight, we can see this as a key step towards our recognition of and understanding of the mathematical phenomenon known as ``chaos'' in the 20th century. However, at the time it was probably only viewed as the final disaster undermining of the goal of solving the n-body problem. (It turns out not to have been such a disaster, in fact. Not only do we now know many interesting but extremely specialized cases of exact solutions, but we have a good enough understanding of the role of chaos to be able to use our mathematics constructively to guide spaceships between planets and other large celestial objects using very little fuel.)

All of that is true and historical, though neither the novel nor the summary above really capture the interesting twists and turns in the story of Poincare and the prize. But, the novel goes farther, using the prize as the motive behind the murders of three Cambridge University mathematicians.

The novel takes the form of letters from Vanessa Duncan, a young schoolmistress in Cambridge, to her ailing twin back home. Duncan has a love of mathematics, and writes a good deal about the arithmetic she teaches her pupils. Through her neighbor, a mathematician at the university who becomes the prime suspect in the murders, and the connections of one of her young students, she eventually is able to get to know the academic community that she initially only watched longingly from afar. She meets historical mathematicians, including Arthur Cayley and Gösta Mittag-Leffler. Although she does not meet any female mathematicians, Duncan does learn about the existence of Grace Chisholm and Sonya Kovalevskaya.

The mathematical details of the n-body problem and the attempts to solve it are not as significant in the resolution of the mystery as are the social aspects of mathematical collaboration. The author has a very good understanding of this complicated dynamic, including the fact that we rarely try to measure how much of the credit for a collaborative effort should go to each of the individual authors, that there is some threshhold below which a contribution does not qualify for joint authorship, that collaboration often takes the form of just talking about ideas that eventually crystallize into a significant result, and that there is a tendency for those involved in such a discussion to each feel that the key contributions were their own. It is easy to see how such a situation could lead to disagreements, though I am not aware of any real murders resulting from mathematical collaborations!

Shaw has a very good understanding of mathematicians as people. The characters seem quite realistic and not the flat stereotypes one often encounters in this genre. Perhaps then it is intentional that the stereotypes of mathematicians which appear in the novel are presented not in the voice of the narrator, but rather by the defense and the prosecution in the trial of Duncan's neighbor (and romantic interest). The prosecution describes quite explicitly the notion that work in mathematics leaves the researcher prone to insanity and violence. (This is, unfortunately, an apparently very common belief, though I have not seen any evidence to support it outside of fiction. Note that a similar diatribe occurs in the 1929 mystery The Bishop Murder Case.) The defense responds with an alternative theory based on the notion that only young mathematicians can produce good results. (This stereotype is widely believed by mathematicians themselves, though I myself am skeptical that this is the case.)

Other reviewers have complained about the believability, period accuracy, and over-estimation of the interest that non-mathematicians may have in the plot on the part of the author. However, from my point of view (keep in mind that I'm a mathematician and no expert on Victorian England) the Three Body Problem successfully captures the feeling of its historical period and the atmosphere of academic mathematics, using them as the venue for a decent murder mystery. I think that many visitors to this site would enjoy reading it and highly recommend it.

Considering the intimate knowledge of mathematics demonstrated by the author, I am not surprised to learn from the brief "about the author" entries on various websites that "Catherine Shaw" is a pseudonym used by a woman who is herself a mathematician and an academic. Moreover, I have seen her Harvard education mentioned in a few press releases. However, I have no more specific information about who she may be. In particular, I do not know whether she actually has a PhD in mathematics and holds a position as a professor of mathematics, but I would be interested in knowing if anyone out there can provide me with more details!

Update: I have been contacted by "Catherine Shaw" who, while wishing to remain anonymous, does confirm that she has a doctorate in mathematics and is an academician.

Update Update: Thanks to Mark Kozek for point out to me that Catherine Shaw's identity is apparently no longer a secret. According to her publisher:

The Notices of the American Mathematical Society has published a review of this novel by Richard Montgomery, who is an expert on the dynamical systems discussed in the book. The review can be downloaded in PDF format from this link.

For Vanessa Duncan's continuing adventures, see Flowers Stained with Moonlight and The Library Paradox.