The opening of this novel tells the story of the tenth muse who refuses to be a muse like her nine sisters. She wants to sing her own song, rather than be an inspiration for others, and as a consequence, all her powers are taken away from her and she has to live as a human. She is reincarnating as the women that stood out in the course of history as an artist, philosopher, or, in the case of this novel as a mathematician, who had to stand their ground in a world dominated by men.
The whole story is told by its main character Katherine, an older successful mathematician, who is reflecting upon her childhood when she grew up in the 1940-50's in Michigan where she showed to be highly gifted with mathematical skills. The main part of the novel is happening while she is entering the university and later as she is working towards a PhD on the (fictional) Mohanty problem that is supposed to be a main opening towards the proof of the Riemann hypothesis. An old (again fictional) Schieling-Meisenbach theorem produced by mathematicians from Göttingen in the 1940's seems to be an essential element to solve the problem but it is also a key element in the novel. Moreover she is going through an identity crisis, and is looking for her, probably German, roots, These two reasons make her decide to spend some time in Bonn (Germany) where she hopes to find what happened to her parents around the time that she was born. Eventually, at the end of the novel, it turns out that Katherine has turned away from (analytic) number theory and has found new challenges in the realm of dynamical systems which has applications in many diverse applied sciences, which is the opposite of what Hardy claimed about number theory.
The author Catherine Chung has a mathematical degree from the University of Chicago but she received her Master of Fine Arts from Cornell University. For the mathematics in this novel she found some inspiration in popular science books and had some help from friends to check the mathematical content. And there is indeed a lot of mathematics mentioned. As a child, Katherine has to sum the numbers 1 to 9 and immediately comes with the answer 45 using the same technique as it is told that Gauss did by pairing numbers symmetrically in the sequence. She is however not praised for her ingenuity but punished instead because she thinks this is all too obvious and does not want to write down anything. In this case the teacher is a women, but for the rest of the novel, the bad guys are all men. She later goes to college where she is betrayed by her best friend. When they both hand in the same answers to their assignment problems, she is automatically accused of plagiarism while it happened the other way around. More depressing affairs happen to her again and again, even her thesis advisor, with whom she has an affair, disappoints her, and it are always men who do this to her. She is the underdog in all situations: she is not only a women, she is Chinese-Caucasian in the Midwest, is on bad terms with her step-mother, she turns out to be Jewish as well, and she is trying to make a career in science, typically dominated by men. How many stereotypes can be bestowed upon one person. And it is not only happening to her, it happens to most of the women in this novel. When during the war Japanese soldiers threaten to kill the boys of a Chinese family, the daughter is sold to spare the life of the boys. Men think to own a woman and that she can be given away. Even if it is done with the best of intentions, to safe the woman, it still is disrespectful.
The reason for reviewing this novel here is that the main character is a mathematician, so there is necessarily some mathematics involved. Obviously the Riemann hypothesis appears, but also the zeta function, the Hilbert problems, and the Boltzmann equation show up but without technical details, and some short sections are included about Hypatia, Emmy Noether, Sophie Germain, Sofia Kovalevskaya, Mary Mayer, Ramanujan, Turing, and what happened in Göttingen during the war also plays a role. In a postscript Chung mentions 30 more names of real mathematicians that make a short appearance in the novel: from Gödel and Poincaré to Selberg and Weyl. The link with fiction is made via a fictional Schieling-Meisenbach theorem. Presumably this theorem can be used to solve the equally fictional Mohanty problem (Chandra Mohanty is in real life a professor at Syracuse University defending transnational feminism). What is well described is the urge of a researcher to find a solution for his or her problem in a competing environment where it is important to be the first to publish and one has to be careful not to share too much before, while collaboration is necessary. As a woman or a student this makes you vulnerable because you will always be in the shadow of the co-author. The reader is however not really informed about the details or technicalities of Katherine's research or of most of the mathematics involved, there are only simple descriptions of what topology is about, or some similar descriptions of other topics. Nevertheless, it is instructive for an outsider to learn that when somebody can solve the Mohanty problem for even integers, then there is immediately the challenge of solving the problem for the more difficult case of odd integers. This is how mathematics is a never ending story. The more we know, the more there is left to investigate. Of course the novel is not about the mathematics, but about Katherine who happens to be doing research on a mathematical topic.
Mix all these issues: mathematics, romantic involvements, treason, the atrocities of the war, gender and race discrimination, and some Buddhist symbolism and Roman mythology and it seems like an overdose that is impossible to concur in one fictional character. And yet, Chung wonderfully succeeds in making it somehow acceptable. It is an engaging story with many twists that keep surprising the reader and that pushes the reader forward, eager to find out what will happen next. There are a lot of mathematical issues that are not revealing much, but still it is remarkable how much of (popular) mathematical issues have been smuggled in by Chung. All of these will be easily assimilated by many readers who would otherwise not be interested in picking up a book about popular mathematics.