I would first of all like to say that this is not primarily a novel about mathematics, but a serious exploration of central human themes such as love, loss, and loneliness. As the three main characters are all mathematicians, there is, however, a number of references to mathematics and mathematicians throughout the text, and mathematical ideas do not only inform the outlook and thought process of the protagonist, but also the structure of the novel itself.

We follow the heroine, Rakel, from her first days at university till some years after she has finished her PhD in mathematics. Along the way she befriends, and later gets involved in an affair with, a much older professor, Jakob. Quite naturally, Rakel's thoughts as well as her conversations with Jakob circle around mathematics, and among other things the reader gets an introduction to infinite cardinals; an example of a connected but not path-connected space; a brief mention of Alexander polynomials; a proof that the sum of a rational and an irrational number is irrational; a recommendation on how to present the proof of the Snake Lemma (kick off your shoes first); and an example of how to use partition problems to attract the attention of the opposite sex. Rakel also has an interest in logical and mathematical puzzles that underscores her playful and creative approach to mathematics.

The list above may seem daunting, but the author has a light touch, and I think (although it is hard for a mathematician to say for certain) that she manages to create a picture of mathematics that is at the same time attractive, accurate, and comprehensible to non-mathematical readers. As Rakel is as interested in classical music and poetry as she is in mathematics, the text conveys an image of mathematics as an art — as something that is to be treated with the same amount of experimentation, playfulness, and seriousness as the other arts.

Most of the mathematical examples appear in the first half of the book, but in the second half, Sofya Kovalevskaya emerges as the novel's third main character. As a partly bedridden Rakel tries to fight back illness, loss, and loneliness, Sofya's story becomes a means to come to grips with her own situation and her own experiences. In Sofya's relationship to Weierstrass Rakel seeks a parallel to her own relationship to Jakob, and only towards the end of the novel does she realize that she has perhaps been trying to read too much of her own life into Sofya's. In this part of the novel, scenes from Rakel's life are interleaved with scenes from Sofya's, and the two stories reflect and contrast each other in a multitude of ways.

Since childhood Rakel has been intrigued by fractals, and with all its reflections, dilations, retractions, and inversions the novel itself takes on a fractal form. Or perhaps one might just as well call it a musical form? César Franck's sonata for violin and piano serves as a leitmotif throughout the novel, and towards the end Rakel muses:

For more information (including excerpts from the novel and a beautiful performance of parts of César Franck's sonata by Henning Kraggerud and Bartosz Sosnowski) I recommend the author's own video on her webpage: https://klarahveberg.no/indexeng.html. Interestingly, Literary Hub has chosen the perhaps most mathematical scene of the entire novel as their excerpt: https://lithub.com/lean-your-loneliness-slowly-against-mine/.

But at the end of the presentation they were shown a film that zoomed in on details of the Mandelbrot set, as if the audience was being taken on an endless journey into it. And that was when the miracle revealed itself. It turned out that the Mandelbrot set contained an entire universe of exotic shapes, like a landscape full of seahorses and spiraling tentacles. Not only that, but ever-increasing copies of the Mandelbrot set popped up, only slightly distorted, as if shown from a new point of view.

As she walked home from the presentation that evening, she thought: Maybe this is something I can fill my life with. If I can’t be a violinist, this might just be something I can do.

Maybe being loved is like being zoomed in on. Like someone undertaking an endless journey into you, enabling you to see all the beauty you contain. That you are an entire universe of exotic shapes, with ever-increasing copies of yourself—only with a slight twist. Like fanciful variations on a known theme from viewpoints you never even knew existed. Everyone deserves to experience such a journey at least once in their life. It’s the most beautiful thing she’s ever known. Not only have new spaces opened up in her, but it’s as if she’s been drawn in an entirely new dimension. And perhaps one day she’ll discover that this dimension is not an integer.

Before she can make a start on her master’s degree she has to get through the course in topology, which is notorious for being so abstract that over half the students fail the exam. But she is rather abstract by nature so suspects that she’ll like this course better than the one on Fourier analysis and partial differential equations. As it turns out, she loves the course. To finally understand why mathematicians view a coffee cup and a doughnut as equivalent objects. To discover that something can be both open and closed at the same time.

The only thing that irritates her is that the lecturer turns up to the sessions unprepared, probably prioritizing his research over his teaching, as many professors do. He therefore stands and stares at the board for ten minutes whenever he encounters an unexpected problem. Rakel feels for him, even though it’s his own fault. Had he thought through the material beforehand, he would have easily seen how each problem could be solved.

“Could you not just take a set that looks like a comb with infinitely many teeth, on which the teeth get closer and closer together, and then remove all of the farthest teeth, apart from the outermost point on the tip?” she asks finally. “This set will be topologically connected, even though it isn’t path connected.”

The professor nods and turns back toward the board. Several of the students turn and look at her. “Imagine correcting the professor of topology,” whispers a boy in the back row.