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Counting Novels with Numbers

Foto del escritor: Daniela RBRDaniela RBR

Mathematical Novels: What Are They and How to Recognize Them?


During my teenage years, I attended a school that followed the guidelines of an International Baccalaureate (IB) program, which meant we had to read at least eight novels each year, all of different genres. In class, the same question always came up: "What is the genre?" To answer that, we relied on the definitions our teacher (in my case) had provided. I never wondered who had established those definitions and labels—until now.


Preamble: My Journey with Mathematical Novels


More than 15 years ago, while walking through downtown Mar del Plata, a coastal city in Buenos Aires, I came across a novel in a bookstore titled The Crime of the Prime Numbers. I had always loved mathematics, and even though I wasn’t an avid reader, the idea of a novel centered around something mathematical fascinated me so much that I couldn’t resist. That purchase, without me knowing it, would mark a turning point.


Years went by, and as a mathematics teaching student, the magic happened again in a bookstore on Av. Cabildo and Juramento: Pythagorean Crimes appeared in the science outreach section. That same excitement I felt during that summer in Mar del Plata resurfaced. Without consciously deciding it, finding "mathematical novels" became my new hobby. And to be honest, it wasn’t an easy task. Ten years ago, although digitalization was already advancing, it wasn’t like it is today, and explaining what I was looking for in a bookstore was a challenge in itself. Sometimes I got lucky and received great recommendations; other times, I simply walked away satisfied that I had shared a curiosity that, until that moment, many didn’t know existed.


And as if it were the next chapter of this story, one day a job offer came along—it seemed like the universe had conspired to merge my hobby with my profession. I would be in charge of, among other things, creating the reading comprehension sections for math textbooks for secondary and primary school. My job consisted of extracting excerpts from novels, short stories, poems, news articles, or anything that touched on a topic from the chapter, and then crafting reading comprehension questions. Without realizing it, I had been preparing for this great challenge over the past 10 years.

You could say that this marked a grand finale for my hobby—but no, my pastime remains as strong as ever. Although social media has its downsides, it also does great things, like spreading love for or sparking curiosity about mathematical novels.

And here we are now, exploring what makes a novel mathematical and why they captivate us so much.


What Is a Mathematical Novel?



The short answer is that there is no answer. So, since there isn’t one, I’m going to try to provide one—and for that, I’ll rely on the following Venn diagram.


Diagrama de Venn idea y diseño: DRBR
Diagrama de Venn idea y diseño: DRBR

In the universe of novels, there are countless sets, but for our purposes, we’ll focus on two that we observe in the diagram above:


V = {Novels authored by a mathematicians} (purple circle)

R = {Novels that include mathematics} (pink circle)


In the intersection of sets V and R (where the purple and pink circles overlap), we find novels where mathematics appears and that were also written by a mathematician.


R ∩ V = {novels with mathematics by mathematicians}


Within the set of novels that include mathematics, we find a subset that contains mathematical novels.


A = {mathematical novels} (yellow circle)


This set is not only included in R but also intersects with V.


A ∩ V = {mathematical novels by mathematicians}

From this, we draw the following conclusions:

  • Not all novels that include something mathematical are mathematical novels.

  • Every mathematical novel contains mathematics.

  • A mathematician can write a novel with or without mathematics, and it may or may not be a mathematical novel.

  • There are novels that include mathematics and mathematical novels written by people who are not professionally dedicated to this science.


From all the points mentioned, the one that gives us a clue to identify a mathematical novel is point 2:


A ⊂ R


In other words, mathematical novels form a subset of novels that include mathematics. This helps us rule out those that are clearly not mathematical, but within the novels that include mathematics, we must distinguish which qualify as mathematical and which do not.


Mathematical Novels vs. Novels That Include Mathematics

In mathematics, there are two types of statements: those that must be proven and axioms. An axiom is a proposition or principle considered self-evident and, therefore, does not require proof. In other words, we accept them as truths without questioning their validity. Axioms are fundamental starting points for building theories. Metaphorically speaking, they are the "rules of the game" that define what is valid within a system.


The use of axioms is very common in mathematics. This means starting from the idea of accepting certain statements as truths even when we cannot prove them. The most well-known example is Euclid's Postulates. In his work Elements, written more than 1,700 years ago, Euclid outlined five axioms that became the foundation of the plane geometry we are taught in school. However, centuries later, in the 19th century, Nikolai Lobachevsky and János Bolyai questioned the universal validity of the fifth postulate, giving rise to hyperbolic geometry. Later, Bernhard Riemann developed elliptic geometry by also modifying this postulate, demonstrating that even "self-evident truths" can be redefined.


Following this logic, I will propose certain axioms that will serve as a starting point for my theory of what constitutes a mathematical novel. However, these axioms are not absolute or immutable laws; rather, they are accepted foundations to define the concept and avoid ambiguities. If these principles change in the future, we could revisit the definition, but for now, they provide a clear basis to work from.


Proposed Axioms for Defining a Mathematical Novel

  1. Every mathematical novel contains mathematics explicitly.

    (Mathematics must be clearly present in the narrative, either as a central theme, a narrative tool, or part of the structure).

  2. In a mathematical novel, mathematics must be essential to the plot.

    (Without mathematics, the story could not progress or would lose a critical component in the development of the plot or characters).

  3. A mathematical novel must explain at least one mathematical concept or prominently showcase its application within the story.

    (This includes problems, theories, reflections, or mathematical elements that are integral to the narrative).

  4. Mathematics in a mathematical novel must be presented in an understandable or clearly relevant way.

    (Mathematical concepts should be conveyed so that a general reader can grasp them or recognize their importance to the plot)-

  5. In a mathematical novel, mathematics must influence the motivations or development of the characters.

    (The relationship between the characters and mathematics must be meaningful and contribute to the progression of the story).

  6. Mathematics must be naturally integrated into the narrative.

    (It should not feel forced or like a decorative addition, but rather as an essential element that enriches the story).


How to Recognize a Mathematical Novel?


The axioms are very clear, but to simplify, recognizing a mathematical novel can be as easy as answering the following questions:


  1. Does the novel include mathematics explicitly in its narrative?

  2. Are mathematics essential for the plot to progress or for the development of the characters?

  3. Does the novel explain at least one mathematical concept or prominently showcase its application in the plot?

  4. Are the mathematical concepts presented in an understandable way or clearly relevant to the narrative?

  5. Do mathematics directly influence the motivations or development of the main characters?

  6. Are mathematics naturally integrated into the narrative, without feeling forced or like a decorative addition?


If the answer to all these questions is "yes," then the novel qualifies as mathematical according to the established axioms. If at least one answer is "no," it means the novel does not meet the criteria to be considered a "mathematical novel" based on the proposed axioms, which, as of today, are the only theoretical foundation available for defining whether a novel is mathematical or not.



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