Literature and mathematics

Summary: Since ancient Greece, literature has drawn on mathematical imagery.

Literature and mathematics share many characteristics despite their apparently different natures. The work of the mathematician is similar to that of the writer, and mathematics has inspired many works of fiction, biography, satire, and mystery. Because of their intelligence and interesting personalities, mathematicians appear as characters in many works of fiction. Biographies of mathematicians and tales of famous mathematical problems also provide fascinating narratives because of their interesting characters and the characters’ struggles with mathematical and personal problems.

At times, mathematics has been a target for attack by satirists for mathematicians’ tendency to overuse mathematics by reducing social and economic issues to mere mathematical equations. Literature is also an effective tool in mathematics education, especially for small children.

The Mathematics–Literature Connection

Few fields of human activity seem, at first glance, as distant as mathematics and literature. Mathematics is a field of rigor, exactness, and absolute truth. It involves formulas, equations, laws, and theorems that do not leave much room for opinion, subjectivity, or individuality. On the other hand, literature is the realm of emotions, characters, imagination, and subjectivity. The author, unconstrained by the strict laws of nature, creates worlds, people, and events as the imagination desires. The resulting stories are usually told by a human or anthropomorphic narrator, and the narrator’s tone and style affect the story and the reader.

Despite these differences, there are many connections and commonalities between mathematics and literature. Mathematics describes relationships between numbers, functions, sets, and other mathematical objects; literature is concerned with relationships between characters. Mathematics tries to describe how nature works; literature describes how people behave. Mathematics often describes paradoxes, unintuitive concepts, and unsolved problems; literature often depicts irrational behaviors, impossible situations, and other situations that defy explanation.

The work of a mathematician is similar to that of an author in many ways. Both mathematics and literature require imagination and creativity, albeit of a somewhat different type; both are mostly individual endeavors; both require intuition and insight; both require a significant amount of time, patience, and persistence; and both provide an immense sense of accomplishment and exhilaration when the product—be it a novel or a proof—is complete.

Early Influences

The relationship between mathematics and literature can be traced back to ancient Greece, the cradle of both modern mathematics and the liberal arts. Greek thinkers were philosophers (lovers of wisdom) and pursued knowledge and beauty in all forms. These philosophers were thus interested in the arts as well as in scientific questions.

This intellectual environment was conducive to cross-fertilization of the arts and sciences, and the great mathematician Pythagoras was among the first to seek the literary and metaphysical meanings of numbers. For the Pythagoreans (followers of Pythagoras), numbers were not merely abstract tools for counting and measuring but also symbols with mystical meanings. For Pythagoras, all things were essentially numbers.

Pythagoras’s notions on the mystical meaning of numbers have little relevance in modern science and mathematics, but they advance the idea that numbers may be used as literary objects. These ideas paved the way for other thinkers seeking greater meanings for mathematics than those constrained within the realm of science.

Mathematical Imagery in Fiction

Mathematics is a field rich in shapes, structures, and relations, and writers may find in mathematics a vast resource of imagery, analogy, and metaphor. Examples of mathematical imagery in fiction abound, and while some are explicit and obvious, others require varying degrees of mathematical knowledge to be fully appreciated.

Edwin Abbott’s 1884 Flatland is perhaps the most famous novel whose characters are mathematical objects. This witty and influential novel takes place in a two-dimensional universe whose denizens are anthropomorphic lines and polygons. The narrator, a square, describes social classes, political unrest, and practical issues of life in two dimensions. He then describes visits to lower dimensional worlds and to Spaceland, the world of three dimensions. The narrator then conjectures the existence of higher dimensional worlds. The novel won renewed recognition near the end of the twentieth century in part because of the development of physical theories, such as string theory, which suggests that the universe may have more than the three spatial dimensions that are visible to us.

The popular 1865 fantasy novel Alice’s Adventures in Wonderland was written by a mathematician, Charles Lutwidge Dodgson, who wrote it under the pen name Lewis Carroll. The novel contains several mathematical themes, such as apparently faulty multiplication (4 times 5 is 12) that can be rationalized by using a different base (4 times 5 is 12 in base 18). Logic (or lack thereof) also plays a role in the novel. During a tea party, the Mad Hatter reproaches Alice for committing the logical fallacy of assuming that a statement implies its converse. There are many other possible mathematical themes in the book; however, because of the light-hearted and fantastic nature of the works, it is impossible to determine which of those were intentional.

Argentinean author Jorge Luis Borges uses many mathematical themes in his stories. In his 1941 short story Library of Babel, he tells the story of a library filled with an infinite number of books, each containing exactly 410 pages. The story incorporates diverse mathematical ideas and concepts ranging from combinatorics to geometry and topology. The concept of infinity is also a recurring theme in the story. The story is so rich in mathematical imagery that it inspired a 2008 book, William Goldbloom Bloch’s The Unimaginable Mathematics of Borges’ Library of Babel, dedicated to the exploration of these themes.

In his 1869 novel War and Peace, Leo Tolstoy argued that history is not driven by major historical characters but rather by the infinitesimal contributions of many people. He uses an analogy with mathematical integration, where the sum of an infinite number of infinitesimal terms is taken, thereby giving the integral its value.

Fictional Mathematicians in Literature

In popular culture, mathematicians are considered to be highly intelligent individuals who possess an investigative mind and a good sense for problem solving. Mathematicians also have a reputation for eccentricity and lack of social skills. These attributes appeal to many authors and readers and make mathematicians interesting literary characters.

In 414 b.c.e., Athenian comic playwright Aristophanes incorporated a fictional mathematician into his play Birds. In the play, the characters decide to build a utopia in the sky in order to escape the routine of Athenian life. Meton, a geometer, joins them and proposes to survey the skies and parcel them into lots. While describing his planned layout, he mentions his plan to circle the square, a mathematical problem that occupied several Greek mathematicians.

The American poet and author Edgar Allan Poe was a science and mathematics enthusiast and used many scientific and mathematical themes in his stories. In the 1843 short story The Gold Bug, the protagonist uses mathematical intuition, common sense, and rudimentary principles of cryptanalysis (code breaking) to decipher an encoded message that describes the location of a buried treasure.

In Poe’s 1841 story A Descent into the Maelström, the narrator uses his knowledge of solid geometry and fluid physics to escape death in a giant whirlpool that is sinking his ship. Thinking of a fabricated result in fluid mechanics that Poe attributes to Archimedes, the narrator recalls that solids subject to whirlpool display differential flotation based on their shape and that cylinders sink slower than other solids. He then saves his life by attaching himself to a water cask and throwing himself into the water with the cask.

Fictional characters may use mathematics as a pastime or as a source of pleasant diversion. In John Cheever’s 1966 story The Geometry of Love, Charlie Mallory distracts himself from his unhappy marriage and unsatisfying professional and personal lives by trying to create Euclidean models of his relationships. To Mallory, these models are simple, elegant, and stable structures, while his life is often unpredictable and turbulent. Through these models, Mallory receives the stability and equanimity that are lacking in his life.

Aleksandr Solzhenitsyn’s 1968 book The First Circle is a quasi-autobiographical novel set in a gulag in the Soviet Union. The novel’s protagonist, Gleb Nerzhin, is a mathematician incarcerated in the gulag and forced to work with other scientists and engineers on secret state projects. The novel takes a close look at the difficult choices that scientists and mathematicians have to make when they have little or no control over their lives or the products of their research.

Arthur Conan Doyle’s iconic detective Sherlock Holmes was a master of deductive reasoning. An expert at deriving surprising conclusions from evidence and clues, Holmes treated crime mysteries as mathematical puzzles and derived great pleasure from solving them. It is fitting that Holmes’s arch-nemesis, Professor James Moriarty, was a mathematician. Moriarty was a genius villain and head of a large crime organization that pervaded England throughout Holmes’s career. In the 1893 short adventure The Final Problem, Holmes and Moriarty are engaged in hand-to-hand combat as they fall to their deaths from a gorge.

Not all mathematical geniuses realize their potential, in fiction or in real life. Aldous Huxley’s 1924 short story Young Archimedes is a tragic tale of a mathematically gifted boy who falls victim to the unscrupulous and selfish behavior of adults. Huxley suggests that the tragedy is not only the victim’s but also that of a society that fails to give its geniuses the environment they need in order to thrive.

Science Fiction

With its emphasis on science and technology, science fiction is a natural genre for mathematical themes. This theme is particularly true with the advent of “hard” science fiction, a branch of science fiction that stresses scientific rigor and theoretically possible technologies. A notable example of hard science fiction is Greg Egan’s 2002 novel Schild’s Ladder, which uses themes from advanced mathematics and physics. The novel describes a futuristic civilization that is forced into perpetual migration and the discord that develops within that civilization.

Isaac Asimov’s classic Foundation series of novels portrays a fictional mathematician, Hari Seldon, as an influential character. Seldon is a brilliant mathematician who developed a branch of mathematics known as “psychohistory,” which he uses to predict the collapse of the Galactic Empire.

Biographies and Memoirs

Many biographies of mathematicians are available in the literary market. While some of these biographies appeal mostly to mathematicians and historians, many appeal to the general public because of their historical narrative and the extraordinary characters they describe.

Perhaps the most popular biography of a mathematician is A Beautiful Mind, written in 1998 by Sylvia Nasar. The book tells the touching and tragic story of John Forbes Nash, a mathematical genius who was diagnosed with paranoid schizophrenia. Nash’s stellar rise in the ranks of mathematics and his tragic fall provide a fascinating juxtaposition of mathematical genius and mental illness. Nash won the Nobel Prize in Economics in 1994 for his work on game theory.

Masha Gessen’s 2009 book Perfect Rigor: A Genius and the Mathematical Breakthrough of the Century tells the story of Grigori “Grisha” Perelman, a Russian mathematician who proved the century-old Poincaré Conjecture in 2003. Perelman’s proof was ensued by a distasteful affair that was fueled in part by Perelman’s reclusive personality and eccentric behavior, as well as by the controversial conduct of his fellow mathematicians. Disappointed and disillusioned, Perelman withdrew from mathematics at a fairly young age. Perleman’s story sheds light on both the often-overlooked world of scientific politics and intrigues and the colorful individuals who supply them. In 2006, Perelman was awarded the Fields Medal, the most prestigious prize in mathematics, for his ground-breaking work. He declined the award.

Memoirs and autobiographies of mathematicians also abound. Notable among these is G. H. Hardy’s A Mathematician’s Apology, a 1940 philosophical memoir that discusses the beauty of mathematics and the life of a mathematician, with its inevitable joys and sorrows. The memoir is highly influential among mathematicians and among laypersons who want a glimpse into the mind of a mathematician.

Satire

Because of the wide-ranging utility of mathematics, there exists a tendency to overuse it and to attempt to reduce social, political, and economic problems to mathematical equations. This attempt at oversimplifying serious societal problems raises the ire of some authors, who use their pens to strike back. By using reductio ad absurdum (reduction to absurdity, also known as “proof by contradiction”), a popular technique for proving mathematical theorems, authors may attempt to defeat mathematicians on the mathematicians’ turf by showing the absurd results of the overuse and abuse of mathematics. The resulting satires describe these absurd results in an entertaining yet serious fashion.

In the 1726 novel Gulliver’s Travels, Jonathan Swift describes the people of Laputa as obsessed with mathematics. They describe everything, even the beauty of women, in mathematical terms, and their constant political bickering reminds the narrator of the mathematicians of Europe. Swift made a similar—albeit less obvious—attack upon mathematical reductionism in his 1729 essay A Modest Proposal in which he proposes that the poor sell their children for food. By offering a preposterous yet simple solution to the problem of poverty, Swift was arguing that not all social problems can be solved by the use of deductive reasoning and mathematical thinking.

In his 1854 novel Hard Times, Charles Dickens criticizes an education system that is based solely on learning of facts, with no room for fancy, imagination, feelings, or arts. The ideal of fancy is embodied in Sissy Jupe, a poor schoolgirl who struggles with a curriculum obsessed with facts. Her frustration rises when she is asked to calculate the percentage of dead if 500 of 100,000 voyagers perished at sea. Jupe, confused and embarrassed, answers that the percentage is nothing, so far as the loved ones of those killed are concerned. Sissy Jupe is thus portrayed as humane and emotional, a person capable of seeing the people behind the numbers. Her schoolteachers, on the other hand, are emotionally paralyzed and see numbers as satisfactory descriptions of everything.

Famous Mathematical Problems

Stories of famous mathematical problems, whether open or solved, make for fascinating reading material for their mathematical content as well as for their narrative. By telling the tale of a particularly difficult mathematical problem, the author can braid an exposition of a difficult mathematical subject with stories about the history of the problem and the lives and personalities of famous mathematicians who tried to solve it.

The Riemann Hypothesis, the most famous open problem in mathematics, has inspired several books. In the 2003 book Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics, author John Derbyshire uses odd-numbered chapters for mathematical exposition and even-numbered chapters for discussion of the history of the problem and the people behind that history.

In the 1997 book Fermat’s Enigma, author Simon Singh tells the story of Fermat’s Last Theorem, a mathematical riddle that tantalized mathematicians for four centuries. Singh tells the tale of the famous conjecture, from its formulation by Fermat in 1637 to its proof by British mathematician Andrew Wiles in 1995. The book combines mathematical exposition with stories about the many mathematicians who struggled with the problem throughout the centuries.

Creativity in Mathematics and in Literature

Fiction writers often face the question “How do you come up with your ideas?” Similarly, mathematicians are often asked how they concoct the brilliant ideas that allow them to solve mathematical problems. Psychologists and neuroscientists have been trying to identify the sources of creativity for a long time. New discoveries are published regularly, and advances in technology, such as brain-mapping magnetic resonance imaging (MRI) machines, may shed further light on the subject. Until scientists elucidate the sources of creativity, the experiences and opinions of creative individuals writers, mathematicians, and others—may provide glimpses into the workings of creative minds.

In his 1846 essay Philosophy of Composition, author and poet Edgar Allan Poe analyzes the creative process he used to compose his famous poem The Raven:

It is my design to render it manifest that no one point in its composition is referable either to accident or intuition—that the work proceeded step by step, to its completion, with the precision and rigid consequence of a mathematical problem.

Another glimpse into the creative process is provided by mathematician Jacques Hadamard in his 1945 work The Psychology of Invention in the Mathematical Field, in which he discusses the psychological processes of discovery and invention in mathematics. While Hadamard acknowledges the crucial role of conscious, logical thought, he contends that mathematical invention is a multi-step process in which intuition, inspiration, and unconscious thought are integral.

Poe’s and Hadamard’s views provide an interesting juxtaposition: while the poet describes his creative work in terms of a mathematical problem, the mathematician emphasizes creative processes that are usually associated with artistic work.

Bibliography

Ahearn, Stephen T. “Tolstoy’s Integration Metaphor From War and Peace.” American Mathematical Monthly 112, no. 7 (2005).

Bloch, William Goldbloom. The Unimaginable Mathematics of Borges’ Library of Babel. New York: Oxford University Press, 2008.

Fadiman, Clifton, ed. Fantasia Mathematica. New York: Springer-Verlag, 1997.

Hadamard, Jacques. A Mathematician’s Mind. Princeton, NJ: Princeton University Press, 1996.

Kasman, Alex. “MathFiction.” http://kasmana.people.cofc.edu/MATHFICT.

Koehler, D. O. “Mathematics and Literature.” Mathematics Magazine 55, no. 2 (1982).

Poe, Edgar Allan. Edited by G. R. Thompson. Edgar Allan Poe: Essays and Reviews. New York: Library of America, 1984.

Whitin, David J., and Phyllis Whitin. New Visions for Linking Literature and Mathematics. Urbana, IL: National Council of Teachers of English, 2004.