Posted by: holdenlee | September 15, 2013

The Math/Writing Divide

I want to be both a writer and a math professor. It’s hard at times because these are two very different professions–fundamentally, writing is creative while math is logical [1]. Sometimes I feel I have to constantly juggle the two–time spent on one is less time spent on the other, and moreover, doing too much of one makes me “forget” how to do the other because the mindsets are so different.

Over the past several years, though, I’ve found similarities between writing and math, and I think doing both gives me a unique perspective. During my time at the educational startup Gliya, I was able to combine my interests to write stories into math lessons. If I had to choose only either math or writing, I would lose part of myself. I think this is true of many people, too: they can’t be pigeonholed into having one “passion,” and it’s the combination of things that you like doing that make you who you are. I’d like to encourage anyone who likes very different, seemingly incompatible things: there is a way to make it work. When you pursue very different interests, you develop a unique perspective simply because not many people will have thought as deeply about those two (or more) things that you like.

At some level, maybe any intellectual or creative pursuit, when you delve deep enough, gives you an angle to look and talk about every other intellectual or creative pursuit. Certainly, each pursuit has some valuable way of thinking that “transfers” to many other areas and that would be helpful for others to learn. For example, Jenny wrote on her blog  that even though she isn’t pursuing architecture, she has learned important life lessons from Course 4 at MIT; David mentioned in his interview how a scientific mindset is useful for humanistic disciplines. I find these conversations very valuable.

As inspiration, I’ll write about how even though math and writing seem incompatible, they have many common ways of thinking.

Why is it hard to be a mathematician-writer?

Writers and mathematicians, or more generally scientists, tend to have conflicting qualities, at least stereotypically. Consider the following comparisons.

  • Scientists make things clear. They want to understand the reasons behind things. When they write up a paper, they make it as transparent as possible (unless they’re trying to falsify data). On the other hand, a story is crafted. Writers can’t just tell something; they have to show it using certain descriptions to evoke a certain effect on the audience.
  • Mathematicians are often so engrossed in math problems to not notice or care about anything in the outside world (because other things aren’t as meaningful). When walking around, their eyes are turned inward (hence absentmindedness).
    Writers, however, have to be constantly open to new ideas, and observe the world around them. Their eyes need to be turned outward more. Talking to other people helps them imagine from other perspectives. Writers may philosophize more, and think deeply about motivations, feelings, relationships. These things would distract mathematicians from their objects of study.
  • Mathematicians think of stuff that is “useless” to the outside world, while writers by nature have to think about humanity, to put real experiences on paper.
  • Mathematicians think very logically. Definitions, for example, are absolute. In writing, though, powerful statements can come from using a word in different context, using its emotional content instead of its rigid definition. Consider this statement: “do not promise me forever–i just need to know that we can still stand each other when forever’s over.”[2]
  • Many writers have other jobs. But although any profession gives you something you can write about, math research isn’t something that gives you clear insight into human psychology (as opposed to something like teaching or human services), nor is it something that gives you a broad range of experiences (except maybe it allows you to travel).
  • Sometimes, when mathematicians see enough examples of something, they tend to forget specific examples and remember the abstraction. Writers, however, always have to have the specific details on hand, because it’s hard to identify with an abstraction.

…but they’re not that different

  • Both math and writing are creative (though math creativity is creativity subject to intense constraints). Rather than try and define creativity here, I’ll say that doing something creative is “like driving a car at night. You can see only as far as your headlights, but you can make the whole trip that way (E.L. Doctorow).” Uncertainty is central to both creative writing and math (or any kind of) research.In both math and writing, often the most direct approach fails, or at least, does not lead to the best work. In both, you tend to perform mediocre if you only have one “chance” to make a piece of research or writing work, because really good research and really good writing require courageous experimentation–coming up with 10 crazy ideas that don’t seem to have much chance of working and trying them out, in the hope that one will succeed, rather than just coming up with 1 idea that seems likely to work.
  • A mathematician and a writer are both “full-time professions,” not in the sense of being 8-5 jobs but in the sense that they don’t just require hard time– time sitting down with paper and pencil (or computer), to either write or crunch out problems–but also soft time.As mentioned above, both research and creative writing, you don’t have a clear path to follow to forge ahead: you have to explore a lot of different directions. This takes a lot of time and you seem like you’re not doing anything when you are exploring. Thus, the best time to do such things is in these “gaps” in everyday life. Hence as professions, both math and writing  tend to fill in the gaps when you’re waiting for the metro, when you’re in line at the café, or when you’re in the shower. Inspiration for both can come at unpredictable moments.
  • Math and writing both require few tools–just pencil and paper. They’re both concerned with the question: how much can you do with the minimal? Math is in a sense, how much can we push knowledge with absolute certainty as a foundation, and with logic as the only accepted method of argument. Writing is in a sense, how much of a story we can capture and recreate in a reader’s mind with text as the only accepted medium of communication[3]. Compare math to science or engineering–in science you have many more methods of argument such as observation, experimenting, and building things. Compare writing to art or filming or anything multimedia. Thus math and writing encourage honing of basic skills.
  • Asking and answering the right questions: Math is often about asking the right questions, because they create the stepping stones for the proof of a difficult theorem, or because the answer turns out to be connected to a lot of other interesting questions. Research itself is pursuing questions.Writing is also about asking questions: creating a character, world, or the beginning of a story, and then asking what would happen? In The Unbearable Lightness of Being, Kundera writes, “[Characters] are born of a situation, a sentence, a metaphor containing in a nutshell a basic human possibility that the author thinks no one else has discovered or said something essential about (p. 221).” The process of writing is hence also pursuing questions that the writer doesn’t know the answer to. During writing workshops, our professor always tells us to question or wonder, because aspects of the world or of the characters you haven’t thought about leads to good places for the story to grow.

What did I learn as a writer from math?

Nazaryan writes in a New Yorker article that writers should learn math! While this is debatable, there are certainly some ways of thinking common to math and writing. (I put these ways of thinking in this section because I learned them first for math before I did for writing.)

  • Precision and conciseness:
    • The conciseness of proof: Math teaches concise writing, because when writing a proof, you don’t consider every possible aspect of the problem and have a lot of little reasons saying why the statement “works.” Instead, you just write down what matters in the correct order, and nothing more–everything in the proof has a purpose for being there. In writing, a good question to ask is, am I using the least amount of words for maximal effect? Does every sentence in the story have a purpose?
    • The precision of theorems and conjectures: A theorem in mathematics has to be precise. An idea in math starts out fuzzy but has to be sharpened when made into a conjecture. In writing, you can build a world or a character by accumulation of details, but sometimes you need a very sharp statement (that doesn’t necessarily have to be correct).My AI professor said one thing he doesn’t like about literature is that it talks about the same topics over and over again. On the other hand,  my friend Semon R. said “math is about continually creating a new idea you didn’t have before.” Math, as with other scientific disciplines, is about building up: once you have some basic concepts, you use them to create more complicated concepts, and then you use those complicated concepts to build even more complicated ones. In each higher math subject, you use the theorems from the previous subject as parts of proofs. Math doesn’t get weaker as you build up because it is precise.In writing, as in the humanities, there is no definite answer (art depends on there not being definite answers), but one way to not feel like you’re going in circles is to embed precise “conjectures” about the way life works in the story, or even in the ethos of the world. Here’s several examples from books I read this summer.”The moment someone keeps an eye on what we do, we involuntarily make allowances for that eye, and nothing we do is truthful (The Unbearable Lightness of Being, 113).”

      “On a bitter-cold day, a person can be frozen numb and it won’t bother him, but a little warmth will make him feel so cold that his heart and his bones ache (Love in a Fallen City, 84).”

      “You need to get a long ways away from people before you can learn to listen properly (The Wise Man’s Fear, 591)”

      “Compassion emerges from imagining the world alive (On Looking, 39)”

      While a reader may agree or disagree, these statements are sharp enough and abstract enough  (in the sense that they can apply to a lot of situations in life) that you can give evidence for or against them–they can be a subject of a debate or interesting conversation, if you wanted.

  • Logic: While “logic” is much more flexible in stories, there has to be some consistency in the ways things happen, and cause and effect. A story has to make sense when you strip it of all fancy poetic language, just like a proof has to make sense when reduced down to its essentials.
  • Breaking apart “black boxes”: Understanding a math subject is not just knowing the theorem statements (and hence taking them as “black boxes”), it’s also about knowing the proofs. What’s interesting about math is breaking apart those black boxes into the atoms of logical reasoning.One function of writing is to break apart these black boxes that we have become to accustomed to, and show us the beauty inside. In On Looking, for example, Alexandra Horowitz takes things we are accustomed to in our walk down the street–the lettering on signs, the way the crowd moves, the limestone wall–and shows that there’s much more to them than we realize–there’s an art to choosing fonts, a science to crowd dynamics, a history to the wall (there are fossils of ancient sea creatures in the limestone).

For a different perspective, Leonid has blogged about some similarities between math and poetry, and the subjectivity of math terms.

What did I learn as a mathematician from writing?

To communicate and teach math more effectively, one thing mathematicians can do is learn to tell stories. (Watch Tyler DeWitt’s TED Talk about telling stories to teach science. Leonid mentions this in his interview (transcript, recording), Simon mentions it in his teaching statement. A story is similar to Dan Myer’s 3-act math.  ViHart tells wonderful mathematical stories, for example, about life on a Mobius strip.)

Stories–at least, stories orally told–are like viruses, because they are their own means of propagation. In general, people have better memories for stories than disjoint facts. Contradicting what I said earlier, a well-written proof contains more than just the minimum number of words needed, because it also gives enough motivation for each statement to follow naturally; it contains some overarching idea or theme, that allows the reader to remember the proof and tell it to someone else. One way of looking at a story is a series of events where each follows in some way naturally from the preceding.

Stories are inherently interesting beyond any moral or message they want to communicate; a well-written math article makes you want to keep reading beyond just knowing the proof of the theorem mentioned at the beginning (because the argument itself is interesting). Writers know how to create “bindings”: you don’t just say something in the abstract but you paint a specific picture for readers, from which they can remember the abstract. (Think of any fable, for instance; it’s an abstract message that comes with a specific story.) In math, we have to remember that it’s partly about finding the most abstract version of a theorem but also about finding the specific things that the theorem demonstrates.


Many writers who don’t know very much about mathematicians often insert a character who’s a mysterious math prodigy who proves some big theorem. All this does is reinforce a stereotype that math is some kind of special talent, like magic, and there are wizards and non-wizards–rather than something that can be learned, and a set of ways of thought. Those writers haven’t been successful at breaking open that “black-box” of who a mathematician is in their writing. (One book that has been successful, in my opinion, is Mark Haddon’s The Curious Incident of the Dog in the Nighttime about an autistic math student.) I’d like to try to write about mathematicians in future stories.

A good example of solid scientific thinking combined with very good writing is my favorite science-fiction book, Ted Chiang’s collection Stories of Your Life and Others. Unlike other science fiction, it shows an internal view of what it’s like to be a scientist and how that scientific viewpoint pervades life; for instance, he carries the reader through the problem-solving process of a linguist trying to decipher an alien language. He makes analogies between scientific principles and life (the kind of thing scientists tend to do!) and even makes the story around those principles (the two interpretations of diffraction–as causation vs. as minimizing  energy). It’s not just about science, though, because at the same time, life is happening (love, death, etc.). He has two mathematical stories (one on an alternate topology for the world, one on what happens when a mathematician proves the inconsistency of the Peano axioms). His last story, “Liking What You See,” explores the societal implications of a piece of technology.

Although I mentioned that math doesn’t give a lot of life experiences for writing material, this is false if you develop a writer’s eye for finding stories in everything: Jane Austen, after all, wrote six books with little more for ingredients than daily life and gossip! The daily fabric of a mathematician’s life is not well-understood by the general populace. Chiang has captured that pretty well, and it’s something I’d like to do, too. (In the meantime, The Princeton Companion to Mathematics I.4 and VIII.6 provides a wonderful general-audience exposition of what it means to do math, and there’s also Mathematicians: An outer view of an inner world.)

The ways of thinking I’ve listed are by no means unique to math or writing. And of course, there are mindsets I have to consciously change as I’m going from one to the other (writing requires a much more flexible creativity), but knowing the commonalities makes it easier for me. In any case, I’d like to see more discussion about the ways of thinking/being involved in different professions, because I feel we’d all learn tremendously from them.

(Please leave comments! What commonalities have you found doing very different tasks? Any other recommendations for mathematical fiction?)



  1. Did you know that Jordan Ellenberg spent a year studying fiction writing at John Hopkins before going back to Harvard for a PhD in math? He’s the main example that comes to mind of someone who is both a writer and a math professor.

    Also, I absolutely love Ted Chiang’s Stories of Your Life and Others!

  2. @Sarah: That’s cool! Have you read his book?

  3. In Lawrence of Arabia, T. E. Lawrence is asked what “personally attracts [him] to the desert.”

    He responds, “It’s clean.”

    That’s something math and writing share.

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