Academic writing, whether it be a math article or a philosophy textbook, most often fails to capture our imagination or even keep us awake long enough to trudge through its convoluted contents. In unlocking the universe’s greatest mysteries, these treatises fail to bring forth the awe and inspiration that is theirs by right. Why should science writing, whose job it is to describe our incredibly complex, inherently magical universe, be a less exciting read than Harry Potter?
I recently refereed an article that had significant and surprising results, a piece of the jigsaw puzzle that fitted beautifully into the set theoretic tapestry. Sadly, only a highly motivated reader could survive the stupor induced by its stale, unnecessarily technical and context-lacking prose long enough to realize the import of its content. It has been an evolving realization of mine for about a year now that my articles weren’t any better. This is all the more depressing because growing up I did not dream about being a mathematician, I dreamt about being a writer.
In a great New York Times article Zombie nouns, Helen Sword identifies an enlightening concept for those who still believe that creative academic writing is not an oxymoron. A nominalization is a noun formed from other parts of speech: liability from liable, relation from relate, activism from active. Sword calls them ‘zombie nouns’ “because they cannibalize active verbs, suck the lifeblood from adjectives and substitute abstract entities for human beings”. Here is her example of this idea expressed with and without nominalizations:
The proliferation of nominalizations in a discursive formation may be an indication of a tendency toward pomposity and abstraction.
Writers who overload their sentences with nominalizations tend to sound pompous and abstract.
What a difference! Academic writing is chock full of nominalizations. There are no heroes, no story, no insightful examples, or interconnecting webs. Sword writes: “In fact, the more abstract your subject matter, the more your readers will appreciate stories, anecdotes, examples and other handholds to help them stay on track.”
I fell in love with math when in a summer library adventure I stumbled upon William Dunham’s books on the history of mathematics. Dunham didn’t only write about mathematics, neither did he write only mathematics. He told the story of mathematics as an organic whole of history, heroics, mistakes, connections, new beginnings, and of course perfectly technical proofs. In high school, while most of my homework got done during TV commercials, I worked for hours on writing assignments. I agonized over sentences, faced an early onset of writer’s block, and terrorized family members by turning them into involuntary critics. By the end of graduate school, I had decided that writing up solved problems was an energy-sapping chore. But now I am coming full circle, realizing that academic writing can and should be artistic. I am realizing that an integral part of my role as an academic is to write in a way that weaves knowledge into a carefully crafted, expressive, exciting narrative. What is my strategy? Be clear but not excessively technical; be precise but not tedious; add history, motivation, examples, asides; stress interconnections. An academic article should tell a story that fits seamlessly into that greatest of human literary projects: the tale of the universe.
Booles' Rings
I agree completely! Let’s all write so as to illuminate our mathematical ideas, rather than obscure them.
yes, yes and yes!
Years ago I read a philosophy of logic papers that seemed silly to me: the first half would explain everything in prose and the second part would explain the same, but in semi-formalized language.
I later thought that this would be an excellent idea for mathematics in general: the first half explains “what’s going on”, the second half contains an abstract proof (maybe even computer-checkable).
Personally, I write my proofs as indented lists following a style that I read about in a paper by Uri Leron (and Leslie Lamport picked it up for machine-checkable proofs but it obviously didn’t catch on). This style forces me to think about the top-level arguments and the proof structure (and I like ot pretend it makes it more readable). It also allows different levels of readers to skim faster (an expert will only need to read “a standard parity argument shows” where a student wants to read the sub-proof).
The biggest obstacle I see is the lack of incentives — our culture of writing seems to have declined over the last few decades as publication numbers have exploded. The advice now seems to be: put as little effort into a paper as possible, just enough to get it by the referee — and then write more papers. That’s destructive and makes papers even less reliable as a source of knowledge in years to come (see Francois’s post).
Anyways, I hope you’ll share some of you experiments in writing here
I really like the approach of including different levels of technicality in the same proof. I never thought about writing proofs like that before. Yes, at minimum, the author should include a “prose” summary of the ideas in the paper in general and in the proofs in particular. If there is a more natural but an unsuccessful approach to a proof or a definition, it would be so much more enlightening if the author writes a comment about it. Most importantly, you made in your comment a deeply significant point that should have been included the post. There is no incentive whatsoever for academics to write well. Great writing requires time and effort. You have to be willing to experiment, explore, rewrite, and rethink. Why, pray tell, would I do that when I can utilize the time to write more papers, assuring myself grants, release time, and tenure? As long as the contribution one make to the scientific enterprise is counted only in terms of the number of papers one writes (regardless of whether anyone can or wants to read them), there is little hope that academic writing will change its mind numbing ways.
You are clearly a writer! I love this. I appreciate set theory because it allows one to express mathematics in colorful paragraphs rather than lists of centered equations. The complication of the argument is left for the mind to index.
Thanks, Erin
! Yes, I also love the overarching reach of the concepts in set theory.