Communicating complexity: New College president suggests less is more

Writing about mathematics can be as challenging as the for those who study it as the problems they solve. Students who enrolled in Chris Kottke’s Writing in Mathematics course got a little help from a familiar face: New College President Donal O’Shea.
O’Shea is the author of numerous mathematics textbooks, including “Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra.” He wanted the book to be accessible to students who were beginning to delve into the discipline.
“Our goal was to write a book that, for a professional mathematician, would be like reading the Hardy Boys,” said O’Shea of the text he authored with colleagues David Cox and John Little.
The approach worked; “Varieties” is now in its fourth edition. O’Shea also wrote “The Poincaré Conjecture: In Search of the Shape of the Universe,” which Publisher’s Weekly described as an “accessible if challenging presentation of a famous problem” rooted in Poincaré’s assertion that there’s only one possible shape for a finite universe. Childhood questions about the shape of the universe prompted O’Shea to bring Poincaré’s conjecture to the masses.
“It’s the first question you think of when you look up at the sky,” recalled O’Shea. “I remember looking at the sky when I was a kid [and wondering] ‘What does curvature look like if you’re living in something? What does that feel like?’ The change I made was to confine the more theoretical stuff to the footnotes.”
O’Shea told the students he believes “writing should be enjoyable to read” and shared advice on how to keep their writing accessible. They should avoid bullet points and overly dense writing, he said, and consider what the content will look like on a mobile device.
“If somebody’s got a really good image that explains something, I don’t mind using that,” responded O’Shea when a student asked for advice on maintaining his style while writing about the work of others. “If I’m too dependent on one image, I don’t really understand it myself.”
Another student asked about the challenges of balancing the complexity of math statements with the explanatory function of the textbook, to which O’Shea responded “Overexplaining makes it more impenetrable.” When it comes to math, less is more.
— Liz Lebron is associate director of communications and marketing at New College.