Can mathematicians learn to write? Steven Krantz says they can

So, you're a newly minted mathematician, you are the awe of academe, you're the envy of colleagues who are struggling to figure out the interest rates and payment schedules of their student loans. As you embark on your career in the realm of numbers and logic, what's the first thing you need to know?

How to be a good writer.

Pardon the fragment, but that's the message in the book "A Primer of Mathematical Writing," which was published this year by the American Mathematical Society.

The book's author, Steven G. Krantz, Ph.D., is a professor of mathematics in Arts and Sciences and a distinguished mathematician. And, rare among mathematicians in the United States, he is an accomplished author and award-winning expository writer who sees a need for mathematicians to improve their professional lives through better writing.

Although his book is slanted toward mathematicians, professionals in other fields can find help in the book's clearly stated practical tips for better writing, its scope of different writing modes and its grammatical examples -- punctuated with memorable humor.

"I started out writing a book on how to write mathematics, but actually it turned out to be a book on how to live," said Krantz, who in this decade alone has published 15 books and has been awarded the prestigious Chauvenet Prize and Beckenbach Award for mathematical expository writing. "It's about how to conduct your professional life, and most of the activities pertaining thereto involve writing."

Part of the equation for a successful mathematics career is writing know-how, said Krantz, who drew motivation and inspiration for writing the book from his own professional experiences.

"Apart from sounding like a fun project, the book's call to me was to provide some guidance for mathematicians who are just starting out," he said. "Certainly, when I got my Ph.D. in 1974, I was essentially kicked out the door of my graduate school. Nobody told me how to teach, how to publish a paper or how to behave in a mathematics department; surprising to some, all of these activities can be very tricky things to learn."

So what does the aspiring mathematical scientist need to learn besides how to find the correct answer to a problem?

E-mail etiquette

"One of the things I've wanted to address for some time is how to use e-mail properly. Believe me, a mathematician, or any professional, can make grievous mistakes by writing hasty or emotional e-mail. The misuse of that medium -- whether sloppiness in a message or nastiness in tone -- can leave a lasting and sorry impression."

As he does throughout all of the book's sections, Krantz provides anecdotes to explain his point about the dangers of e-mail. Chief among these is that a message can be hastily sent and then cannot be retrieved. He tells of the pre-electronic days when he wrote a scathing letter to a colleague who had taken him to task over a professional matter. After musing over the consequences of his anger, Krantz retrieved the letter from the departmental mailbox and then wrote a more subdued version. The process continued throughout the day until he eventually wrote a letter of apology thanking the colleague for bringing the matter to his attention.

"I have always been happy for this outcome," he writes in the book. "With e-mail, matters would have been quite different."

Krantz strongly advises both proofreading each e-mail message before sending it and using an e-mail editor (many equipped with spell-checkers), if available. He urges brevity and clarity in the message, and he discourages using e-mail when the message is sensitive. For such discreet messages, he suggests hard-copy letters and/or the telephone, with this advice: "Any superuser on your system can eavesdrop on your e-mail, and computer bandits can break into your system and perform all sorts of nasty deeds."

'The Basics'

In discussing how to avoid ending a sentence with a preposition, Krantz relates in the book the old joke of a visitor who asked a student on the Harvard campus, "Where's the library at?" After being corrected for poor use of grammar, the stranger rephrased the question: "Where's the library at, jerk?"

Krantz parodies the use of faddish, if not politically correct, prose. He writes: "If you say 'fraternally affiliated, ethically challenged young male' to mean 'gang member,' or 'peregrinating, fashion-challenged, pulchritudinally advanced hostess' to mean 'prostitute,' then you may be politically correct today but you will be strictly out to lunch tomorrow."

In preparing that all-important document, the curriculum vitae, or CV, Krantz cautions against such careless devices as writing the CV as one simple paragraph or stanza, which he has seen on numerous occasions. Furthermore, he strongly suggests beginning the document with one's name in boldface centered at the top, using precisely the name found on your birth certificate. "Your friends may call you 'Goober,' but you should save that information for another occasion," he says in the book.

Doing what comes naturally

"In today's world, there is a great tradition of mathematical expository writing in France -- and to a lesser extent Germany and Great Britain -- but in this country that tradition is rather feeble," he said. "Suppose that you approach a good American mathematician and ask: 'Would you rather prove a theorem or write an expository article?' The knee-jerk choice will be the former because the general perception is that exposition isn't going to get him professional recognition or a promotion or a new research grant. That's the way the value system is set up."

Mathematics writing shares common properties with expository writing in other disciplines -- among them the need for a lively introduction, a strong body, and a forceful conclusion so that the reader leaves with a vivid impression. But the technical nature of mathematics and the methodical approach of mathematicians to problems make the task of writing unusually difficult for them.

"In expository writing, the mathematical writer has to make difficult decisions, and some of these will run counter to the very culture of mathematics," Krantz said. "The mathematical culture is axiomatic and rigorous, leaving nothing to the imagination. But in exposition, you sometimes have to omit nasty details, you have to oversimplify and paraphrase, and these things don't come naturally to mathematicians."

-- Tony Fitzpatrick