The mathematician’s tricks

A long time ago an older and well-known number theorist made some disparaging remarks about Paul Erdős’s work. You admire Erdős’s contributions to mathematics as much as I do, and I felt annoyed when the older mathematician flatly and definitively stated that all of Erdős’s work could be “reduced” to a few tricks which Erdős repeatedly relied on in his proofs. What the number theorist did not realize is that other mathematicians, even the very best, also rely on a few tricks which they use over and over. Take Hilbert. The second volume of Hilbert’s collected papers contains Hilbert’s papers in invariant theory. I have made a point of reading some of these papers with care. It is sad to note that some of Hilbert’s beautiful results have been completely forgotten. But on reading the proofs of Hilbert’s striking and deep theorems in invariant theory, it was surprising to verify that Hilbert’s proofs relied on the same few tricks. Even Hilbert had only a few tricks!

—Gian-Carlo Rota, “Ten Lessons I Wish I Had Been Taught”

“My brain is open!”

[Paul] Erdős (pronounced “air-dish”) structured his life to maximize the amount of time he had for mathematics. He had no wife or children, no job, no hobbies, not even a home, to tie him down. He lived out of a shabby suitcase and a drab orange plastic bag from Centrum Aruhaz (“Central Warehouse”), a large department store in Budapest. In a never-ending search for good mathematical problems and fresh mathematical talent, Erdős crisscrossed four continents at a frenzied pace, moving from one university or research center to the next. His modus operandi was to show up on the doorstep of a fellow mathematician, declare, “My brain is open,” work with his host for a day or two, until he was bored or his host was run down, and then move on to another home.

Erdős’s motto was not “Other cities, other maidens” but “Another roof, another proof.” He did mathematics in more than twenty-five different countries, completing important proofs in remote places and sometimes publishing them in equally obscure journals. Hence the limerick, composed by one of his colleagues:

A conjecture both deep and profound
Is whether the circle is round.
In a paper of Erdős
Written in Kurdish
A counterexample is found.

When Erdős heard the limerick, he wanted to publish a paper in Kurdish but couldn’t find a Kurdish math journal.

—Paul Hoffman, The Man Who Loved Only Numbers

Writing with chemicals

Earlier this morning, I was feeling more out of it than usual, so instead of my usual thermos of green tea, I brewed a pot of coffee. I did this automatically, without giving much thought to it, much as a doctor might write a slightly stronger prescription for a patient who wasn’t responding to the usual course of treatment. Later on, however, it gave me pause. Some form of caffeine has been a part of my writing life ever since I was in college, and I wouldn’t think of starting my day without coffee or tea any more than I’d decide not to brush my teeth. (And I’m not the only one: my wife, a journalist, notes that ever since Argo Tea opened a branch on the ground floor of the Tribune Tower, the reporters there don’t even need to leave the building.) The writing life, with all its physical and psychological challenges, naturally invites forms of self-medication, and although authors have tried everything from peyote to opium, most end up using some combination of the big three: nicotine, alcohol, and caffeine. But is it worth it?

Of the three, nicotine is perhaps the most easily dismissed. It’s true that the association between writers and smoking goes back a long time—for proof, just check out the photos accompanying my Quotes of the Day, a startling number of which depict a novelist with a cigarette—and attempts have often been made to link nicotine with alertness, concentration, and creativity, a point with which many artists would probably agree. The issue, as with all chemical substances, is what kind of thinking you’re getting. While smoking does seem to make people think faster, they may also think worse, at least according to one recent study, which noted that subjects given nicotine before cognitive tests score higher on response time but lower on accuracy. (As the gunslinger said: “Speed’s fine, pardner, but accuracy’s final.”) And while it’s possible these days for writers to get the benefits of nicotine without the side effects of smoking, my own suspicion is that they’re gaining an expensive addiction for little real benefit—which I’m sure won’t dissuade many of them from doing it anyway.

Drinking, too, has played a large role in the careers of many writers, to the point where alcoholism has been rightly described as the single greatest occupational hazard of the writing life. In contrast to the stimulating effect of cigarettes, alcohol is a kind of self-anesthesia, a way of enduing the pain of facing the empty page. Yet it seems clear that all our great alcoholic writers were great in spite of their drinking, not because of it. And while I wouldn’t deny a drink to a working writer, my own experience tells me that it’s better to have that glass of wine after finishing the day’s work. The degree of concentration and attention to detail required to write a good novel, or even a publishable bad one, is hard to sustain under any circumstances, and alcohol robs the writer of his most precious instrument: his detachment. At the very least, revision needs to be done while sober. And for the most part, I’ve always thought that Norman Mailer, no stranger to substance abuse himself, had the right idea:

Amateurs write when they are drunk. For a serious writer to do that is equivalent to a professional football player throwing imaginary passes in traffic when he is bombed, and smashing his body into parked cars on the mistaken impression that he is taking out the linebacker. Such a professional football player will feel like crying in the morning when he discovers his ribs are broken.

Which brings us back to caffeine. If nicotine is about quick stimulation and alcohol is about killing the pain, caffeine, at least to me, is about endurance. It’s about writing whether you want to or not, staying on task, or at least remaining reasonably conscious. To my eyes, it’s the drug of necessary compromise, of doing just well enough to finish the rough draft of a chapter, and of surviving to write another day. As such, it’s the drug of choice for journalists, bloggers, and all working writers. My own routine, aside from the occasional coffee fix, is fueled by two thermoses of green tea each day, and while I might be better off without it, I don’t think I’d be nearly as productive. As I’ve said before, a writer’s life is really a series of practical answers to the particular problem of sitting down and writing for hours at a time, and caffeine, for me, is part of the solution. And at this point, I can only conclude, to misquote the mathematician Alfréd Rényi by way of Paul Erdos, that a writer is a device for turning coffee into novels.