PGS Dialogue: Mircea Pitici, editor of The Best Writing on Mathematics 2010

Math is everywhere — and yet until now there has been no annual anthology of the best writing in mathematics. Editor Mircea Pitici spoke with math editor Vickie Kearn about how he came up with the idea for The Best Writing on Mathematics series and how he selected articles for inclusion. Read on below.



How did you get the idea for The Best Writing on Mathematics?

In March 2004, a full-time father at the time, I walked with my 18-month old daughter into a bookstore in Hartford, Connecticut. On the shelves close to the entrance I saw several annual anthologies of short stories, essays, science, travel, sports. I asked an assistant for the similar book on mathematics, confident that there was one. They had no such book, so hours later I searched the catalog at Wesleyan University in Middletown, only to find that such a series was not being published. I thought that was odd, given the quantity of good writing on mathematics—and I envisioned, somehow unrealistically given my outlook at the time, that I might start the series myself.

Every year since then I worked on a book similar to this, despite lacking a publisher. I liked the idea and I pursued it for my pleasure. When enough interesting material accumulated, usually every autumn, I sent a book proposal to two-three publishers but I never got a positive reply. My idea for this series remained just an idea until the fall of 2009, when Princeton University Press liked it.

Meanwhile an important development made me feel some urgency. The Knight Institute for Writing in the Disciplines at Cornell University offered me the chance to teach, for several semesters, a Freshman Writing Seminar focused on mathematical topics, which I titled Certainty and Ambiguity. Most of my students were majors in mathematics, computer science, sciences, or engineering, and therefore among the best in the school, in mathematics. Yet they had read little about mathematics, were unfamiliar with the literature on mathematics, or were not even aware that it exists. That surprised me and convinced me that a series like this can have a positive impact on mathematics instruction.

How did you decide which journals you would look through to select papers?

I have read many periodicals for a long time, both academic and non-academic. Starting as a mathematics undergraduate in Romania, but especially after coming to the U.S, I looked into hundreds of journals on a regular basis—not just mathematical literature but also in other disciplines. I glimpse into many areas and I read as much as time allows me. I like to know what people think, and how, and why.

When Princeton expressed interest in The Best Writing on Mathematics project I easily started into action, based on my familiarity with the sources and on the experience I had gained during the previous years by doing a sort of virtual volume, for my own use. I decided to split my methodology into a chaotic phase and a meticulous phase. I believe in serendipity, so for some time I looked randomly into scores of books and publications, with no preconceptions as to what might come my way. But when I do that I subtly keep track of the randomness, I am organized. That allows me to switch to a systematic search at the right time, by covering the gaps I incur in my random sampling and by diminishing the chance that I might overlook remarkable texts. Finally, in a wrap-up phase, I ask other people for comments and suggestions, and I settle on the final content.

How many articles did you read when making your decision?

It’s difficult to give an estimate, but let me try. I see several thousand articles in one year but obviously I discard most of them quickly (as far as this particular book series is concerned). Not necessarily because they are not worthy of my attention or do not deserve reading; I just know by reading the first paragraph or by a cursory look at the prose and the exposition that they wouldn’t fit in the book I envision. Perhaps I gave serious attention and read thoroughly in direct connection with this volume about four-five times more texts than I finally chose—which means 150 or so. That is a rough approximation.

No one person could subscribe to all of these journals. I imagine you spent many hours in the library or did you do your reading on line?

I read materials both in hard copy and electronically. I go into libraries often, as a matter of habit—and I have done so ever since childhood, with brief interruptions. I feel at large in libraries. When I enter the library I resemble a good hunter entering a vast but familiar forest. I know where to go, where the best spots are for finding what is new, and where I can explore the old. Even in huge libraries I learn the topography quickly, so that it is easy to find the recently arrived materials. Without the excellent library facilities at Cornell University I would not have been able to edit this volume.

Jorge Luis Borges wrote that he imagined Paradise as a kind of library; I feel affinity for the message he conveyed metaphorically. Books, journals, magazines, and newspapers are idea repositories. They encapsulate potentialities and open up minds toward life possibilities. When I visit new places I always seek out the libraries and the bookstores, whether it is a tiny Maine village or it is Shanghai. My conclusions after such surveys are revealing and often surprising. My living places tend to resemble libraries, too. Recently a librarian chuckled, alluding to the number of books I had borrowed over time: “You are well into the Renaissance!” Yet I am far from being a bookworm, don’t get me wrong. Moreover, my love affair with books got me into serious trouble a few times, in unexpected ways—but that is beyond the subject matter of this interview!

Did you choose a certain text just because you liked it?

I aim to select well written texts, insightful, informative, substantive. If I read texts with these qualities I consider them good even if I disagree with the views expressed there. I have certain views on mathematics, formed over many years of thinking about it and teaching it at all levels (except graduate level). My views can differ from the ideas in some of the articles I include, but that is not a factor in my selection. Informed dissent in mathematics is welcome and fertile.

What criteria made you reject a paper?

The word “reject” in this context is too harsh for my relation to some of the texts I did not include in the book. The selection process is comparative and competitive. I weigh texts against each other. I want good writing on mathematics as the most important quality—that is the overriding criterion. But I also want diversity of themes, of authors, sources, countries. I try to avoid overlapping articles. If two are similar I choose one, except if a deepening of perspective is obvious from the succession of the two.

Were there more papers you would have liked to include but couldn’t?

Yes. Constraints of space and concerns related to copyright are the main culprits. For instance in a volume of about 400 pages it’s not realistic to include texts longer than 25-30 pages, since they would make up a large proportion of it, leaving a shrinking proportion available for the other texts. I had to discard several excellent pieces for this reason only. In addition, as I mentioned earlier, I want a diverse assortment, so I am on the lookout for over-representation of certain themes or publications.

How many hours did you spend putting together this volume?

That is impossible to answer, even approximately. Editing this volume became an ongoing task; it was with me all the time, but that does not mean that I focused on it all the time. I have multiple duties, academic and at home—as well as other projects and research, on which I might work at the same time. I might work several hours one day but just give it a few moments’ thought some other day.

After all is said and done, do you plan another similar volume for 2011?

The next volume is in advanced planning stage. I hope it will be at least as interesting as the current one.

What do you plan to do differently?

The Best Writing of Mathematics reflects the literature on mathematics available out there in myriad publications, some difficult to consult even for people who have access to good academic resources. The content of each volume builds itself up to a point; I only give it a coherent structure and present it to the reader. That means that every year some big themes will be new, others will reappear. I’ve got a good working plan but I am eager to listen to what other people suggest after the first volume is available to the public.

One thing I am considering (but I haven’t yet decided on it) is to add a list of “also runs” that mentions notable texts I had looked at before the final selection but ultimately chose not to include. That would be a useful and informative reference for the reader but it might leave the impression that I attempt to be quixotically exhaustive. I will see what others say. I will be receptive to anything that helps improve this endeavor.

What do you hope that readers will learn from reading your book?

I suppose most readers of this book are engaged with mathematics in some way, at least by being curious about it. But most of them are inevitably engaged with only a (small) part of mathematics. That is true even for professional mathematicians, with rare exceptions. Mathematics today has far reaching tentacles, in pure research branches as well as in mundane applications and in instructional contexts. No wonder the stakeholders in the metamorphosis of mathematics as a social phenomenon can hardly be well informed about the main ideas and developments in all the different aspects connected to mathematics. I hope this series of volumes makes it easier for readers, insiders and outsiders, to identify the main trends in thinking about mathematics in areas unfamiliar to them. There is plenty of room for everybody to learn more about mathematics.

By editing this series I also want to make widely available, cheaply and conveniently, excellent texts about mathematics that otherwise would be lost in the deluge of information that surrounds us. Writing about mathematics has become a genre, with its own professional practitioners—some highly talented, some struggling to be relevant, some well established, some newcomers. Every year these authors, considered together, publish many books, more or less successful. My selection concerns mostly literature that is not yet available in book form, either articles from academic journals or good writing in the media that goes unobserved or is forgotten after a little while. I see my task as restitution to the public of remarkable writing on mathematics that deserves enhanced reception beyond the initial publication.

What other projects do you have?

Mathematics is my professional preoccupation but I have other interests, some far remote from mathematics (at a first impression). I hope that I can find the time and the means to pursue them, too.

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