ABOUT PAUL HALMOS
Paul Halmos died on October 2, 2006, at the age of 90. He was a master of mathematics in multiple ways, and he influenced mathematicians and mathematical culture throughout his career. Unlike most other master mathematicians, Paul’s legacy was not merely mathematics but rather advice and opinion about mathematical life—writing, publishing, speaking, research, or even thinking about mathematics. Paul wrote about each of these topics with an extraordinary mixture of conviction and humility. Paul Halmos’s writing affected the professional lives of nearly every mathematician in the latter half of the twentieth century, and it will continue to influence the profession for years to come.
Paul Halmos’s life was a work of art. You see this in the film I Want to Be a Mathematician and in Paul’s autobiography. Halmos tells you not just what he did, but how he did it.
Is this art of his right for everybody? Perhaps not. Look at the selections titled “Work, Preparation and Spontaneity” in the bonus features, especially David Eisenbud’s remarks about trying to incorporate Paul’s ideas when David gave a colloquium at Bloomington, Indiana. But we can all learn from Paul.
How does one move from studying to learning, to doing research, and onward in a career? There is no single path for all, but there are examples to learn from. In I Want to Be a Mathematician, the book and the film, Paul Halmos tells us how he did it—with grace, charm, and wit.
—Peter Renz, Brookline, Massachusetts, January 2009
ABOUT THE FILM
It might seem unnecessary to insist that in order
to say something well you must have something to
say, but it’s no joke. Much bad writing, mathematical
and otherwise, is caused by a violation of that first principle.
The 1999 interview with Paul Halmos that forms the backbone of I Want To Be A Mathematician: A Conversation with Paul Halmos was initiated to gather some comments from Halmos about R. L. Moore for the Educational Advancement Foundation’s (EAF) R.L Moore Legacy Project. Halmos was an advocate of the Moore method of teaching mathematics, and had been a friend of Moore’s. EAF commissioned Peter Renz and myself to do the interview at Halmos’s retirement home in Los Gatos, California. During the day that Peter and I spent preparing questions for Halmos, Peter conveyed his enormous respect for Halmos and his work. I asked Peter to explain why Halmos was so important to educators, mathematicians, and writers. As he responded, the list of questions we would ask Halmos the next day expanded.
The interview was conducted on August 4, 1999, and we came away with a little under 3.5 hours of videotape. During the following months I selected the Halmos sound bites about R. L. Moore and edited a 10-minute piece about Moore that is still being used by EAF.
Having watched all the footage, I realized that Halmos had delivered something of lasting value to teachers and mathematicians. Everyone involved—Harry Lucas, Jr. and Albert Lewis of EAF, Don Albers from MAA, Peter Renz, and Paul Halmos himself—eventually agreed. I resolved to turn the rest of the interview into a film.
There things stood until early 2008. Paul Halmos died in 2006, and it was perhaps the fact of his absence that awoke a keener awareness of his significance.
In early 2008 both EAF and MAA agreed to fund completion of the film. We were able to augment the edited initial interview with an ample supply of still photographs—many taken by Paul Halmos—selected by Don Albers. We also organized a day of shooting to re-shoot Peter Renz’s side of the 1999 interview with Halmos, and to supplement it by filming additional interviews with mathematicians who had known or worked closely with Halmos. All of these scenes were filmed in November 2008 at spectacular locations on the campus of Santa Clara University where Paul Halmos had taught until his retirement. A few clips from these interviews are inserted in the body of the 44-minute film.
The film follows a Q&A format, but is organized into sections with subject titles:
• Becoming a Mathematician
• The Moore method
• Great teachers
• Designing a course
• The state of education
• Getting results
The depth and power of his personality infuse each section with a special Paul Halmos flavor that makes watching him on video such a compelling experience. His elegant performance shows his consummate skill as a communicator. I Want To Be a Mathematician: A Conversation with Paul Halmos has a message about successful communication for anyone who has ever addressed an audience, taught a class, or written an essay or article.
— George Csicsery, February 2009
Five bonus features on the DVD include comments and reminiscences about Paul Hamos from interviews with mathematicians Robert Bekes, David Eisenbud, Jean Pedersen, Peter Renz, and Donald Sarason.
Who am I?
An entertaining story about Halmos told by Don Sarason.
Mathematician, teacher, communicator
Assessments of Halmos, his contributions, and his legacy.
Work, preparation, and spontaneity
Paul Halmos was meticulous and exacting. Some of these stories show just how rigorous he was, both as a presenter, and as a writer.
Paul Halmos at Santa Clara University
These are stories about Halmos as a colleague, and how he raised the stature of mathematics at Santa Clara University.
These comments depict Halmos as someone who tried to achieve clarity in teaching and communication, and demanded the same of everyone else. There are hints of his arcane wit, especially in the section about cats.
Halmos Automathography Selections
This selection of material from Paul Halmos’s book, I Want to Be a Mathematician: An Automathography, was made to accompany the film, I Want to Be a Mathematician: A Conversation with Paul Halmos. The Automathography was first published by Springer-Verlag, New York, in 1985. This text is from the paperback edition, copyright 1987, by The Mathematical Association of America (MAA). The selection and comments here are copyrighted 2009 by the MAA.
George Csicsery’s film I Want to Be a Mathematician: A Conversation with Paul Halmos gives you a sense of Halmos’s ideas and his presence. His Automathography fills out the picture, giving you a broader and deeper view of what Paul did and how he did it. These selections fill out areas covered in the film and provide background material. For the complete picture, go to Halmos’s Automathography itself.
Selection 1, book pages 3–19, Chapter 1, “Reading and Writing and ‘Rithmetic.” Background. Note the discussion of Bessel’s inequality on book page 4, which emphasizes conceptual understanding. PDF pages 4–20.
Selection 2, book pages 47 and 48, Chapter 3, “Graduate School,” section “Good morning, analysis.” Here Halmos describes the moment when he first understood the basic ideas of calculus, the moment when he “became a mathematician.” PDF pages 21–22.
Selection 3, book pages 74–78, Chapter 5, “Learning How to Think,” sections “Optimal skipping” and “Roller coaster.” “Optimal skipping” sets up Halmos’s thesis problem and “Roller coaster” describes the ups and downs of the solution of that problem. PDF pages 23–27.
Selection 4, book pages 108–118, Chapter 7, “Winning the War.” This selection includes sections “Teaching at Syracuse,” “Research at Syracuse...” and “Radiation Laboratory.” This last section describes Halmos’s brush with applied mathematics. His essay “Applied Mathematics Is Bad Mathematics” in Mathematics Tomorrow (edited by Lynn Arthur Steen, Springer-Verlag, New York and Heidelberg, 1981) also deals with his ideas about applied mathematics and is worth reading. PDF pages 28–38.
Aside. On book page 116, Halmos surprisingly suggests not solving problems of those seeking help. This may seem peculiar, but it is advice also found in Gian-Carlo Rota’s Indiscreet Thoughts (Birkhauser, Boston, 1979, page). Rota’s take on this is:
"When an engineer knocks at your door with a mathematical question, you should not try to get rid of him or her as quickly as possible. You are likely to make a mistake I myself made for many years: to believe that the engineer wants you to solve his or her problem. This is a kind of over simplification for which mathematicians are notorious. Believe me, the engineer does not want you to solve his or her problem. Once I did so by mistake (actually I had read the solution in the library two hours previously, quite by accident) and he got quite furious, as if I were taking away his livelihood. What an engineer wants is to be treated with respect and consideration, like the human being he is, and most of all to be listened to with rapt attention. If you do this, he will be likely to hit upon a clever idea as he explains the problem to you, and you will get some of the credit. Listening to engineers and other scientists is our duty. You may learn some interesting mathematics while doing so."
Selection 5, book pages 133–139, Chapter 8, “A Great University,” section “Teaching.” Halmos explains his approach to teaching. PDF pages 39–45.
Selection 6, book pages 253–279, Chapter 12, “How to Teach.” Halmos’s gives advice on teaching, especially on using the Moore Method. PDF pages 46–70.
Selection 7, book pages 3199–348, Chapter 14, “How to Do Almost Everything.” Broad advice on professional activities: research, friendships, recommendations, advising, and more. PDF pages 71–100.
Halmos Interviews and Articles
This material begins with a tribute to Paul taken from the Mathematical Association of America’s website, MAA Online, and continues with two interviews Donald Albers conducted with Paul Halmos. Then follow articles by Halmos on writing, speaking, and teaching. Edwin Moise and George Piranian join Halmos in contributing to the final article on teaching.
These materials give a sense of Paul Halmos and his approach. See also the selections from Halmos’s Automathography included on the DVD of the film I Want to be a Mathematician. The materials in this file are listed below. The PDF pages are given in bold type at the end of the item’s description.
Section 1, “Paul Halmos: A Life in Mathematics,” the tribute to Halmos from MAA Online, copyright 2009 by the MAA. PDF pages 3–5.
Section 2, “In Touch with God: An Interview with Paul Halmos,” Donald J. Albers, The College Mathematics Journal, January 2004, pages 2–14, copyright 2004 by the MAA. PDF pages 6–18.
Section 3, “Paul Halmos: Maverick Mathologist,” Donald J. Albers, The Two-Year College Mathematics Journal, September 1982, pages 226–242, copyright 1982 by the MAA. PDF pages 19–35.
Section 4, “How to Write Mathematics,” P. R. Halmos, l’Enseignement Mathematique, May-June 1970, pages 123–152, copyright 1970 by that journal and its sponsor. PDF pages 36–65.
Section 5, “How to Talk Mathematics,” P. R. Halmos, The Notices of the American Mathematical Society, April 1974, pages 155–158, copyright 1974 by the American Mathematical Society. PDF pages 66–69.
Section 6, “The Problem of Learning to Teach,” P. R. Halmos, E. E. Moise, and George Piranian, The American Mathematical Monthly, May 1975, pages 466–476, copyright 1875 by the MAA. PDF pages 77–87.
Section 7, “What Is Teaching?,” Paul R. Halmos, The American Mathematical Monthly, November 1994, pages 848–854, copyright 1994 by the MAA. PDF pages 70–76.
There are three articles here, joined under the title of the second article, which is by Edwin Moise. Halmos’s is the lead and is about teaching how to solve problems. These selections are used by permission from the copyright holders cited above and may not be reused without their permission, except as provided by sections 104 and 109 of the copyright law.
—Peter Renz, Brookline, Massachusetts, February 2009
Photos courtesy of
PAUL HALMOS PHOTO ARCHIVE