Obituary: Philip J. Davis

We first met Phil on the famous fifth day of the International    Congress on Mathematical Education in Budapest during the     summer of 1988. Phil, jet-lagged, had slept in and was late for     his opening lecture on “Applied Mathematics as Social    Contract.” A huge audience waited respectfully. Then Phil    appeared, his wild hair upraised, apologizing — with his    special unforgettable blend of highly knowledgeable    mathematician, wise old man, and brilliant youthful performer!    From that day on our personal friendship grew, as did our     admiration for his and Hadassah’s human warmth and insight.    We were lucky to enjoy Phil’s inspiring friendship for many    years. — Sussi and Bernhelm Booss-Bavnbek, Copenhagen,    Denmark    I heard many of Phil’s stories in the best possible way — told    by Phil himself over coffee or dinner, at conferences, and most    recently in his office at Brown. What a storyteller he was!    Anyone who dips into any of his books will immediately agree.    I’m a longstanding fan of Phil’s writing. He drew on his    extensive knowledge and interest in math but  also philosophy,    literature, art, and so much more. The arrival of those essays lit    up my days as the editor of SIAM News, and many readers    wrote in to say that his articles were the first thing they turned    to upon receiving a new issue. I wish I could have had more     conversations with him. — Gail Corbett, former managing    editor of SIAM News    My first encounter with Phil was in a numerical analysis class    he taught when I was a graduate student at Brown. He was a    wonderful teacher. What set Phil apart from other applied    mathematicians was his interest in and ability to communicate    mathematics to a wide audience. I witnessed this when I    attended his annual “holiday lecture” at Brown. Towards the    end of the first term, Phil would give an afternoon talk that    was partly a public lecture. These talks covered a wide variety    of topics, showing his interest not only in mathematics and    history but also cultural and philosophical subjects related to    our discipline, such as philosophy, history of science, and    pedagogy. This interest was evident in the many articles that    Phil later wrote for SIAM News. We at SIAM will miss those    great contributions, but will cherish those he left behind.     — Jim Crowley, executive director of SIAM    I was one of Phil’s early Ph.D. students at Brown. Phil was a    special guy, easygoing and friendly. I liked his sense of humor.    I once asked him if he did any physical exercise, and he said    that whenever he had an urge to exercise, he would lie down    until the urge went away. I do not know of anyone who was    a better expositor of mathematics than Phil. May he rest in    peace. — Frank Deutsch, Penn State University    I met Phil when I was 35 and he was 72. I’d seen a flyer    advertising his seminar on “common sense and mathematics,”    which I thought might speak to my then-job. I was out of my    league in that seminar, but Phil took an interest in me and my    work and we became fast friends. I’ve never understood why    Phil—world-renowned and surrounded by mathematical    cognoscenti—had any use for me, a mathematical nobody.    But he became my biggest supporter as I moved into    academia and left for California three years later. I visited him    every year when I traveled back east — visits that always    ended with his crushing, grandfatherly bear hug. Phil made me    feel as if I were among a handful of the most special people in    his life. The amazing thing is that he probably made a hundred    other people feel this same way. — Julie Gainsburg, California    State University, Northridge     Phil was essential to my career in the philosophy of math.    Collaboration with both him and Hadassah produced our    1981 prizewinner, The Mathematical Experience. — Reuben    Hersh, University of New Mexico    What I loved about Phil were all the conversations engendered    by our shared love of math history and math philosophy. I    argued endlessly with him about Platonism, which I embraced    and he totally rejected. It was great fun to reconcile our    divergent views on Henri Poincaré in our joint Notices of the    American Mathematical Society paper—“Henri’s Crystal Ball”    —and in “What Should a Mathematical Professional Know    About Mathematics?” I miss his wide-ranging curiosity and    insights so much. — David Mumford, Brown University    When Phil became my advisor in 1976, he stated the following    “rules of conduct”: I was responsible for choosing the topic of    my thesis, writing it, and defending it, and could expect no    help from him. On the other hand, I could discuss with him    any topic at any time. That felt like a level of freedom given to    very few graduate students at the time. Often after such a talk,    Phil would come up with a stack of copied material related to    our discussion; it did not feel like contradiction of his last rule.    I kept in touch with Phil up until the last two weeks before his    departure. I miss him very much. — Igor Najfeld, University    of Vermont    In 1975, Phil invited me to join him at a computer calculus    short course he was teaching for college-level mathematics    teachers, in which we delved into various aspects of “meta”    mathematics. This workshop was also unforgettable because    many of us watched the seventh game of the epic 1975 World    Series between the Red Sox and the Cincinnati Reds. I associate    that best of games with Phil. I also thoroughly enjoyed his wit    and clever turns of phrase; two of my favorites were his    disparaging “the holy trinity of definition, theorem, and proof”    that neither of us believed was all there was to mathematics,    and his “infinitesimals are the ghosts of departed quantities.”    How fitting that Phil should pass away on 3.14, the    ultimate approximation. — Edwina L. Rissland, University    of Massachusetts Amherst    As a senior at Harvard in 1977, I was writing my    undergraduate thesis with Garrett Birkhoff when a surprising    effect turned up on the computer. Birkhoff suggested I drive    down to Brown and talk to Phil Davis. I did that, and had a    wonderful encounter. Phil pulled a journal off his shelf,    pointed out a relevant article, and told me to read it. It was    in German. “You should learn German!” he advised. An    encounter like that means a lot to a 21-year-old. Phil has been    an inspiration for me as both the author of my favorite    approximation theory book and a founding father of Fourier    and Chebyshev technologies in numerical computation.    — Nick Trefethen, University of Oxford

With deep sorrow, we announce the passing of Philip J. Davis on March 14, 2018, at the age of 95. Phil was one of the founding fathers of SIAM and a prolific contributor to SIAM News; he was an innovative mathematician, an inspiring teacher, an entertaining and wide-ranging author, and a profound thinker on the nature and significance of mathematics.

Phil was born in Lawrence, Mass., on January 2, 1923. He majored in mathematics at Harvard College and graduated in 1943. In 1940, he met Hadassah Finkelstein—a student at Radcliffe College—at an anti-Lindbergh rally in Boston. They were married on their joint 21st birthday: January 2, 1944. For the remainder of World War II, Phil worked for the National Advisory Committee for Aeronautics in Langley Field, Va., performing mathematical calculations on dangerous instabilities in flight. He returned to Harvard after the war and earned his Ph.D. in 1950 under the supervision of Ralph Boas, Jr. He then remained at Harvard for several more years, conducting postdoctoral research with Stefan Bergman and Joseph Walsh.

From 1954 to 1963, Phil worked in the Numerical Analysis division at the National Bureau of Standards (now the National Institute of Standards and Technology). Along with colleague Phil Rabinowitz, he carried out numerical computations on the SEAC, a first-generation electronic computer; they were awarded the mock title “Heroes of the SEAC” for writing a program for Gaussian integration that ran correctly on the first trial. Phil played a prominent role in writing and planning the Handbook of Mathematical Functions, also known as “the big red book,” and authored the chapter on the Gamma function.

In 1963, Phil moved to Brown University as a faculty member in the Division of Applied Mathematics, and remained there for the rest of his life. He was a popular and entertaining lecturer, enlivening his classes with striking physical demonstrations, a sharp sense of humor, and a gift for storytelling. Together with colleague Charlie Strauss, he created one of the first courses on computer graphics. After his retirement, Phil continued to deliver an annual lecture on mathematical topics every Thanksgiving. His magnetic charm and conversational brilliance, combined with Hadassah’s hospitality and warmth, brought them many close friends among faculty and students at Brown.

In 2004, Phil took part in the SIAM project to collect oral histories of applied mathematics. He interviewed colleagues such as Walter Gautschi, Paul Garabedian, and Eugene Isaacson. Phil was also a prolific author; his bibliography includes 22 books, 52 technical papers, 92 essays, and 185 book reviews, most of which were published in SIAM News. He received the Chauvenet Prize in 1963 for a paper on the history of the Gamma function and the Paul R. Halmos-Lester R. Ford Award in 1982 for his paper about mathematical coincidences.

In his early years, Phil’s books were focused mostly on technical mathematics. Selected titles include the following: Interpolation and Approximation (1963); The Mathematics of Matrices: A First Book on Matrix Theory and Linear Algebra (1965) (he always preferred the phrase “matrix theory” to “linear algebra”); The Schwarz Function and its Applications (1974); Methods of Numerical Integration, coauthored with Phil Rabinowitz (1975); Circulant Matrices (1979); and Spirals: From Theodorus to Chaos (1993).

Later in life, Phil’s attention turned to the philosophy of mathematics in a broad sense. Among his most important works were two books with Reuben Hersh: The Mathematical Experience (1981), which won a National Book Award in Science, and Descartes’ Dream: The World According to Mathematics (1986). These two beautifully-written books expound an expansive view of mathematics, grounded in real-world applications but transcending far beyond them. Interwoven with the lives, experiences, and social interactions of mathematics practitioners, they are bright threads in the fabric of intellectual history, connecting us with thinkers of all ages.

Phil’s most influential essays—“Fidelity in Mathematical Discourse: Is One and One Really Two?” (1972) and “Visual Geometry, Computer Graphics, and Theorems of the Perceived Type” (1974)—similarly argue that mathematical knowledge and evidence are not limited to formal definitions and rigorous proofs, but rather can involve other forms of reasoning and apprehension. His later books in this genre—Mathematical Encounters of the Second Kind (1997), The Education of a Mathematician (2000), Mathematics and Common Sense: A Case of Creative Tension (2006), and Unity and Disunity and Other Mathematical Essays (2015)—combine philosophy, history, biography, and personal reminiscences.

And then there were books that were just for fun. The Thread: A Mathematical Yarn (1983) is an entertaining account of his search for the origin of Pafnuty Tschebyscheff’s unusual first name. Thomas Gray: Philosopher Cat (1988) and Thomas Gray in Copenhagen: In Which the Philosopher Cat Meets the Ghost of Hans Christian Andersen (1995) are academic fantasies about a cat. Ancient Loons: Stories Pingree Told Me (2011), a memorial volume for Phil’s friend David Pingree, is a collection of anecdotes about oddball intellectuals through the ages.

Phil was fond of the concrete details of history, biography, and mathematics. He disliked extreme abstraction and distrusted large, universal, intellectual schemes that claim to explain everything. He loved stories—long or short, pointed or meandering—and was a splendid raconteur. “Life,” Phil often said, “is one story after another.” We will miss his stories and his wisdom.