Photos by Paul Halmos

Science Friday mentions Who’s That Mathematician? Images from the Paul R. Halmos Photograph Collection. 

In late August, SciFri writer Annette Heist sent out a call for photographs of women in mathematics. The article, titled “Picture Another Mathematician”, featured two photos from the Halmos Collection of Olga Taussky-Todd (pictured) and Mary Ellen Rudin.

Heist wrote:

Laura McHugh of the Mathematical Association of America wrote to tell me about mathematician and photographer Paul Halmos. Throughout his career, Halmos snapped thousands of photos of his fellow mathematicians. After his death, Halmos’s wife donated the photos to the University of Texas’s Archives of American Mathematics. The photos are in the process of being digitized and made available online according to archivist Carol Mead, who sent the photos below.

Photo Caption: M Atiyah 29 Mar 69 

“The Atiyah-Singer index theorem was the toughest hurdle for me, but, somehow, we conquered it too. (To be sure, after it appeared in print, Singer told me that it didn’t come out quite right—the relation with the Riemann-Roch theorem was unclear or perhaps even misstated—but there it was, and I feel sure that my fellow ignoramuses and I learned something worth knowing that we hadn’t known before.)”–Paul R. Halmos, I Want to Be a Mathematician

Michael Francis Atiyah contributed to a wide range of topics in mathematics centering on the interaction between geometry and analysis. His work showed how the study of vector bundles on spaces could be regarded as the study of cohomology theory, called K-theory. He was awarded the Fields Medal in 1966.

The ideas which led to Atiyah being awarded a Fields Medal were later seen to be relevant to gauge theories of elementary particles.

The theories of superspace and supergravity and the string theory of fundamental particles, which involves the theory of Riemann surfaces in novel and unexpected ways, were all areas of theoretical physics which developed using the ideas which Atiyah was introducing. 

In addition to the Fields Medal, Atiyah received many honors during his career including the Feltrinelli Prize from the Accademia Nazionale dei Lincei in 1981, the King Faisal International Prize for Science in 1987, the Benjamin Franklin Medal, and the Nehru Medal. In 2004, he and Isadore Singer were awarded the Neils Abel prize of £480 000 for their work on the Atiyah-Singer Index Theorem.

Michael Francis Atiyah Biography

Photo Caption: Ed Begle

“Ed started out as a topologist, a student of Lefschetz’s at Princeton, but then became famous for two other reasons. He was, for one thing, Secretary of the AMS between 1951 and 1956, and, as one of the prime movers of the SMSG (School of Mathematics Study Group) he was also one of the prime movers of the “new math”. A lot of people liked the SMSG and worked hard for it, but, in the interests of historical honesty, I must report that some of the others referred to it as Some Mathematics, Some Garbage.” –Paul R. Halmos, I Have a Photographic Memory

Begle was awarded a thesis in 1940 for his thesis Locally Connected Spaces and Generalized Manifolds. In his thesis, Begle started with the concepts of a realization and a partial realization of finite complex on a space which had been by Lefschetz in a 1936 paper. He gave new definitions of these concepts which allowed him to use other techniques and simplify the study of generalized manifolds. He used Vietoris cycles throughout his thesis.

Edward Griffith Begle Biography

Photo Caption: Budapest 1931

“My family lived in a third floor apartment, in Budapest, that faced out on a busy street (now called Lenin Boulevard). It was an exciting street—colorful, crowded, noisy. There were many shops—a glamorous hardware store displaying shiny knives behind its huge plate glass front, several bookstores with books of many colors piled and strewn around, coffee houses with grouchily servile waiters carrying white napkins on their black left sleeves, and stores full of toys and candy and crutches and clothes and shoes and watches. The sidewalk was broad, and milling, crowds of people separated the shop windows from teh curb-side trees and scales (your weight for a penny) and newspaper kiosks and taxi stands. The crowds seemed always to be there—they were there when went to school early in the morning and they were there on the rare occasions when I was brought home late at night from an excursion or from a movie. Later, when I grew up, went to Hungary as an American tourist, and was out real late at night, the crowds were still there. The lights were bright and gypsy music could be heard from the coffee houses.” —Paul R. Halmos, I Want to Be a Mathematician…

Photo Caption: RL Wilder Lansing Aug 1960 

“Ray Wilder has been president of both the major mathematical organizations in the U.S.; he was a member of the National Academy, and the author of several books and many articles. When he was 80, fifteen years after he retired from the University of Michigan, he told me that his days of study were definitely not over (and neither was the feeling of pressure that makes one study): he was still reading mathematics, going to colloquia, and trying to keep up with what was going on.” —Paul R. Halmos, I Want to Be a Mathematician…

Wilder moved to the University of Texas in 1921 where again he was appointed as an instructor while he worked for his doctorate. It was here that his interests moved towards pure mathematics under the influence of Robert Moore. When he asked permission from Moore to take his topology course, Moore replied”-

No, there is no way a person interested in actuarial mathematics could do, let alone be really interested in, topology.

After Wilder persuaded Moore to let him take the course, Moore proceeded to ignore him until he solved one of the hardest problems Moore posed to the class. Wilder gave up his plans to study actuarial mathematics and became Moore’s research student. He suggested Wilder write up the solution to the problem for his doctorate which indeed he did, becoming Moore’s first Texas doctorate in 1923 with his dissertation Concerning Continuous Curves.

R.L. Wilder Biography

Photo Caption: McLaughlin, Ann Arbor, 1963 

“Jack is a hard-working and broadly informed algebraist, but the sort of algebra he writes papers about is not the sort I am fond of. Example: he discovered one of the notorious sporadic simple groups. I am a hard-working and quite knowledgeable operator-theorist, and the kind of operator theories that interest me leave Jack completely cold. It turned out, however, that there is a part of mathematics we both know and like. It is a small subject, not considered deep. It has, they say, no intrinsic importance; it is merely a useful tool and an occasional source of examples in other subjects. Both Jack and I tend to be shamefaced about admitting we like it; it is a little like admitting that you read westerns. The subject I am talking about is linear algebra.” —Paul R. Halmos, I Want to Be a Mathematician. 

Jack McLaughlin’s research ranged widely, encompassing several subfields of algebra—lattice theory, finite groups, and commutative algebra. He discovered one of the sporadic finite simple groups, that of order 898,128,000, which now bears his name. He also participated in the discovery of a module of finite projective dimension with a negative intersection multiplicity. His work on group cohomology, most of which passed on through the writings of his students, has had an important impact on the field. He was well respected by his colleagues in the field. Paul Halmos, his UM colleague, once said that there are a number of ways to tackle a mathematical problem, but when all else fails, ask McLaughlin.

“Jack McLaughlin (1923 – 2001)”, ContinuUM, The Newsletter of the Department of Mathematics at the University of Michigan (pdf)  

Photo Caption: Anneli Lax 

“Anneli is an outstanding mathematical editor (look at any volume of the New Mathematical Library).” —Paul R. Halmos, I Have a Photographic Memory

Anneli Lax Cahn’s greatest contribution to mathematical literature was triggered by a very different sort of event. The launch of the Soviet satellite Sputnik in 1957 was a shock to the American scientific community, a shock felt at every level. Much thought was devoted to the education of a new generation who would accelerate the pace of American scientific productivity. It was at this point that Lax realized the major contribution that could be made in mathematics education. Out of this endeavor grew the New Mathematical Library. The idea was to make accessible to interested high school students deep results in mathematics described by research mathematicians.

Anneli Lax Cahn