Photos by Paul Halmos

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Wed, 10 Apr 2013 11:51:12 -0400

Thanks for following our Tumblr! New Halmos photos are posted weekly to our online collection on the Mathematical Association of America’s Mathematical Sciences Digital Library. The collection is curated and managed by Janet Beery and Carol Mead.

We present here a weekly-increasing subset of the 342 photos by inveterate photographer Halmos, and we invite you to share what you know about them by using “Discuss this article” at the top or bottom of this page, or by contacting Janet Beery or Carol Mead directly. Please provide or correct names, dates, locations, and events (e.g. conference, invited speaker, social visit, etc.). Please also share any other pertinent information, warm memories, etc. connected to the photograph. And be sure to look for new photos at this site each week throughout the year!

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

Functional analyst Billy James Pettis (1913-1979) was...

Tue, 25 Dec 2012 17:30:11 -0500

Functional analyst Billy James Pettis (1913-1979) was photographed by Halmos in August of 1975 at the Joint Summer Mathematics Meetings in Kalamazoo, Michigan. Pettis earned his Ph.D. in 1937 from the University of Virginia with the dissertation “Integration in Vector Spaces,” written under advisor Edward J. McShane. In fact, Pettis was McShane’s first Ph.D. student. (McShane is pictured on page 34 of this collection.) Pettis was a faculty member at Tulane University in New Orleans, Louisiana, and, from 1957 onward, at the University of North Carolina, Chapel Hill. (Sources: Mathematics Genealogy Project; A Guide to the B. J. Pettis Papers, 1938-1980, Archives of American Mathematics)

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

Halmos photographed George Pólya (1887-1985) and Alexander...

Tue, 18 Dec 2012 17:30:19 -0500

Halmos photographed George Pólya (1887-1985) and Alexander Ostrowski (1893-1986) in 1958. Another photo of Ostrowski appears on page 38 of this collection, where you can read more about him.

Born in Budapest, Hungary, George (György) Pólya entered the University of Budapest (now Eötvös Loránd University) in 1905. After studying law, languages, literature, philosophy, and, finally, physics and mathematics, he received his Ph.D. in mathematics in 1912 with a thesis in geometric probability written under Leopold (Lipót) Fejér. He then spent a year studying at the University of Göttingen, Germany, with its who’s who of eminent mathematicians, and then another few months studying in Paris, before being invited byAdolf Hurwitz, then Chair of Mathematics at Eidgenössische Technische Hochschule (ETH) in Zürich, Switzerland, to join the faculty there, which he did in 1914. Pólya worked closely with Hurwitz until Hurwitz’s death in 1919.

Although he may be best known today for his contributions to mathematics teaching and learning, Pólya was a prolific and formidable researcher who made important contributions in complex analysis, probability, combinatorics, geometry, and mathematical physics. Besides writing many papers (O’Connor and Robertson of the MacTutor Archive pointed out that he published 31 papers just from 1926 to 1928), he also wrote influential books. In 1925, after years of work, Pólya and Gábor Szegő published Problems and Theorems in Analysis, Volumes I, II (Springer), and in 1924 Pólya began to work with G. H. Hardy and J. E. Littlewood (page 31 of this collection) on the book Inequalities (Cambridge, 1934). In 1940, Pólya moved to the United States and, after short stints at Brown University and Smith College, he joined the faculty at Stanford University in Palo Alto, California, where Szegő had been based since 1938. He and Szegő continued their collaboration, producing another influential book, Isoperimetric Inequalities in Mathematical Physics (Princeton, 1951).

In 1945, Pólya published what may be his best known book, and certainly is the one that established him as a leader in mathematics teaching and learning, How to Solve It: A New Aspect of Mathematical Method (Princeton), which has been translated into 17 languages. Other books on mathematical reasoning and surveys/textbooks include:

Mathematics and Plausible Reasoning: Volume I, Induction and Analogy in Mathematics; Volume II, Patterns of Plausible Inference (Princeton, 1954);
Mathematical Discovery: On understanding, learning, and teaching problem solving: Volume I (Wiley, 1962), Volume II (1965);
Complex Variables, with Gordon Latta (Wiley, 1974);
Mathematical Methods in Science, with Leon Bowden (MAA, 1977); and
Notes on Introductory Combinatorics, with Robert Tarjan and Donald Woods (Birkhäuser Boston, 1983).

Pólya advised at least 30 Ph.D. students at ETH and Stanford, plus one more at England’s Cambridge University, Imre Lakatos, who received his Ph.D. in 1961. Lakatos’ Ph.D. dissertation, titled “Essays in the Logic of Mathematical Discovery,” eventually became the book Proofs and Refutations: The Logic of Mathematical Discovery (Cambridge University Press, 1976). (Sources: MacTutor Archive, Mathematics Genealogy Project, MathSciNet, WorldCat)

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

Richard Rado (1906-1989), Robert Rankin (1915-2001), and Hans...

Tue, 11 Dec 2012 17:30:15 -0500

Richard Rado (1906-1989), Robert Rankin (1915-2001), and Hans Reimann, left to right, were photographed by Halmos in April of 1965 at the British Mathematical Colloquium in Dundee, Scotland. Halmos was one of three main speakers at this conference (I Want to Be a Mathematician, Springer, 1985, pp. 290-292). Another photograph of Rankin appears on page 7 of this collection, where you can read more about him.

Born in Berlin, Germany, Richard Rado earned doctoral degrees from the University of Berlin in 1933 and from Cambridge University in 1935. At the University of Berlin, he wrote the dissertation, “Studies on combinatorics,” under advisor Issai Schur and at Cambridge, he wrote the dissertation, “Linear Transformations on Bounded Sequences,” under advisor G. H. Hardy. Although he would write papers in both fields, his research throughout his career was primarily in combinatorics. In 1934, Rado met Paul Erdős, who had earned his Ph.D. in Budapest that year and accepted a fellowship at the University of Manchester in England, and the two began to collaborate. Erdős described the strengths each brought to their collaboration as follows:

I was good at discovering perhaps difficult and interesting special cases and Richard was good at generalising them and putting them in their proper perspective (quoted by O’Connor and Robertson in their MacTutor Archive biography of Rado).

After spending 1935-36 at Cambridge University, Rado was on the mathematics faculty at the University of Sheffield, England, from 1936 to 1947, then at King’s College, London, from 1947 to 1954, and finally at the University of Reading in England from 1954 onward. Much like another couple featured in this collection, Leonard and Reba Gillman (see page 17), Richard Rado and his wife, Luise Zadek Rado (d. 1990), were highly accomplished musicians, he as a pianist and she as a singer, and gave both public and private concerts. (Sources: MacTutor Archive, Mathematics Genealogy Project)

Hans-Martin Reimann earned his Ph.D. in 1969 at the Eidgenössische Technische Hochschule (ETH) in Zürich, Switzerland. If our identification is correct (based on the notation “Reimann (Swiss)” by Halmos), Reimann would have been a beginning graduate student at the time this photograph was taken. He has spent most of his career at the University of Bern, Switzerland, becoming Professor Emeritus in 2006, and lists his research interests as complex analysis, quasiconformal mappings, Lie groups, symplectic geometry, and wavelets. (Sources: Mathematics Genealogy Project, Universität Bern Mathematics)

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

Halmos photographed Martin Gardner (1914-2010) in New York City...

Tue, 04 Dec 2012 17:30:24 -0500

Halmos photographed Martin Gardner (1914-2010) in New York City on Oct. 26, 1974. The magazine Scientific American paid tribute to Gardner, the “Mathematical Gamester,” as follows: “For 25 years, he wrote Scientific American’s Mathematical Games column, educating and entertaining minds and launching the careers of generations of mathematicians.” The magazine also credits Gardner with “single-handedly populariz[ing] recreational mathematics in the U.S.” Gardner wrote his first article for Scientific American in 1956 and was immediately invited to write the magazine’s “Mathematics Games” column, which he did from 1957 to 1981. The 15 books containing all of his columns are among the over 100 books and pamphlets he published during his career. (Sources: Scientific American,MacTutor Archive)

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

James Tanton will present the MAA Carriage House and Gathering for Gardner event “Weird Ways to Work with Pi” on December 5, 2012, at the MAA Carriage House in Washington, D.C.

Martin Gardner thought deeply about the number pi, wrote about our attempts to come to terms with this troublesome number, and shared with the world a multitude of surprising puzzles whose solutions involve circles and use of the number pi. But who said the concept of “pi” applies only to circles? What is the value of pi for a square? What interesting non-circular problems can be solved with non-circular pi-values?

In this 2012 Celebration of Mind event at the MAA we shall explore some weird and wonderful ways to play with pi for shapes that might or might not be circles. This talk will be lively and accessible to all—students and teachers, mathematics professionals and mathematics enthusiasts alike—and chock-full of insight and gotchas! and ahas! Let’s continue to roam the exciting mathematical landscapes that Martin Gardner shared with the world and enjoy, in his honor, the jewels still to be found in them.

Halmos photographed Natalie Davis and Alfréd Rényi (1921-1970)...

Tue, 27 Nov 2012 17:30:20 -0500

Halmos photographed Natalie Davis and Alfréd Rényi (1921-1970) in August of 1961.

Natalie Zemon Davis, wife of mathematician Chandler Davis, is a noted social and cultural historian, primarily of early modern France. Her best known book is The Return of Martin Guerre (1983), also the title of a popular film released at the same time. Natalie and Chandler Davis were victims of the “Red scare” in the United States during the 1950s, with Chandler Davis losing his job at the University of Michigan in 1954 and even being imprisoned for six months. They moved to Toronto, Canada, in the early 1960s, at about the time this photograph was taken. Chandler Davis is now Professor Emeritus of Mathematics at the University of Toronto (Wikipedia, University of Michigan History, University of Toronto Mathematics)

Born in Budapest, Hungary, Alfréd Rényi earned his doctoral degree in 1945 from the University of Szeged, Hungary, under advisor Frigyes (Frédéric) Riesz. According to O’Connor and Robertson of the MacTutor Archive, this was after graduating from the University of Budapest, where he studied from 1940 to 1944 under Lipót Fejér and Paul Turán, escaping from a forced-labor camp, hiding out to avoid capture, and rescuing his parents from the Budapest ghetto by impersonating a soldier. After a postdoctoral year in Russia (1946-47) during which he obtained important results on the Goldbach Conjecture, Rényi continued to obtain results in number theory, probability, and analysis as a professor at the University of Budapest and a member of the Hungarian Academy of Sciences and director of its Institute for Applied Mathematics before dying suddenly at age 48. Rényi’s wife was the mathematician Katalin (Kató) Rényi, and possibly she and/or Chandler Davis were among the assembled party as well. We will search for photographic evidence! (Source: MacTutor Archive)

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

Sisters Julia Robinson (1919-1985), left, and Constance...

Tue, 20 Nov 2012 17:30:31 -0500

Sisters Julia Robinson (1919-1985), left, and Constance Reid (1918-2010) were photographed by Halmos in July of 1984 in Eugene, Oregon. Constance Reid was the well-known author of popular books about mathematics, most notably From Zero to Infinity: What Makes Numbers Interesting (MAA, 1961), and of biographies of mathematicians, including E. T. Bell (or John Taine), Richard Courant (photographed on page 10 of this collection), David Hilbert, Jerzy Neyman (photographed on page 38 of this collection), andJulia Robinson. Another photograph of Julia Robinson appears on page 30 of the collection, where you can read more about her. (Sources: MacTutor Archive, MAA obituary: Constance Reid).

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

Science Friday mentions Who’s That Mathematician? Images...

Tue, 13 Nov 2012 17:30:21 -0500

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.

The photo shows Lloyd Lininger (left) and Sir Michael...

Tue, 06 Nov 2012 17:30:18 -0500

The photo shows Lloyd Lininger (left) and Sir Michael Atiyah (right) in Ann Arbor, Michigan on April 3, 1968. Halmos was a faculty member at the University of Michigan from 1961 through 1968. Atiyah had won the Fields Medal in 1966 and published his book K-theory, which included discussion of the Atiyah-Singer Index Theorem, in 1967 (MacTutor History of Mathematics Archive). He was knighted in 1983. According to the Mathematics Genealogy Project, Lininger had earned his Ph.D. in 1964 at the University of Iowa with the dissertation “Some Results on Crumpled Cubes” under Steve Armentrout, whose photograph appears on page 1 of this collection. Ken Millett (University of California, Santa Barbara) suggests that the young man in the background facing the camera may be topologist William Thurston, who would have been in his first year of graduate school at the University of California, Berkeley. Bill Thurston would win the Fields Medal in 1982.

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

Halmos photographed Phillip Jones, Bartel van der Waerden, and...

Tue, 30 Oct 2012 17:00:12 -0400

Halmos photographed Phillip Jones, Bartel van der Waerden, and Theophil Hildebrandt on April 2, 1968, in Ann Arbor, Michigan. That spring, Halmos was still a faculty member at the University of Michigan in Ann Arbor, but he would move to the University of Hawaii in Honolulu for the 1968-69 academic year and then to Indiana University in Bloomington in the fall of 1969.

Phillip S. Jones (1912-2002) earned his Ph.D. in 1948 from the University of Michigan, where he had earned bachelors and masters degrees in mathematics ten years earlier, with a dissertation on the history of geometry and linear perspective written under the mathematics historian Louis Karpinski. He became a faculty member at Michigan in 1947 and remained there for the rest of his career, specializing in mathematics history and education. He was a national leader in both of his specialties and was perhaps best-known for combining the two: using mathematics history as a mathematics teaching tool and writing the history of mathematics education in the U.S. (Source:Phillip S. Jones (1912-2002) (pdf file), History and Pedagogy Newsletter 64, March 2007, 1-4)

Bartel van der Waerden (1903-1996) earned his Ph.D. in 1926 from the University of Amsterdam with the dissertation, “The algebraic foundations of the geometry of numbers,” after studying also at the University of Göttingen, Germany, with Emmy Noether (algebra) and Hellmuth Kneser(topology). After studying for a semester with Emil Artin at the University of Hamburg, van der Waerden began writing his most famous book, Moderne Algebra, basing Volume I (1930) on work of Noether and Artin and Volume II (1931) on his own work in algebra. He was professor of mathematics at the University of Leipzig from 1931 through the end of World War II in 1945 and at the University of Zürich, Switzerland, from 1951 onward. Although he was interested in mathematics history throughout his career, he published most of his work in this field later in his career. (Source: MacTutor Archive)

Theophil H. Hildebrandt (1888-1980) earned his Ph.D. in 1910 from the University of Chicago under advisor E. H. Moore. He joined the mathematics faculty at the University of Michigan in 1909 and spent his career there, specializing in functional analysis and integration theory. Hildebrandt is best known for giving the first general proof of the principle of uniform boundedness for Banach spaces and for serving as president of the American Mathematical Society during 1945-1946. (Source: Mathematics Genealogy Project, MacTutor Archive: Moore, AMS Presidents)

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

This is a photograph of Gerald (Jerry) Alexanderson,...

Tue, 23 Oct 2012 17:04:44 -0400

This is a photograph of Gerald (Jerry) Alexanderson, Halmos’ colleague at Santa Clara University in California. Halmos joined the mathematics faculty at Santa Clara in 1985, at the invitation of Alexanderson, who had taught there since 1958. Alexanderson was largely responsible for the donation of Halmos’ papers and photographs to the Archives of American Mathematics and, in particular, for the monumental task of organizing Halmos’ photograph collection for the Archives.

Alexanderson (left) is pictured with Vladimir Drobot at Santa Clara University, where both were faculty members, in March of 1984, the year before Halmos joined them as a faculty member there. At the time this photo was taken, Alexanderson was First Vice President of the MAA. He would become MAA President in 1997. Vlad Drobot taught at SCU for 17 years and then, in 1990, moved across town to San Jose State University, where he taught for 16 years.

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

Photo Caption: Lancaster 1984 - Sheldon Axler and Halmos “[This...

Wed, 08 Jun 2011 17:18:00 -0400

Photo Caption: Lancaster 1984 - Sheldon Axler and Halmos

“[This photo*] was taken at a conference in Lancaster (England) in 1984, and it represents four mathematical generations. I am at right, next to me is Don (D.E. Sarason), my student, next to him is Sheldon, his Ph.D. student, and next to Sheldon is Pam (Axler), who is, of course, Sheldon’s Ph.D. student.” –Paul R. Halmos, I Have a Photographic Memory

*This photo is a slightly different angle than the photo featured in I Have a Photographic Memory

Photo Caption: Sheldon Axler August 75

Sheldon Axler is Dean of the College of Science & Engineering at San Francisco State University. In 1996, he received the Lester R. Ford Award for expository writing from the Mathematical Association of America for his article “Down with Determinants!” He also served as an Associate Editor of The American Mathematical Monthly.

Sheldon Axler Homepage

Sheldon Axler Biography by MSRI

Photo Caption: M Atiyah 29 Mar 69 “The Atiyah-Singer index ...

Thu, 02 Jun 2011 17:30:06 -0400

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: Amir Moez, 1967 “Ali has been a linear...

Fri, 27 May 2011 17:30:06 -0400

Photo Caption: Amir Moez, 1967

“Ali has been a linear algebra enthusiast for much of his professional life.” — Paul R. Halmos, I Have a Photographic Memory

Ali Reza Amir-Moez earned his BA at the University of Teheran in 1942, and served as a Math Instructor at Teheran Technical College from 1942 - 46.

He immigrated to the United States in 1947. His first love was drama and the performing arts, however, he was forced to study math to receive an extension on his visa, and thus he continued his education earning his MA in 1951, and PhD in 1955, both from UCLA. He served as a Professor of Math at the University of Idaho; Queens College, New York City; Purdue University; University of Florida, Gainesville; Clarkson College, Potsdam, New York; and Texas Tech University, Lubbock.

Amir-Moez was dedicated to mathematics research and established scholarships at both Texas Tech University and the University of California at Los Angeles. In 1975, he was awarded the medal of Pro Mundi Beneficio, Academia Brasileira De Ciencias Humanas.

He was the author of books including, Elements of Linear Space; Extreme Properties of Linear Transformations and Geometry in a Unitary Space; Classes Residues et Figure ance Ficelli; and plays including Kaleeleh and Demneh and Three Persian Tales. His writings included over 150 papers, articles, and books, and he was often featured in Highlights for Children. a

Ali Reza Amir-Moez Obituary (Texas Tech University, August 25, 2007)

Dr. Ali Reza Amir-Moez (Lubbock Online, August 27, 2007)

Photo Caption: Ed Begle “Ed started out as a topologist, a...

Tue, 17 May 2011 18:03:00 -0400

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...

Tue, 19 Apr 2011 10:00:06 -0400

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...

Tue, 12 Apr 2011 10:00:06 -0400

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: Emma and Dick Lehmer, May 1986 “Emma...

Wed, 23 Mar 2011 15:00:06 -0400

Photo Caption: Emma and Dick Lehmer, May 1986

“Emma Lehmer: A collaborator of Dick Lehmer’s in more senses than one, she is also a known and respected mathematical translator; we must be grateful to her, in particular, for translating Pontrjagin’s Topological groups.” —Paul R. Halmos, I Have a Photographic Memory

Emma Lehmer wrote around 60 papers on different aspects of number theory, about 20 of these being joint publications with her husband, Derrick Henry Lehmer. Their initial collaboration began as a three-way one with Lehmer working with both her husband and her father-in-law, Derrick Norman Lehmer. Her collaborations were both over deep mathematical results, as well as developing computers and computational methods to assist in solving number theory problems.

Emma Lehmer biography

Photo Caption: WVD Hodge and ML Cartwright (1950) “Bill Hodge...

Thu, 17 Mar 2011 10:00:00 -0400

Photo Caption: WVD Hodge and ML Cartwright (1950)

“Bill Hodge (later Sir William) did algebraic geometry; there is something called a Hodge variety. His book with Pedoe was a large and difficult step forward when it came out.” — Paul R. Halmos, I Have a Photographic Memory

William Vallance Douglas Hodge was a Scottish mathematician, specifically a geometer.

“Hodge returned to Cambridge in 1932. He was appointed as a university lecturer in the following year and, in 1935, was elected to a fellowship at Pembroke College, Cambridge. During this period he developed the relationship between geometry, analysis and topology and produced some of his best remembered work on the theory of harmonic integrals. For these contributions Hodge won the Adams Prize in 1937 and Weyl described this contribution as ‘… one of the great landmarks in the history of science in the present century.’

Hodge published a polished account of his important theory in 1941. This work marked an important change in direction for the Cambridge school of geometry which, under Baker’s leadership, had become somewhat isolated from other areas of mathematics.” Read More

William Vallance Douglas Hodge Biography

William Valance Douglas Hodge Obituary by M.F. Atiyah

Related entry: Dame Mary Cartwright

Photo Caption: Doob, Aug 1, 1974 “Ambrose and I were ...

Tue, 15 Mar 2011 10:00:00 -0400

Photo Caption: Doob, Aug 1, 1974

“Ambrose and I were blasé graduate students; we knew everything about the department, we knew everyone, and we could be trusted to deal with anything that was likely to come up that was likely to come up one early September afternoon—the department secretary left us in charge to watch over the main office. This boy came in, looking like a new graduate student, crew cut, shirt sleeves, and all. He was 25 years old at the time, I later learned, but he looked 19 or 20. What do you want?, we asked. Is Coble here?, he wanted to know; my name is Doob, D,O,O,B. Ambrose and I had heard of the bright young hot shot who was coming to Illinois from a fellowship at Columbia; we yanked our feet off the desk and told him who we were.” —Paul R. Halmos, I Want to Be a Mathematician

Joseph Leo Doob’s work was in probability and measure theory, in particular he studied the relations between probability and potential theory. Building on the work by Paul Lévy, Doob developed basic martingale theory and many of its applications during the 1940s and 1950s. His work has become one of the most powerful tools available to study stochastic processes. In the introduction to his Stochastic Processes (1953),Doob states that:

“… [a stochastic process is] any process running along in time and controlled by probabilistic laws … [more precisely] any family of random variables {xt| t ∈ T [where] a random variable is … simply a measurable function.”

Joseph Leo Doob