# Edwin Ford Beckenbach

### Born: 18 July 1906 in Dallas, Texas, USA

Died: 5 September 1982 in Los Angeles, California, USA

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**Edwin Beckenbach**was known as Ed. His parents were Charlie Geiger Beckenbach and Lucy Emma Richardson. He entered The Rice Institute (now Rice University) in Houston as an undergraduate and was awarded his B.A. in 1928, continuing his studies there and obtaining his M.A. in the following year. His research at Rice was supervised by Lester Ford, and Beckenbach was awarded his doctorate in 1931 for his dissertation

*Minimal Surfaces in Euclidean N-Space*.

After being awarded his doctorate Beckenbach was awarded a National Research Council Fellow for the two years 1931-33 which enabled him to study at Princeton, Ohio State University and the University of Chicago. He married Madelene Shelby Simons on 30 August 1933. They had three children, Edwin Simons Beckenbach, Madelene Lenann Beckenbach (later Lenann Nye), and Sonya Suzann Beckenbach (later Suzann Morse). Beckenbach returned to Rice in the autumn of 1933 where he was appointed as an instructor in mathematics. In 1940 he was appointed as an Assistant Professor of Mathematics at the University of Michigan, then two years later as an Associate Professor of Mathematics at the University of Texas at Austin. In 1945 he moved to the University of California at Los Angeles as a Professor of Mathematics and held this post until he retired in 1974.

John W Green, Ernst Straus, and Kirby Baker, colleagues of Beckenbach who wrote an obituary of him, described his major contributions to the University of California at Los Angeles:-

In June 1960 Beckenbach and Madelene were divorced and he married Alice Curtiss Tucker on 24 June 1960. His colleagues write:-At UCLA, he was a leader in developing the graduate program, from the moment of his arrival. The first Ph.D. in Mathematics at UCLA was awarded in1947to a student of his(jointly with W T Puckett). He also was Acting Chairman of the Mathematics Department for a year. In addition, he made two very important special contributions. First, he almost single-handedly brought to bear the influence that caused the creation in1948of the Institute for Numerical Analysis on the UCLA campus. This was a branch of the National Bureau of Standards devoted to computing and the construction and use of computing machines. Its SWAC computing machine, built at UCLA, was for a number of years one of the half dozen most powerful computers in the world. The group of mathematicians who gathered in connection with it made UCLA well known world-wide and influenced the development of mathematics here ever after. Second, he was(together with František Wolf, of Berkeley)a main influence in the establishment in1951of the Pacific Journal of Mathematics, a major international mathematical research journal sponsored by a dozen or more West Coast universities. Its headquarters and Managing Editors, of whom Ed was the first, have always been at UCLA - something that has contributed strongly to mathematics at UCLA and to the visibility of its mathematical group.

Among Beckenbach's first publications areWe will long remember the hospitality they extended so often and graciously to local and visiting scientists and their other friends. Not the least of these events were the famous "Mother-ins." These were receptions, held on or near Mothers Day, to which all UCLA mathematicians and their families were invited to hike, swim, and have a good time.

*The area and boundary of minimal surfaces*(1932), and two papers written jointly with Tibor Radó and published in the

*Transactions of the American Mathematical Society*in 1933, namely

*Subharmonic functions and minimal surfaces*and

*Subharmonic functions and surfaces of negative curvature*. He wrote a series of books and acted as editor for several more texts. For example he edited

*Modern mathematics for the engineer*(1956) which was in three parts, namely mathematical models, probabilistic problems, and computational considerations. Each part consisted of a number of chapters, each having been given as a lecture in an extension course at the University of California, Los Angeles, and also at the Corona Laboratories of the National Bureau of Standards. In 1961 he edited a second series of

*Modern mathematics for the engineer*which was divided into three parts as was the earlier volume. The lectures on which the chapters were based had been given at the University of California during session 1958-59.

He also wrote texts for the Monograph Project of the School Mathematics Study Group which were aimed at able high school students. One such text, written jointly with Richard Bellman, was

*An introduction to inequalities*(1961). The book begins with a study of axiomatics, then examines several classical inequalities of analysis such as the relationship between the arithmetic mean and geometric mean, the Cauchy, Hölder, and Minkowski inequalities, and the triangle inequality. Applications to geometric maximum and minimum problems are given, and the final chapter studies some special distance functions. C Brumfiel, reviewing the text, writes:-

The topic of inequalities was of interest to Beckenbach for many years. As well as the above text, and a secondThis is not a light, popular treatment of the subject. Students with a superficial interest in mathematics will soon lose interest as they are confronted with details of proofs. But the excellent student who works through the book carefully will acquire valuable skills and understandings.

*Inequalities*also written with Richard Bellman and published in 1971, he helped organise three international conferences on the topic at Oberwolfach in Germany in 1976, 1978 and 1981. He was an editor of the Proceedings of these three conferences which were published in 1978, 1980 and 1982 respectively.

Beckenbach contributed to mathematics with a series of texts for schools and colleges. We have mentioned one such text above, but let us give an incomplete list:

*College Algebra*(1964),

*Modern Introduction to Analysis*(1964),

*Applied Combinatorial Analysis*(1964),

*Essential of College Algebra*(1965),

*Integrated College Algebra and Trigonometry*(1966),

*Modern School Mathematics*(1967),

*Algebra*(1968),

*Pre-algebra*(1970),

*Modern College Algebra and Trigonometry*(1969),

*Analysis of Elementary functions*(1970),

*Intermediate Algebra for College Students*(1971),

*Modern Analytic Geometry*(1972),

*Concepts of Communications: Interpersonal, Intrapersonal and Mathematical*(1972), and

*College Mathematics for Students of Business and the Social Sciences*(1987).

Another major contribution made by Beckenbach was through his work for the American Mathematical Society. He served as a member of the Council and as Chairman of the Committee for printing and publishing from 1956 to 1961 and Chairman of the Committee to study the financial problems of Mathematical Reviews from 1963 to 1964. He also did extensive committee and editorial work for the Mathematical Association of America being Chairman of their publications committee from 1971 to 1982. He was elected a fellow of the American Academy of Arts and Sciences, the Indian Mathematical Society, the French Mathematical Society, and the Mathematical Circle of Palermo. The Mathematical Association of America decided to give him their Award for Distinguished Service for outstanding service to mathematics, apart from research, and shortly before his death he received word of this decision. The award was presented posthumously at the meeting of the Association in January 1983.

As to his interests outside mathematics:-

Any report on Ed Beckenbach would be hopelessly incomplete without mentioning his(and Alice's)love of tennis. In fact his interest in tennis may have extended over a longer period than his interest in inequalities. He played intercollegiate tennis at Rice, was Captain of the team and later was Coach. He played a game of tennis the morning of the day he suffered his fatal stroke.

**Article by:** *J J O'Connor* and *E F Robertson*

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