Agnes Scott College

Dorothy Maharam Stone

Dorothy Maharam Stone
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July 1, 1917 - September 27, 2014


The following biographical note by Professor John C. Oxtoby is reprinted with permission of the American Mathematical Society. It appeared in Measure and Measurable Dynamics: Proceedings of a Conference in Honor of Dorothy Maharam Stone, R. Daniel Mauldin, R.M. Schortt, and Cesar E. Silva, Editors, Contemporary Mathematics, Vol. 94, American Mathematical Society, 1989.
Dorothy Maharam Stone was born in Parkersburg, West Virginia, in 1917. After attending the Pittsburgh Public Schools she entered the Carnegie Institute of Technology. Her unusual talent soon became apparent, and when she received her B.S. degree in 1937, Professor L. L. Dines suggested that she pursue graduate work at Bryn Mawr College. Its small graduate department was at that time chaired by Anna Pell Wheeler, the leading American woman mathematician of her day. Dorothy came to Bryn Mawr too late to encounter Emmy Noether, who had died two years earlier, but she studied with Professor G. A. Hedlund, with J. R. Kline at the University of Pennsylvania, and with Mrs. Wheeler, who took a special interest in her from the start. During her third year, she wrote her dissertation, "On measure in abstract sets." Mrs. Wheeler was formally her thesis advisor, but the ideas were all Dorothy's own. I came on the scene in 1939, but interaction with me was confined to its final stages. However, she was a member of my first graduate class. Needless to say, I had reason to boast about the quality of graduate students at Bryn Mawr! After she was admitted to the "ancient and honorable company of scholars" in 1940, it was Mrs. Wheeler's earnest desire that she should have a post-doctoral year in the Institute for Advanced Study. Fellowship support was at that time not easy to come by, but Byrn Mawr had a very small fund that had been collected as a memorial to Emmy Noether and which was intended to encourage women in mathematics. On the Department's recommendation, Dorothy was designated the first Emmy Noether Fellow in Mathematics. Whether or not the small stipend "enabled" her to go to Princeton, at least she did go, and that move turned to be even more serendipitous than the move from Pittsburgh to Bryn Mawr had been. There she encountered Shizuo Kakutani, whose influence can already be detected in the P.N.A.S. note which first brought her world recognition. And, of course, it was there that she met Arthur Stone. He had come from Cambridge, England, the year before, and was to receive his Ph.D. from Princeton in 1941 and to spend the following year as a member of the Institute for Advanced Study. He and Dorothy were married in April of 1942. They spent the next two years at Purdue University. And after a year in Washington, D.C., went to Cambridge, England, where for two years Arthur was a Fellow of Trinity College. In 1948 they moved to Manchester and remained there until 1961, except for 1950-51, during which Dorothy was a visiting Lecturer at Wellesley College. From 1952 on, they both taught at the University of Manchester. In 1961 they returned to U.S. as professors at the University of Rochester, and except for various leaves of absence, remained there [until their "first" retirement]. They spent the year 1965-66 at Yale, while Dorothy was a Senior Post-doctoral Fellow of the National Academy of Sciences, the year 1971-72 at Berkeley, and a semester of 1978 at the Australian National University, Canberra. Dorothy has served national organizations in a variety of posts: Member at large of the National Research Council, Council of the A.M.S., Committee on the Undergraduate Program of the M.A.A., A.A.A.S. (Chairman, Section A), and has served on the organizing committees of numerous mathematical conferences at Oberwolfach and elsewhere. Through her research and other activities, Dorothy has earned a world-wide reputation as a truly outstanding mathematician. Moreover, she and Arthur have over the years created a unique relationship. There have been other notable husband-wife teams in mathematics, but probably none in which each has so consistently stimulated and participated in each other's work. In addition, their two children, David and Ellen, have both become professional mathematicians and have given their parents ample cause for pride.

Margaret Murray [1] describes Dorothy Maharam as having been "a true loner in graduate school, doing research work largely in isolation, and essentially without help from mentors." Anna Pell Wheeler became quite ill during Maharam's time at Byrn Mawr, and John Oxtoby only arrived during her final year there. In an article [2] about "Paul Erdos and Finitely Additive Measures," published in 2002 in a volume celebrating Paul Erdos and his mathematics, Maharam writes:
"When I came to the Institute for Advanced Study, as a shy post-graduate student, I expected to be ignored, and that everyone would assume that I had been admitted as a pretty face. My graduate education had been scanty — my advisor had been ill while I was developing my thesis. So I persisted in staying quiet, not wanting to breathe a word about any mathematics I was doing.

Paul Erdos absolutely insisted on bringing me out, pulling from me to the work I had done, and discussing it with me. When I had new results, he (and Kakutani) went around to the other mathematicians there, saying 'Dorothy has proved a theorem' and explaining them."

Part of Dorothy Maharam's PhD thesis about measure in abstract sets was published in the Transactions of the American Mathematical Society, Vol. 51 (1942), 413-433 [Abstract]. During her stay at the Advanced Institute she also published a paper "On Homogenous Measure Algebras" in the Proceedings of the National Academy of Sciences that characterized measure algebras in which the power of every principal ideal (other than the null ideal) is equal to the power of a σ-basis of the algebra. Over the next 55 years she continued her research on measure theory and allied subjects, and published a total of at least 46 mathematical papers (under her maiden name Maharam). A 1976 milestone paper pioneered the research of the density measures on integers. In this paper she wrote "Some years ago S. Bochner remarked to the author that finitely additive measures are more interesting, and perhaps more important, than countably additive ones. Certainly there has been increasing interest in them shown by mathematicians and statisticians." Some of her other contributions included foundational results on positive operators, the characterization of homogeneous measure algebras, and disintegrations. One of her last research papers, published at the age of 80, was on "Spectral representation of generalized transition kernels."

When Arthur Stone and Dorothy Maharam Stone went to Purdue University, nepotism rules blocked her full-time employment with the university so she only taught occasional courses as a part-time instructor. In an interview with Milvin Henriksen (http://at.yorku.ca/t/o/p/c/49.htm), Leonard Gillman, chair of the mathematics department at the University of Rochester, discussed how he was able to hire both of them at Rochester.

"The senior appointments my first year were Dick Johnson, a ring theorist at Smith College; J. H. B. Kemperman, a live wire analyst and applied mathematician whom I stole from Purdue; Arthur Stone, a world leader in general topology, and his wife Dorothy Maharam Stone, a highly respected measure theorist, from the University of Manchester in England; hiring both required persuading Mac Hazlett to waive the rule prohibiting married couples in the same department. Women were still routinely treated as second-class citizens in those days, and my hiring of Dorothy Stone as a full professor was singled out in Winning Women into Mathematics, a recent MAA publication, as an exception."
There is also an interview with Arthur Stone at this same website (Volume 2 #1 of Topological Commentary, http://at.yorku.ca/t/o/p/c/16.htm) in which he talks about his collaboration with Dorothy:
"I have been enormously helped by Dorothy, not only in being able to discuss mathematical problems with her, but also with specific questions she has raised (and still raises). For instance, I have studied and used what we first called 'Dorothy's crazy topology,' now renamed the 'topology of close approximation.' I have contributed to her work, in a minor way, by solving some technical topological problems that arose in it, and in a major way by editing and typing her manuscripts. (She would probably interchange 'minor' and 'major' here.) I am also responsible, in a way, for two of her major papers. In one, I was unimpressed by a 'direct sum' representation of measure spaces; as a result, Dorothy found a much better 'direct product' normal form. In the other, I made a casual remark that topologists could 'smooth' spaces by multiplying them by powers of the real line; this led her to smoothing measure spaces in a somewhat similar way. We have also written several joint papers."
A special conference on Measure and Measurable Dynamics was held in Dorothy Maharam Stone's honor at the University of Rochester on September 17-19, 1987. Part of the conference proceedings discusses her work in measure theory, ergodic theory, and category algebras. Stone taught as an adjunct professor of mathematics at Northeastern University from 1988 until her retirement in 2001. Her husband, Arthur Stone, died August 6, 2000.

References

  1. Murray, Margaret A.M. Women Becoming Mathematicians, MIT Press, Cambridge, MA, 2000.
  2. "Paul Erdos and finitely additive measures," in Paul Erdos and his mathematics, I (Budapest 1999), Bolyai Soc. Math. Stu., Vol. 11 (2002), 27-29
  3. Dorothy Maharam Stone, Celebrating Women in Mathematics, Fields Institute, Research in Mathematical Science, Toronto.
  4. Mauldin, R. Daniel, R. M. Shortt, andCesar E. Sliva (editors). Measurable and Measurable Dynamics, Contemporary Mathematics, Vol 94, 1989.
  5. MathSciNet [subscription required]
  6. Author Profile at zbMath
  7. Mathematics Genealogy Project
Photo Credit: The first photograph is used with the permission of the University of Rochester Mathematics Department. The second photograph is courtesy of the University of Rochester Archives.