This biography, written by J J O’Connor and E F Robertson, has been republished with permission from the School of Mathematics and Statistics at the University of St Andrews, Scotland.
Born: 11 April 1914, United States
Died: 5 February 1988
Country most active: United States
Also known as: NA
Dorothy Bernstein was the daughter of Jacob Louis Bernstein (1880-1956) and Tillie Lewis (1887-1969). Jacob Bernstein was Jewish and had been born on 2 January 1880 in Lisovich, Russia, the son of Nuchem Bernstein and Dobche Karsunsky. His family emigrated to the United States in 1886. Tillie Lewis was born on 18 June 1887 in Shubovka, Ukraine into a Jewish family with parents Shloime and Sureh Loyev. After she emigrated with her family to Milwaukee in 1905, they all adopted the name of Lewis. Jacob and Tillie were married in Milwaukee on 19 December 1912. Let us note at this point that census forms do give some different versions of names and also some inconsistencies over dates. For example in the 1920 US census, Tillie’s name is given as Matilda. Jacob and Tillie Bernstein were both naturalised in 1914.
Dorothy Bernstein, the eldest of her parents children, was born in Chicago in 1914. Her father had been in the dairy business there since 1911. Two sisters for Dorothy were born in Chicago before the 1920 census, Naomi Ruth Bernstein (1915-1996) born 22 November 1915, and Myrtle Bernstein (1917-1992) born 30 November 1917. In 1918 the family moved to Jackson, Wisconsin where they were living at the time of the 1920 census in which Dorothy’s father is recorded with the occupation “farmer”. Two further children were born in Jackson, Elinor Bernstein who was born in the summer of 1919 but died of gastroenteritis on 8 February 1920, and Clarice Bernstein (1922-2010) born 19 May 1922. The family moved again in 1924, this time to Milwaukee where Jacob founded the Sunshine Dairy. Sheldon Bernstein (1927-2014), Dorothy’s youngest sibling, was born in Milwaukee on 23 March 1927. The 1930 census records the family living in rented accommodation on Thirty Eight Street.
Before we continue with Dorothy Bernstein’s biography, let us give a brief description of the lives of her four surviving siblings. Naomi Bernstein attended Washington High School in Milwaukee, married Eziel Golan on 10 September 1939 in New York, and was awarded a Ph.D. in Social Work from The University of Chicago in 1969. She died in Jerusalem, Israel in February 1996. Myrtle Bernstein attended Washington High School in Milwaukee, married Edwin LeBow on 29 December 1951 in Milwaukee, was awarded an MD degree and died in Jerusalem, Israel in January 1992. Clarice Bernstein was known as Yaffa. She attended Washington High School in Milwaukee, married the author Julius Nathan Draznin and was awarded a Ph.D. in History from the University of Southern California. She died in Chicago on 23 June 2010. Sheldon Bernstein attended Washington High School in Milwaukee, married Estelle Lou Katz on 27 June 1948 in Milwaukee. He was awarded a Ph.D. in Biochemistry from the University of Wisconsin in 1952.
Since Dorothy’s four siblings all attended Washington High School in Milwaukee, we might expect her to have also been a pupil there but that is not the case. After attending a public primary school in Milwaukee, Dorothy Bernstein entered the Roosevelt Junior High School in Milwaukee in 1926, the year the school opened. It was the first junior high school to be built in Milwaukee situated on Lapham Park. After one year at this school, she entered the North Division High School. This was one of the largest schools in Milwaukee and had opened in 1906. She graduated from the North Division High School in 1930, at age sixteen, as valedictorian. She gave the Valedictory Address The New Frontier at ‘The Commencement’ held on Thursday evening, 19 June 1930. Some of Bernstein’s achievements and activities over her three years at the school are listed:-
Mathematics Course. Entered as Sophomore from Roosevelt Junior High School. A. A., 1927-30; Cadet, 1927-30; Forensics, 1929; Girls’ Club, 1927-30, Treasurer 1930; Elected to National Honor Society, 1930; Leaders, 1930; Local Honour Club, 1928, 1929; Writers’ Club, 1928-30; Library Monitor, 1928-29; Valedictorian, 93.71%.
She entered the Honor Role for April 1930 having achieved 90% or above in all subjects and won a scholarship of two hundred and fifty dollars, given annually by the American Association of University Women. This was obtained in a competitive examination.
After graduating from the North Division High School, she entered the University of Wisconsin at Madison where she majored in mathematics. Let us quote from Dorothy Bernstein’s own description:-
… it was an exciting time to be a student, since Alexander Meiklejohn’s experimental college was just finishing its short but brilliant career at the university, and one of its legacies was the system of advanced independent study, in which I spent my junior and senior years. For two full years, including summers, a student was allowed to study his major subject on his own, attending such lectures as he desired and talking with any member of the department he wished, but with no exams or grades. He was expected to write a thesis during his second year and take a comprehensive examination at the end of the period. On the basis of these two things (the thesis and the single examination), he was awarded either a B.A. degree or B.A. and M.A. degrees, together with the appropriate number of credits and a single grade that was determined by the department. Most students, of course, were unwilling to take the gamble, but the few of us who did thoroughly enjoyed it. In my case, I would study some subjects like advanced calculus or introductory abstract algebra for a month at a time, by myself, meeting weekly with my advisor, Mark Ingraham. For other things, such as complex variables or Galois theory, I attended the regular graduate course lectures. My thesis was on finding complex roots of polynomials by an extension of Newton’s method. I received my B.A. and M.A. degrees at the end of four years and then returned to Wisconsin for an additional year of graduate work as a teaching fellow. Besides Professor Ingraham, I especially remember among my teachers Rudolf Langer and C C MacDuffee. All three encouraged me to continue graduate study in mathematics, but at another university.
In 1934 Bernstein was awarded B.A. and M.A. degrees, and spent 1934-35 doing teaching and research at the University of Wisconsin before moving to Brown University to continue studying for her Ph.D. with a two-year scholarship. It was at Brown that she first encountered what she considered stupid discrimination because she was a woman. Bernstein and a colleague Hugh Hamilton were asked to teach a remedial course, Bernstein at Pembroke College, the associated women’s college, and Hamilton at Brown. She had three women students and he had forty-five male students. Much more sensible, she said, to divide the class into two groups of twenty-four. The head of the department, however, would not hear of it, saying that the boys would object to having a woman teacher, so for the whole semester she taught three students at Pembroke College. After one year Bernstein took the examinations to qualify for the Ph.D. course. The oral examination by the full Brown Mathematics Department consisted of two afternoons of four hours each. Her fellow students had examinations lasting between two and three hours so she asked why her examination had lasted so long. She was told it was partly because she was a woman and partly because she had taken most of her courses at a Midwestern university. She said:-
I am not sure which of the two was more prejudicial.
She undertook research at Brown advised by J D Tamarkin and at the same time worked as an Instructor in Mathematics at Mount Holyoke College from 1937 to 1940. We should quote how she managed to get this appointment:-
… R G D Richardson, … was Dean of the Brown Graduate School and also Secretary of the American Mathematical Society for many years. In his latter capacity, he was consulted by many people about hiring personnel – I have heard stories, perhaps exaggerated, that he was a one-man employment bureau for mathematicians throughout the country. I do know, however, that when I came to see him, as we all did, about a college teaching job, he took out a map of the United States, covered the region west of the Mississippi and said: “You can’t get a job there, because you are a woman.” Then he covered the part south of the Ohio River and said: “And you can’t get a job there, because you are Jewish.” So that left the Northeast quadrant. Well, it happened that I heard of a job at Mount Holyoke and after a visit to South Hadley, I got the position. When I told the Dean, he expostulated “But I had that job all reserved for Hamilton!”
Bernstein was awarded a Ph.D. by Brown University in 1939 for her thesis The double Laplace integral. She published a paper containing the main results of her thesis, and with the same title, in the Duke Mathematical Journal in 1941. It was reviewed by Ralph Boas who writes:-
The author studies functions of the form [of the double Laplace integral]. … Some properties are analogues of known properties of single Laplace integrals; others are rather different. Much of the theory of double Dirichlet series generalises to [the double Laplace integral]. Some of the author’s results have been previously stated by other writers in more or less complete, and occasionally incorrect, form (the author gives an extensive bibliography). This paper, however, seems to be the first systematic exposition of any substantial part of the subject. As in the theory of double Dirichlet series, the useful kind of convergence for [the double Laplace integral] is bounded convergence. The existence of associated abscissas of bounded convergence is established, and several formulas for them are obtained. Absolute convergence and uniform bounded convergence are also discussed.
The position as instructor at Mount Holyoke College ended in 1940 and she returned to Milwaukee for a while before returning to the University of Wisconsin in 1941 as an instructor. She began to broaden her mathematical interests to look more generally at integration theory and its associated measure theory and worked with Stan Ulam who had been appointed to Wisconsin in 1940. She presented a joint paper with Ulam, namely On the problem of completely additive measure in classes of sets with a general equivalence relation, to the American Mathematical Society meeting in Chicago on 17 April 1942.
After the Japanese attack on Pearl Harbor in December 1941, the United States entered World War II and before the end of the month were at war with Japan, Germany and Italy. Many mathematicians became involved in the war effort and, in June 1942, Bernstein was appointed as research associate to Jerzy Neyman at the Statistical Laboratory of the University of California at Berkeley where much secret work was being undertaken on behalf of the US Army. She worked on various probability problems which Neyman gave her and also taught a graduate course on probability theory for the Department of Mathematics. She explained why she left after eight months:-
Neyman and I did not see eye-to-eye on what was the mathematical justification of a statistical procedure. Of course, since then I have learned that this is not unusual – mathematicians and statisticians do have fundamentally different points of view, even though they may use the same techniques.
Neyman explained her leaving in the following way:-
Dorothy Bernstein … has just come to me and said she doesn’t like the kind of stuff that we do because it’s not really nice mathematics. She wants to leave.
She had left without having any other employment so for several months she sought a position. In the autumn of 1943 she was employed by the University of Rochester, a private university in New York. At this time the university had the River Campus for male students and the Prince Street Campus for female students. At first she taught at the Prince Street Campus but after a while all science was taught at the River Campus, women having to take science courses there, and from that time on Bernstein taught at the River Campus. Appointed as an Instructor, she was promoted to Assistant Professor in 1946, to Associate Professor in 1951 and to full Professor in 1957.
Charles Brown Tompkins (1912-1971) had held a visiting lectureship at the University of Wisconsin and got to know Bernstein when they both worked there. Tompkins did war work involving high speed computing and, in 1949, he organised, on behalf of the Office of Naval Research, the Logistic Research Project at George Washington University. He asked Bernstein to make a study of existence theorems in partial differential equations, believing these would play a significant role in solving non-linear problems on computers. Her study became the book Existence Theorems in Partial Differential Equations (1950). In reviewing this book, D H Parsons writes:-
Professor Bernstein has compiled a comprehensive, and most interesting, collection of existence theorems, which will be a welcome addition to the libraries of those who are interested in the theory of partial differential equations. All conditions of continuity, differentiability, etc., which are assumed in each theorem are meticulously stated; and the proofs, which are mostly given in outline only, are nevertheless thorough and rigorous. Ample references are provided throughout the text to literature dealing in detail with each problem, and the book thus fulfils a valuable function in helping the reader to find both statements and proofs of the less well-known theorems. Unfortunately the very abridged and rather artificial notations employed, though providing excellent economy of words in the careful statements of conditions, prevent the work from being really pleasant or easy reading.
Bernstein was a member of the Institute for Advanced Study in 1950-51 and spent her sabbatical year 1957-58 as a visiting professor at the University of California’s Institute for Numerical Analysis in Los Angeles. While at the University of Rochester Bernstein supervised the Ph.D. studies of Geraldine “Jerry” Alma Coon (1913-2008):-
Coon was born in 1913, in North Stonington, Connecticut. She received a bachelor’s degree from the Connecticut College for Women in 1935 and a master’s degree in mathematics from Brown University in 1937. She worked as an instructor in shop mechanics for high school graduates at the Scovill Manufacturing Company in Waterbury, Connecticut, from 1939 to 1944. She then moved to Taylor Instrument Companies in Rochester, New York, where she was a research mathematician from 1944 to 1958. While working at Taylor Instrument, Coon received a Ph.D. in mathematics from the University of Rochester in 1950. Her dissertation, entitled “The Double Laplace Transform and Its Application to Partial Differential Equations,” was overseen by Dorothy L Bernstein.
Bernstein and Coon published the joint paper Some properties of the double Laplace transformation in the Transactions of the American Mathematical Society in 1953. They went on the publish two further joint papers, Some general formulas for double Laplace transformations (1963) and On the zeros of a class of exponential polynomials (1965). T E Hall, reviewing the 1963 paper, writes:-
Several theorems are presented about the convergence of the Laplace transforms of certain functions, and their derivatives. The latter are required to satisfy certain continuity requirements, and also some restrictions on their growth with increasing size of variable, or variables.
In 1959 she left the University of Rochester and moved to Goucher College, a private liberal arts college in Towson, Maryland. During the twenty-one years that Bernstein worked there, 1959 to 1979, Goucher College was a women’s college, only becoming co-educational in 1986. She served as chair of the Mathematics Department from 1960 to 1970 and director of the Computer Center from 1962 to 1967:-
While at Goucher, Bernstein became very active in the uses of the computer in education and in the spring of 1971 was part of a group that founded the Maryland Association for the Educational Uses of Computers. She was instrumental in obtaining funds for computers at Goucher and helped run an National Science Foundation summer institute in computer-based mathematics for high school teachers.
After retiring in 1979, Bernstein was made professor emeritus. She was awarded an honorary degree from Towson State University in 1981 and in 1985 she was awarded a Certificate for Meritorious Service from the Maryland-District of Columbia-Virginia Section of the Mathematical Association of America. In fact she served the Mathematical Association of America in many different roles, the most prestigious being vice president 1972-73 and president 1978-80; she was the first woman to be elected president. She presented talks, by invitation, to the Association, for example How to make and break codes – cryptanalysis and mathematics (5 May 1973), A differential equation of literary criticism (27 April 1979), Mathematical modeling and existence theorems (26 October 1979), Who is the MAA? (15 February 1980), Preparation for careers in applied mathematics (11 April 1980), A small college’s experience with applications in the mathematics curriculum (18 April 1980), The biography of a theorem (20 April 1981), Mathematical expectation (17 January 1982).
Jerry Coon, Bernstein’s former research student, became a colleague of Bernstein’s at Goucher College from 1964 until 1979 when they both retired. Coon and Bernstein then shared a home on the Pawcatuck River in Connecticut. Writing about Bernstein in 1979, Coon wrote a clear description of Bernstein’s mathematical activities and work at Goucher. She then writes:-
… whenever possible, [Dorothy Bernstein] indulges in her favourite hobbies of gardening, canning, and freezing. She intends to maintain the famous Bernstein Box at the Preakness, where annually the laws of probability and statistics fall into complete disarray.
Bernstein was treated for her final illness in Rhode Island Hospital, Providence, where she died at the age of seventy-three. She was buried in Anshai Lebowitz Cemetery, Milwaukee where her father and mother had been buried.