January 21, 1908 - January 16, 1980

Reprinted with permission from the Newsletter of the Association for Women in Mathematics, Vol. 12, No. 4 (1982), 16-19. This article also appears in *Complexities: Women in Mathematics,* Bettye Anne Case and Anne M. Leggett, Editors, Princeton University Press, 202-204.

L. Rosenbaum was the first woman to receive a Ph.D. in mathematics at the University of Colorado [along with Marjorie Beaty, the same year.]

Laura Louise Johnson was born on Jan. 21, 1908 in Carrollton, Illinois. When she was ten, she and her parents moved to Boulder, Colorado, and lived on a farm northeast of town. Boulder and the University of Colorado had undergone dramatic changes in the years before and were on the eve of equally important ones to come. The town had begun about 1860 with the discovery of gold and other minerals in the foothills and was first incorporated in 1871 with a population of less than a thousand. The University considered itself founded in 1876, but the only tangible evidence of this was a building (Old Main), completed in July of that year, and the fifty-two acres on which it was built. The following Spring the Regents elected two faculty members: President Joseph Sewall (Ph.D., Harvard) and Professor Justin E. Dow, formerly principal of Boulder's High School, at salaries of $3000 and $2000 respectively. The first students entered in the fall of 1877 and the first graduating class, consisting of six students, received their degrees in 1992.

By 1907 mining had begun to wane and the University had freed itself of its Preparatory Department by donating some of its meager funds to help support the public schools. Nevertheless, when Louise entered high school fourteen years later it was still known by the name of "Prep".

She had gone to a country school through grade 9; but, since Latin was not offered there, she took a light-housekeeping room in town—at age 13!—in order to complete her high-school education. The program at "Prep" was notably strong; for example, Latin was taught by Mrs. Fred B. R. Hellems, whose husband was for many years Dean of the College of Arts and Sciences of the University and who often gave lectures at "Prep". The couple were affectionately nicknames "Mother Nature" and "Father Time".

After World War I, the University increased in size until when she entered in 1924 it contained about 2500 students. Charles A. Hutchinson was head of the Department of Applied Mathematics in the College of Engineering; and Ira M. DeLong, of the somewhat smaller department in the College of Arts and Sciences. The following year Aubrey J. Kempner (Ph.D., Göttingen under Landau in 1911) took DeLong's place, and the other members of the department were Professor George Light (Ph.D., Yale, 1916), Assistant Professor Claribel Kendall (Ph.D., Chicago, under Wilczynski, 1923), an instructor and probably some assistants. Louise, as a sophomore, was a member of Kempner's first class in Calculus in Boulder. The early years of the thirties brought the depression. A number of the men of the town took to the hills to make a bare living by working old mining claims, grubstaked by the local hardware store, but the days of the narrow gauge railroads were almost past.

Louise's financial resources for her undergraduate career consisted of a contribution of $50 from her parents. Throughout her 4 years she worked as a checker in the University cafeteria; the canonical compensation was board for 3 hours of work per day and room for 1 hour. As a lover of the outdoors, she often skimped on meals to have time for the weekend outings of the Hiking club. She might have majored in geology if she could have afforded the laboratory and field trip fees. But, in those days, a female geologist was even rarer than a female mathematician!

Some of Louise's contemporaries at the University became well-known in the mathematical world. A. J. Lewis, head of the mathematics department at the University of Denver for many years, received his Ph.D. degree under Kempner in 1932. Jack R. Britton, another of Kempner's students (Ph.D., 1936) had a large part in the coming of age of the Applied Mathematics Department. In 1931, Edwin J. Purcell wrote a Master's thesis under Professor Kendall, went on to receive his Ph.D. degree at Cornell University and to teach for many years at the University of Arizona; he wrote a very successful textbook in Analytic Geometry and Calculus still in use. Earl D. Rainville received his B.A. degree in 1930 and went on to the University of Michigan. In 1934 a B.A. degree was granted to D.C. Spencer who had a distinguished career at Princeton and Stanford Universities, is now retired and living in Durango, Colorado.

Upon graduating from the University in 1928, with election to Phi Beta Kappa, Louise began teaching high school in eastern Colorado, where her teaching duties included physics, civics, and economics, as well as the compete curriculum in mathematics. After two years of high school teaching, she returned to Boulder and supported herself with various sub-faculty and part-time faculty teaching assignments at the University while doing graduate work in mathematics. As is still common for people with such status, she would not know until the last minute what her assignment would be, or, indeed, whether she would have a job at all. For administrative reasons, she was always described as a "part-timer", even during those (rare) quarters when she taught 17 or 18 hours per week, the full-time load being 16 hours. With scrupulous attention, Kempner saw to it that she received __more__ than a full-time salary on such occasions. During one year of the early thirties, Louise commuted substantial distances to a CCC installation to teach mathematics.

She received her Master's degree in 1933 under Kempner with a thesis on transfinite numbers. It contains the basic ideas of set theory and the various kinds of "simply and well-ordered aggregates [sets]". The fundamental properties of ordinal numbers and Aermelo's axiom are discussed in detail and the list of twelve references ranges from Cantor to Whitehead.

There were two women who received their Ph.D. degrees under Kempner in 1939. One was Marjorie Louise Heckel Beaty, writing on "Complex Roots of Algebraic Equations," who went on to the University of South Dakota where she is now Emeritus Professor. Louise's thesis was on the Diophantine equation:

P_{n} = x(x+1) ⋅ ⋅ ⋅ (x+n–1) = y^{k}, n and k > 1.

After a rather extensive review with some proofs of solutions of special cases of this equation as described in Dickson's "History of the Theory of Numbers" and some papers not there listed, she proved four little theorems followed by two rather significant results:

- If n = 2k, there are no solutions.
- The equation has at most one solution if n = 4, 5, 6, or 7 and k is a prime greater than 5.

For the former a rather involved argument is given using symmetric functions and based on work of Liouville, Sylvester, and Schur. The latter uses the following result of C.L. Siegel ["Die Gleichung ax^{n} – by^{n} = c^{n}, Math. Ann., 114 (1937), 57-68]:

| ax^{n}– by^{n}| ≤ c, for a, b, c positive integers and n ≥ 3, has at most one solution x,y in relatively prime positive integers if| ab |

^{n/2 – 1}≥ λ_{n}c^{2n–2}, where λ_{n}= 4 [ n ∏_{(p | n)}p^{r}]^{n}, r = 1/(p–1).

Her proof uses some ideas of S. Narumi ["An Extension of a Theorem of Liouville's", Tohoku Math. Jour., 11 (1917), 128-142]. Her thesis, except for the expository material, was published in the American Mathematical Monthly 47 (1940), 280-89. At the close of her paper a communication was mentioned of Paul Erdös, dated February 22, 1940, to the effect that he had proved but not published her first result above and that G. Szekeres (no reference given) had proved that the title equation has no solutions for n ≤ 9.

Louise was very active assisting Professor Hutchinson in the University Recreation Department. In the summers and at other times of the year she arranged and guided tours of students into the mountains by bus or back-packing and climbed many of the high peaks of Colorado. She assisted in the entertainment of the members of the Mathematical Association of American and the American Mathematical Society and their families at their summer meeting in 1929, frightening Mrs. James Pierpont and Dunham Jackson, among others, by her nonchalant driving on narrow dirt mountain roads. Mrs. Hutchinson remembers that they found her very dependable and were thankful when on occasion, she offered to stay with their children when she and her husband were out of town. She also recalls that Louise was a very attractive red-headed girl who preferred the informal dress of the out-of-doors and got along very well with people.

After receiving her degree she was told by Kempner that there was really no future for her in Boulder since two of the four professorial members of the department were women. She went to Reed College on a General Education Board Fellowship to work with Professor F. L. Griffin on the preparation of an integrated mathematical curriculum for a small liberal-arts college, the other fellows in the program being Harry Goheen, Robert Rosenbaum, and Henry Scheffe. She and Rosenbaum remained at Reed as faculty members after the fellowship year, and they were married in 1942. While her husband served as a naval aviator in the Pacific, Louise continued to teach at Reed, carrying a particularly heavy load in a military pre-meteorology program. She and Professor Griffin were proud that the Reed unit stood first in the nation on the uniform exams administered to all students in the program.

Despite the duties of a growing family—three sons were born and reared—there was no semester during which Louise did not teach at least one course, but she often experienced the tension between the demands of her career and those of her home. Nevertheless, she functioned smoothly in both environments, directing some notable undergraduate theses, serving on major College committees, running a household with minimal help, and joining her husband and sons in skiing and hiking in Oregon, in Europe, and especially in her beloved Colorado.

In 1953 she gave up her position at Reed to go to Connecticut, where her husband was appointed to the Wesleyan University faculty. Louise held visiting appointments in the mathematics departments of Trinity, Connecticut, and Smith Colleges, and a professorship at St. Joseph College in West Hartford, Connecticut. She was active in mathematics education, serving on a School Mathematics Study Group committee, directing summer institutes for teachers in Connecticut and Oregon, collaborating with her husband on a *Bibliography of Mathematics for High School Libraries* (which went through five editions), and writing a highly successful booklet on *Mathematical Induction* for Houghton-Mifflin. For the eleven years during which her husband held various positions in Wesleyan's central administration, Louise was called upon to do very extensive entertaining of University visitors, as well as the informal entertaining of students and colleagues which she had begun at Reed with warm natural hospitality.

For much of the last ten years of her life she was afflicted with a progressive circulatory disorder. She endured the end of her hiking and the imposition of other restrictions with quiet stoicism, and she succumbed to the disease on January 16, 1980.

Although she curtailed her mathematical activity to devote time and energy to her family, she never complained of the jewels of theorems that she sacrificed. She was proud of the upbringing she provided her sons, and might well have echoed the Roman matron who introduced her children to a bedecked guest with the words, "Ecce, gemmae meae!"

Photo Credit: Photo of Louise Rosenbaum reading to her eldest son courtesy of Robert Rosenbaum