Lisl Gaal
1924 – 2024
Ilse Lisl Novak, who was always known as “Lisl”, was born in Vienna in 1924, the oldest daughter of a doctor and a nurse who met while working at a military hospital in World War I. Two younger sisters joined the family a few years after Lisl was born. Lisl’s father was not a practicing Jew but he came from a Jewish family, which put the family in grave danger when the Nazis annexed Austria. To keep 14-year-old Lisl safe, her father escorted her to Amsterdam, left her with some distant relatives, and then returned to help the rest of the family in Vienna. Lisl stayed briefly with various people in Paris, London, and Glasgow, then went to a boarding school in the English countryside. Of necessity, Lisl learned English fast, and studied hard to catch up with her classmates in subjects she knew nothing about, like English history and literature. Thankfully, her mother’s bridge-playing friend Lord Runciman agreed to take Lisl’s sisters to England in his airplane, so that they could attend another boarding school there. Later, her father obtained a U.S. visa and traveled to the United States alone, while her mother arranged to pick up the children in Liverpool and sail with them to New York City, where the family was finally reunited in 1940. Lisl was responsible for rounding up her sisters and taking them by train to Liverpool, which was challenging because her mother insisted that they avoid London, where everyone anxiously anticipated German bombing.
In New York City, Lisl began attending Hunter College, although she never formally graduated from high school. Like the schools she attended in Austria and England, Hunter only admitted female students at the time. Lisl majored in mathematics and chemistry, excelled in her classes, and was selected for Phi Beta Kappa. She wanted to be an engineer, but that seemed to be out of the question for a woman in that era. Lisl went on to obtain an M.A. and Ph.D. in mathematical logic from Harvard University, through Radcliffe College. Her Ph.D. thesis, “On the Consistency of Gödel’s Axioms for Set Theory Relative to a Weaker Set of Axioms”, was jointly supervised by Lynn Loomis and Willard Quine. In it, she solved a long-standing problem, proving that “the von Neumann system, which has both classes and sets, is consistent provided that the Zermelo system, which has only sets, is consistent.” For this achievement, she won Radcliffe’s Caroline I. Wilby Prize for “the best original work in any department.” Supporting faculty wrote “This is an excellent piece of research in mathematical logic, a field notorious for its difficulty.’’ and “Her result seems to have startling further consequences … they seem to threaten a new crisis in the foundation of mathematics.” Her thesis was completed in 1948, and the results presented to the American Mathematical Society in December 1948 and April 1949. The ensuing paper was published in Fundamenta Mathematicae; it is dated 1950, although, due to production issues, it did not appear in print until 1951. In the paper that immediately follows hers in that issue of the journal, Mostowski strengthened her result, citing both her paper and a 1950 paper by Rosser and Wang that, as they note therein, found a different proof of her fundamental result, which continues to be cited to this day — for example in survey papers by Kanamori in 2009 and Dean in 2020.
From 1948 to 1950, Lisl was an Instructor at Wellesley College. She spent the next year as a post-doctoral fellow at UC Berkeley, where she worked with Alfred Tarski and formed many close friendships, particularly with the Lehmer family and Julia and Rafael Robinson. By this time, her mathematical work had been recognized by Mademoiselle magazine, which gave her a merit award, along with eight outstanding young women in other fields “who not only have begun the climb [to the top] but have made a real achievement along the way.” Among the other winners for 1951 were ballerina Maria Tallchief, fashion designer Jeanne Campbell, tennis player Maureen Connolly, and actresses Shelley Winters and Maureen Stapleton.
The following academic year, Lisl continued her post-doctoral research at the Institute for Advanced Study (IAS) in Princeton. Albert Einstein was still there and enjoyed chatting in German with Lisl. She also met many other scholars at IAS, including Steven Alexander Gaal (aka István Sándor Gál), a fellow mathematician and Hungarian refugee. Lisl and Steven were married the same year; she took her husband’s last name and used it both socially and professionally thereafter. Upon finishing their post-doctoral fellowships at IAS, Lisl and Steven worked at Cornell University from 1952 until 1958. They were both promoted to Assistant Professor, and thus Lisl became the first woman to receive this title in the department. Lisl was also the first female faculty member at Cornell to supervise a Ph.D. thesis, that of Angelo Margaris, entitled "A Problem of Rosser and Trucquette in Many Valued Logic”. Lisl subsequently moved to New Haven so that Steven could take a position at Yale. Their two daughters, Barbara and Dorothy, were born while they were on the east coast. In 1960, Lisl and Steve moved to the Twin Cities, where they both worked for the School of Mathematics, raised their children and stayed for the remainder of their careers, although they divorced during this period. Lisl was initially hired as a Lecturer on a temporary basis; she became an Assistant Professor in 1970 and an Associate Professor in 1979. She taught countless students calculus, linear algebra, and other mathematical subjects, “illuminat[ing] complex concepts with clarity and passion.” In 1973, she published a well-received textbook, entitled "Classical Galois Theory: With Examples", which ended up being reprinted five times. In 1997 she was awarded a Citation for Meritorious Service by the North Central Section of the Mathematical Association of America in recognition of her teaching, scholarship, and years of service to the profession, including serving as president and past president of the section during 1984-87. Lisl retired in 1998 and assumed the title of Associate Professor Emerita.
Being a female mathematician was not easy in her day. At more than one institution, she was not allowed in the Faculty Club, where her male colleagues went daily to discuss mathematical developments over lunch. Nepotism rules hampered her career, as did customs such as sending schoolchildren home for lunch every day. When chemist Shyamala Rajender brought a sex discrimination lawsuit against the University of Minnesota, Lisl joined the class action and helped her friend and colleague Charlotte Striebel compile the statistics that were instrumental in obtaining a landmark consent decree, which “paved the way for greater participation of women in academia and served as a model for other women who felt discriminated against to follow.”
On the personal side, Lisl had an adventurous streak. When her husband started flying small airplanes as a hobby, so did she. When her husband went to India on an extended business trip, she packed up her two young children, one uncooperative cat, two hamsters, and three pet turtles and drove the whole crew from the Twin Cities to Boulder, where she taught in a summer program at the University of Colorado. When she became fascinated by the arctic and Inuit art, she took her teenage daughters to Baffin Island for a backpacking trip at Auyuittuq National Park, even though she had no backpacking experience and they had no guide, gun, or even bear spray.
Lisl was artistic and creative throughout her life. She was active in the Art Section of the Faculty Women’s Club. When she moved from the family home to an apartment building that houses fellow faculty members, she designed a colorful mural for the exercise room and enlisted many of the other residents to help paint it. When she became a grandmother, she lovingly sewed Halloween outfits for her grandchildren. She also learned lithography, making playful prints depicting a wide range of subjects, including local scenes, animals (she especially loved dogs), and clever illustrations of mathematical concepts. She won some prizes at the Minnesota State Fair and other juried shows. She incorporated most of her mathematical pictures into a book, “A Mathematical Gallery”, that the American Mathematical Society published when she was 93.
At about the same time, Lisl moved from Minnesota to Connecticut, where her daughter Dorothy and her husband could provide loving assistance. In early 2024, Lisl celebrated her 100th birthday with much of her family; other family members were able to visit later in the year, including her 6-month-old great-grandson. Lisl and the youngster were fascinated by each other and compatible in their limited mobility. Lisl died peacefully at home not long after that visit, keeping her sense of humor and creative spirit to the end. She is survived by her daughters Barbara and Dorothy Gaal and their families. She will be greatly missed.
