Lisl Gaal
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(Ilse) Lisl Novak Gaal (January 17, 1924 – October 7, 2024)[1] was an Austrian-born American mathematician known for her contributions to set theory and Galois theory.[2] She was the first woman to hold a tenure-track position in mathematics at Cornell University,[3] and was an associate professor emeritus at the University of Minnesota.[4] Gaal died in 2024, at the age of 100.[5]
Gaal's dissertation work was in the foundations of mathematics. It proved that two different systems for set theory that had previously been proposed as foundational were equiconsistent: either both are valid or both lead to contradictions. These two systems were Zermelo set theory and Von Neumann set theory. They differed from each other in that von Neumann had added to Zermelo's theory a notion of classes, collections of mathematical objects that are defined by some property but do not necessarily form a set. (Often, intuitively, proper classes are "too big" to form sets; for instance, the collection of all sets cannot itself be a set, by Russell's paradox, but it can be a class.) Gaal's work showed that introducing this extra notion of a class is a safe step, one that does not introduce any new inconsistencies into the system.[2]
Gaal was also the author of two books:
