A History of Women in Mathematics Exploring the Trailblazers of STEM by Dale DeBakcsy

Author:Dale DeBakcsy
Format: epub

Chapter 21

Varieties: The Life and Mathematics of Hanna Neumann

Of all the realms of mathematics, there are few where more people feel more at home than in the safe harbours of algebra. From the age of 8 or 9, we are made familiar with the classic moves involved in Solving For X, how a(b+c) = ab + ac, how if a = c then a-c = 0, and a fleet of other manipulations besides that become so second nature to us that we rarely stop and think about just what we are doing. What sort of a thing is it we are engaging in when we employ the laws of algebra, and might the moves that we have got used to be nothing more than very restricted cases of a much bigger world?

These questions began intriguing mathematicians in the late nineteenth century, leading to the explosion of the field of Universal Algebra in the 1930s and 1940s, which sought to answer the question of what makes algebra algebra, and how we might construct things that follow the rules we most associate with the algebra we’ve learned since youth, but which present us with often strange new mathematical vistas. Some of the most interesting results of universal algebraic thinking came when mathematicians began playing with the properties possessed by different categories of algebras, including the field of ‘Varieties of Groups’ pioneered by the mathematical power couple of Hanna and Bernhard H. Neumann.

Hanna’s mathematical journey would take her all over the world, first in flight and later in triumph. Born Hanna von Caemmerer on 12 February 1914 to a family of long-standing Prussian military background, she lost her tradition-flouting historian father early in the First World War, and her Huguenot-descended mother had to make do on a slim war pension that required she and her two siblings to contribute to the household as best they could. Hanna’s academic gifts were such that, at the age of 13, she was able to earn money coaching other children. From 1922 to 1932 she attended the Augusta-Victoria Schule, where she took fifteen subjects and, on her final examinations for college, scored highly on all areas except music.

Hanna began her first year at the University of Berlin in 1932, where the foundational topologist Georg Feigl and function theorist Ludwig Bieberbach were among the mathematical luminaries offering courses to undergraduates. Hanna allowed herself to experience the full breadth of the university’s offerings, taking courses from Gestalt theory psychological pioneer, Wolfgang Kohler, Nobel prize-winning physicist Walther Nernst, and Germany’s most famous academic lawyer, Martin Wolff. She threw herself into the coffee break academic discussion culture of the university, and soon became good friends with doctoral student Bernhard H. Neumann.

Their romance, for soon it became such, would determine the course of their lives, for with the ascension of the Nazis to power in 1933, Bernhard, of Jewish descent, knew his days in the German university system were numbered, and emigrated to England to continue his studies at Cambridge. He and

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