Grete Hermann and Effective Methods in Geometry

Sometimes in the history of science we can find scientists who were not acknowledged at their time and only later the scientific community has recognized the importance of their work. Among them there is Grete Hermann, who worked in mathematics, philosophy, and physics during the early to mid twentieth century. To mathematicians she is known as the first Ph.D. student of Emmy Noether in Gottingen and a pioneer of modern computer algebra, but she also discovered a flaw in John von Neumann’s proof of the impossibility of hidden variables theory in quantum mechanics and she did further interesting work on the foundations of quantum mechanics. Her collaboration with Emmy Noether and the philosopher Leonard Nelson in Gottingen, her involvement with Heisenberg’s group in Leipzig, some aspects of her work in philosophy and education, her activities in socialist groups and in the anti-Nazi underground movement make of Grete Hermann a very interesting intellectual of last century. In this note we will illustrate Hermann’s work and discuss one of her mathematical results, which has had many improvements and now is much cited.