Grete Hermann

Grete Hermann (2 March 1901 – 15 April 1984) was a German mathematician and philosopher noted for her work in mathematics, physics, philosophy and education. She is noted for her early philosophical work on the foundations of quantum mechanics, and is now known most of all for an early, but long-ignored critique of a "no hidden-variables theorem" by John von Neumann. It has been suggested that, had her critique not remained nearly unknown for decades, the historical development of quantum mechanics might have been very different. Hermann studied mathematics at Göttingen under Emmy Noether and Edmund Landau, where she achieved her PhD in 1926. Her doctoral thesis, "Die Frage der endlich vielen Schritte in der Theorie der Polynomideale" (in English "The Question of Finitely Many Steps in Polynomial Ideal Theory"), published in Mathematische Annalen, is the foundational paper for computer algebra. It first established the existence of algorithms (including complexity bounds) for many of the basic problems of abstract algebra, such as ideal membership for polynomial rings. Hermann's algorithm for primary decomposition is still in contemporary use. From 1925 to 1927, Hermann worked as assistant for Leonard Nelson. Together with Minna Specht, she posthumously published Nelson's work System der philosophischen Ethik und Pädagogik, while continuing her own research. As a philosopher, Hermann had a particular interest in the foundations of physics. In 1934, she went to Leipzig "for the express purpose of reconciling a neo-Kantian conception of causality with the new quantum mechanics". In Leipzig, many exchanges of thoughts took place among Hermann, Carl Friedrich von Weizsäcker, and Werner Heisenberg. The contents of her work in this time, including a focus on a distinction of predictability and causality, are known from three of her own publications, and from later description of their discussions by von Weizsäcker, and the discussion of Hermann's work in chapter ten of Heisenberg's The Part and The Whole.