Hermann studied mathematics at Göttingen under Emmy Noether and Edmund Landau, where she achieved her Ph.D. in 1926. Her doctoral thesis, "Die Frage der endlich vielen Schritte in der Theorie der Polynomideale", published in Mathematische Annalen, is the foundational paper for computer algebra. It first established the existence of algorithms 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.
Quantum mechanics
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. From Denmark, she published her work The foundations of quantum mechanics in the philosophy of nature. This work has been referred to as "one of the earliest and best philosophical treatments of the new quantum mechanics". In this work, she concludes: In June 1936, Hermann was awarded the Richard Avenarius prize together with Eduard May and Th. Vogel. Earlier, in 1935, Hermann published a critique of John von Neumann's 1932 proof which was widely claimed to show that a hidden variable theory of quantum mechanics was impossible. Hermann's work on this subject went unnoticed by the physics community until it was independently discovered and published by John Stewart Bell in 1966, and her earlier discovery was pointed out by Max Jammer in 1974. Some have posited that had her critique not remained nearly unknown for decades, her ideas would have put in question the unequivocal acceptance of the Copenhagen interpretation of quantum mechanics, by providing a credible basis for the further development of nonlocal hidden variable theories, which would have changed the historical development of quantum mechanics. In 2010, Jeffrey Bub published an argument that Bell had misconstrued von Neumann's proof, claiming that it does not attempt to prove the absolute impossibility of hidden variables, and that it is actually not flawed, after all. The validity of Bub's argument is, in turn, disputed.
By 1936, Hermann left Germany for Denmark and later France and England. In London, in order to avoid standing out on account of her German provenance, she married a man called Edward Henry early in 1938. Her prescience was justified by events: two years later the British government invoked its hitherto obscure Regulation 18B of the Defence Regulations 1939, identifying several thousand refugees who had fled Germany for reasons of politics or race as enemy aliens and placing them in internment camps. After the war ended in 1945 she was able to combine her interests in physics and mathematics with political philosophy. She rejoined the Social Democratic Party on returning in 1946 to what would become, in 1949, the German Federal Republic. Starting in 1947 she was one of those contributing behind the scenes to the Bad Godesberg Programme, prepared under the leadership of her longstanding ISK comrade Willi Eichler, and issued in 1959, which provided a detailed modernising platform that carried the party into government in the 1960s. She was nominated professor for philosophy and physics at the :de:Pädagogische Hochschule in Bremen|Pädagogische Hochschule in Bremen and played a relevant role in the Gewerkschaft Erziehung und Wissenschaft. From 1961 to 1978, she presided over the :de:Philosophisch-Politische Akademie|Philosophisch-Politische Akademie, an organisation founded by Nelson in 1922, oriented towards education, social justice, responsible political action and its philosophical basis.
Works
;Articles:
Grete Hermann: Die naturphilosophischen Grundlagen der Quantenmechanik, Naturwissenschaften, Volume 23, Number 42, 718-721,
Grete Hermann: Die Frage der endlich vielen Schritte in der Theorie der Polynomideale. Unter Benutzung nachgelassener Sätze von K. Hentzelt, Mathematische Annalen, Volume 95, Number 1, 736-788, — The question of finitely many steps in polynomial ideal theory
