Discovery of flaw in von Neumann’s no–hidden‑variables proof

In 1935, Grete Hermann published a detailed critique revealing a logical flaw in John von Neumann’s influential 1932 argument that hidden‑variable theories in quantum mechanics were impossible. While the exact calendar day of her discovery and publication is not securely documented, the year 1935 is consistently cited for this landmark intervention.

Von Neumann’s theorem had been widely interpreted as a rigorous proof that any attempt to supplement quantum mechanics with underlying "hidden" variables would fail. Hermann carefully analyzed his assumptions and demonstrated that the proof relied on an unjustified constraint on the additivity of expectation values, which did not follow from physical principles. Her work showed that the impossibility of hidden variables had not been established, thereby reopening the conceptual space for alternative interpretations of quantum theory.

This critique, published in German and rooted in Hermann’s neo‑Kantian philosophy of physics, was largely overlooked by the physics community for decades. Only later, with John Bell’s 1960s work on hidden variables and Bell’s theorem, did historians recognize that Hermann had anticipated key aspects of the debate.

As one of the earliest and most rigorous challenges to the orthodox reading of von Neumann’s result, Hermann’s 1935 analysis stands as a genuine first in the foundations of quantum mechanics: a woman mathematician‑philosopher exposing a central flaw in a canonical proof at a time when women were rarely acknowledged in theoretical physics.