 It was von Neumann’s hope that his program for generalizing quantum theory would emerge from a new mathematical structure known as “continuous geometry”. He wanted to use this structure to bring together the three key elements that were mentioned above: the algebraic approach to quantum mechanics, quantum logics, and rings of operators. He sought to forge a strong conceptual link between these elements and thereby provide a proper foundation for generalizing quantum mechanics that does not make essential use of Hilbert space (unlike rings of operators). Unfortunately, it turns out that the class of continuous geometries is too broad for the purposes of axiomatizing quantum mechanics. The class must be suitably restricted to those having a transition probability. It turns out that there is then no substantial generalization beyond the separable Hilbert space framework. An unpublished manuscript that was finished by von Neumann in 1937 was prepared and edited by Israel Halperin, and then published as von Neumann (1981). A review of the manuscript by Halperin was published in von Neumann (1961–1963, Vol. IV, No. 16) years before the manuscript itself was published. In that review, Halperin notes the following: