Rapid progress in relativity theory, especially during the second half of the twentieth century, greatly contributed to the development of geometry. New physical problems required the sharpening of known geometric methods and the invention of new ones. In fact, the necessity to consider more and more abstract spaces gradually led to the broadening of the notion of geometry itself. The process of the geometrization of physics has changed both physics and geometry.

Noncommutative geometry

It seems that a long dialogue between science and religion has made people more cautious about drawing theological conclusions from scientific premises, but there is still one lesson the theologian can learn from this process. The degree of generalization of spatial and temporal concepts one meets in geometry and its applications to physics is a good warning against anthropomorphisms in theological language.

One notable achievement in geometry at the end of the twentieth century is the creation and rapid progress in the so-called non-commutative geometry, which has some roots in the mathematical formalism of quantum mechanics. One of its aims is to deal with spaces that are intractable with the help of the usual geometric methods. Non-commutative spaces are, in general, purely global entities; no local concepts have, in general, any meaning. For example, the concept of point, as a typically local concept, has no meaning in many non-commutative spaces. The number of attempts to apply non-commutative geometry to physics, for instance to create a fundamental physical theory, is constantly increasing.

Some such attempts can have a profound philosophical meaning. For example, it is possible to create a model of the fundamental physical level in which there is no space and no time in their usual senses (space consisting of points and time consisting of instants, which are local concepts) and yet, in spite of this, an authentic dynamics (i.e., equations modeling behavior of physical systems under the action of forces) can be defined in them. Even if such models will turn out to be false, they demonstrate, by being logically consistent, that time (in the usual sense as transient succession of events) is not the necessary condition for an authentic activity. This seems to falsify the claim of some theologians that the idea of an active agent existing outside the flow of time is contradictory in itself.