Soon it became manifest that by playing with axioms an infinite number of geometries could be created. In fact, in the second half of the nineteenth century many new geometric systems were created and extensively explored. The philosophical significance of this mathematical revolution was comparable to that of Copernicus (1473–1543): Humans are not only creatures from the outskirts of the universe, but even the universe, at least conceptually, is not unique; it is a member of an infinite family of geometric universes.
German mathematician Georg Friedrich Bernhard Riemann (1826–1866) in his 1854 inaugural lecture created a broad conceptual setting for modern geometry, which admitted more than three spatial dimensions. He also foresaw its physical applications: The world, with all its physical fields, could be but a system of fluctuating geometries.
Relativity
At the end of the nineteenth century, peoples’ imaginations were fed with multidimensional geometric pictures. Some philosophers started speculating on “other dimensions” as living places for spirits, and the popular writer Edwin A. Abbot published a book in 1884 entitled Flatland, the principal aim of which was criticism of Victorian England, but which in fact inspired both philosophers and scientists to deal with new geometric spaces.
With the advent of the special and general theories of relativity the concept of space-time entered the imaginary requisites of popular and philosophical literature and became a powerful tool of scientific investigation. From then on, geometry would not only deal with the problem of space but also with at least some aspects of the time problem.
Consider only two such problems that have repercussions in theological matters. The first problem concerns the nature of time flow and its relationship to eternity. The theory of relativity favors, but does not require, a picture of space-time as existing in one totality with the idea of the flowing time being only a “projection” of human psychological experience onto the world. Such a picture is consonant with the traditional idea of God’s eternity (going back to Augustine of Hippo [354–430 C.E.] and Boethius [c. 480–c. 526 C.E.]) as existence outside time rather than existence in time flowing from minus infinity to plus infinity. The second problem concerns the interpretation of the initial singularity appearing in some solutions of Einstein’s equations describing the evolution of cosmological models. The question whether such a singularity (for instance the one corresponding to the Big Bang in the standard cosmological model) could be identified with God’s act of creation was once heatedly discussed. The prevailing view at the start of the twenty-first century is that such interpretations should be postponed (if they are methodologically legitimate) until a trustworthy quantum cosmology becomes available.
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.
