Creating a universe out of nothing seems an impossible task. A closer investigation shows that some difficult steps pose problems, but most steps are feasible and realistic. This document explains the realistic steps and analyses the steps that pose problems. The analysis intensively applies the concept of vector space and the extensions of this concept, such as number systems, the Hilbert space, and the Hilbert repository. Set theory plays an important role in the exploration of the behavior of the universe. The paper shows that it is impossible to comprehend physical reality without comprehending these parts of mathematics. The paper also shows that the mentioned mathematical concepts are not yet fully explored and might reveal more of the secrets of physical reality. For comprehending physical reality, it is crucial to be able to grasp the change in behavior of a set of numbers when irrational numbers are added to the rational numbers. This occurs in the one-dimensional real numbers and the one-dimensional or three-dimensional spatial numbers. It appears that the change in the behavior of spatial numbers explains the origin of gravity. The typical behavior also explains the existence of dark energy objects and dark matter objects.