The concept of a "center of the universe" can be somewhat misleading when applied to cosmology. In modern cosmological theories, such as the Big Bang theory and the currently accepted standard model of the universe, there is no well-defined mathematical center.
In cosmology, the universe is typically described as homogeneous and isotropic on large scales, meaning that it looks roughly the same from every point in space. This property is known as the cosmological principle. However, it's essential to understand that the cosmological principle describes the overall large-scale structure of the universe, not necessarily the distribution of individual galaxies or structures within it.
In an infinite universe, there is no geometric center that can be identified as the precise center of the universe. Instead, the universe is considered to be spatially infinite, without a specific boundary or center. This implies that the universe extends uniformly in all directions, and no single point can be considered the center.
It's worth noting that the observable universe, the portion of the universe that we can see, is finite due to the finite speed of light and the age of the universe. However, the actual universe may extend beyond the observable universe, and its overall structure remains unknown.
In summary, the mathematical definition of the center of the universe is not well-defined in modern cosmology, and in an infinite universe, there is no specific center. The cosmological principle suggests that the large-scale structure of the universe is homogeneous and isotropic, but this does not imply a geometric center.