Can any point be considered the center of the universe?

The answer to the question is no. If the conception of the universe were that it is infinite, that it has no borders, as the metaphysicists thought, then the answer would be: yes, any point in the universe can be considered the center of that universe,

The notion of center is related to distance and also to border or border. A point is the center of a system if it is the same distance from all points as the edge. To get an idea, let's think about a sphere, a compact wooden ball, for example. The edge is formed by the surface of that sphere, it is what we can touch, and there is a point inside that ball that is the same distance from any point on the edge. That's the center of the sphere. If the surface of that sphere were to expand to infinity, and we would think of the new edge, which would now not be such, infinitely distant, all the points of the new "infinite sphere" would be at the same distance from that supposed edge: at an infinite distance; this is why all the points could be considered the center, with that definition that we have given as a center, and that is why the answer would be: yes, with the previous conception of an infinite universe.

When talking about distance we are implicitly thinking of a reference system

However, the universe is currently thought to be finite, although it is also true that it is believed to be continuously expanding. Being finite, any point cannot be the center, as with the compact wooden ball, but assuming that it is permanently expanding, it is not easy to find its center. If it existed (think, for example, on a sheet of paper; we could talk about a center of mass, which is a physical concept, but there is no center on that sheet in terms of offset because no point is the same distance from the edges - except if the sheet were a circle)..) Thus, any point cannot be considered the center of the universe, according to the current conception of it,

Also when talking about distance we are implicitly thinking of a reference system. The International Celestial Reference System (ICRS) is the current standard, adopted by the International Astronomy Union (IAU). Its origin is located in the baricenter of the solar system and is composed of 212 very distant quasars that are practically fixed points, given its remoteness. Quasars are very powerful sources of radiation and consist of a supermassive black hole surrounded by a cloud of gas that, as it rushes into the black hole, emits energy in the form of an electromagnetic field,

Math Noether found the meaning of General Relativity: energy conservation is in connection with symmetry

Giving the coordinates of a place on the Earth's surface means using a reference system. If we add a fourth coordinate for time to the location coordinates, we will have the reference system that the mathematician Hermann Minkowski designed to represent the relativity of space and time, discovered by Einstein, which can be understood by a simple experiment that uses the Pythagorean Theorem, and that has the consequence that the time for those who observe from within a moving system is different from time for those who do so from outside the system.

Mathematics and physics are closely connected, not only thanks to the Pythagorean Theorem, as we mentioned. In 1912 Einstein struggled to achieve the Theory of General Relativity, which came after hard work and after the participation of sophisticated mathematical technology, as he himself acknowledged. It was the Emmy Noether mathematician that found the meaning of General Relativity: energy conservation is in connection with symmetry. His famous theorems on Relativity were presented in 1918. In this regard, Einstein would write to Hilbert: "I am impressed that someone can understand these matters from such a general point of view. I wouldn't do any harm to The old guard of Gothenth if I learned from her a couple of things."