Einstein's theory of relativity, both special relativity and general relativity, can be mathematically formulated and described using a set of equations. These equations have been extensively tested and verified through various experiments and observations. However, it is important to note that in science, theories are not "proven" in the same way that mathematical theorems are proven.
In mathematics, a proof establishes the truth of a statement based on a logical deduction from a set of axioms and previously proven theorems. The conclusions derived from mathematical proofs are absolute and irrefutable within the given mathematical framework.
In contrast, scientific theories, including Einstein's theory of relativity, are developed to explain and describe natural phenomena based on observations, experiments, and mathematical models. They are subject to continuous testing, refinement, and evaluation in light of new evidence.
Einstein's theories of relativity have been supported by numerous experimental tests and observational data, including the famous confirmation of the bending of light during a solar eclipse, the precision of atomic clocks in satellites, and the detection of gravitational waves. The consistency of these experimental results with the predictions of Einstein's equations provides strong empirical support for the theory.
However, it is worth noting that science always remains open to revision and refinement based on new evidence or the development of more comprehensive theories. While Einstein's theory of relativity has withstood many tests and is widely accepted by the scientific community, it is still subject to ongoing research and investigation.
Therefore, while the mathematical formulation of Einstein's theory of relativity provides a powerful framework for understanding and describing the behavior of spacetime and gravity, it is ultimately the empirical evidence and experimental confirmation that lend support to its validity.