I wanted to know that, what can we assume as the result of some experiment which we have not conducted on the basis of mathematical proofs? I mean, in general, equations are created after analyzing the real things that we have studied. But can we assume the being of things in a way based on mathematical proofs?
I wanted to know that can we assume the result of some experiment which we have not conducted on the basis of mathematical proofs?
The answer is yes, assuming that the experimenter starts with good data. My example here is the discovery of the planet Neptune (1846). Astronomers had noticed errors in their description of the orbit of the planet Uranus, at that time the farthest known.
The errors could be explained by the presence of a farther planet. Astronomers worked on a likely location for the new object.
When the calculations were finished, they put the new planet behind the sun in relation to the earth. So the location of the new planet could not be known; it could only be predicted. But when that part of the sky became visible again, the planet was there, as the mathematics had shown.
Source: Pannekoek, A. 1969. A history of astronomy (New York: Barnes and Noble, Inc.)