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?

  • What do you mean by "assume"? You can assume anything, with or without support, but you may be wrong. If you predict something using a mathematical model, you can't be sure it's correct. You might have very good reason to expect it to be correct, but that's not the same thing. You might assume it as a basis for further reasoning, but it still might not be correct. – David Thornley Nov 16 '18 at 21:30
  • Generally empiricism is used to 'prove' a theory. The theory is often mathematical in origin. But clearly the experiment is intended to prove the theory. – Richard Nov 16 '18 at 23:30

Of course YES.

See Dirac's prediction (1928) of the existence of the positron (observed 1929) as well as Higgs boson, predicted in 1964 and whose existence has been confirmed in 2013.

  • Thanks for the answer but i didn't want examples. – Aayush Aggarwal Nov 16 '18 at 12:23
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    @AayushAggarwal - "can we assume the being of something in a way based on mathematical proofs?" The answer is YES. See Dirac mathematical prediction of the positron as a solution of an equation. – Mauro ALLEGRANZA Nov 16 '18 at 13:52
  • Dirac also predicted the magnetic monopole, as I remember, and nobody's found evidence of them. – David Thornley Nov 16 '18 at 21:31

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.)

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