In science, there is theory and hypothesis, and evidence supporting these things. There is no proof, only probability.
I can prove something to you, and that works at the level of psychology and belief, it is not mathematical. Even logical and mathematical proof depend on convincing you that the logic is sound. The most carefully constructed logical or mathematical proof may be incorrect, the logic erroneous. Even with the correct logic, something that can not necessarily be established in most real world complex cases, the argument may yield incorrect results, as the premises may be wrong. In the end, the reader of the logical argument must be persuaded that the logic is sound, the mathematics correct. Again, in the end, there are no proofs, in a platonic sense.
“In the empirical sciences, which alone can furnish us with information about the world we live in, proofs do not occur, if we mean by ‘proof’ an argument which establishes once and for ever the truth of a theory.” The Open society and its Enemies by Karl Popper
The Open Society and Its Enemies; Karl Raimund Popper, Alan Ryan, E. H. Gombrich
Princeton University Press, 2013 – Philosophy – 755 pages