In its rigorous sense, “proof” applies only to logic and mathematics. We can prove that 2 + 2 = 4, just as we can prove that “the whole is greater than the part.” And yet science proceeds by inference, rather than by the deduction so characteristic of mathematical proof.
A series of observations is accumulated, forcing the deeper questions: What must be true if we are to explain what is observed? What “big picture” of reality offers the best fit to what is actually observed? What is the best explanation of these observations?