Theories are also necessary for facts to be established. An example of this is that theorists had predicted the existence of the Higgs boson which is a particle in the Standard Model of particle physics for more than five decades ago, which then encouraged the experimental physicists to search for the Higgs. And now the existence of the Higgs has been established as a fact. Another example is that the theory of gravitation predicted the behavior of objects on the moon and other planets long before the activities of spacecraft and astronauts confirmed them. In the previous two examples, the theories helped narrow facts that are found from a wide range of experiment and researches to a narrower scope providing few simple rules that summarize hundreds of observations. These rules make scientists have a focused area of research to examine.Some theories that have been regarded and accepted for centuries had a great impact on the new compelling theories supported by facts but can a theory supersede and replace the need for data and testing? Deducing a theory in mathematics for example does not require any objective facts gathered from our surroundings in order for it to be true. In a sense, Mathematics is true without reference to reality. Purely analytic statements can be demonstrated a priori. A proof of a theorem cannot involve experiments or other observed evidence in the same way such evidence is used to support scientific theories. In the previous two examples, the variables in the theories were directly observable which led to the theories making specific, clear predictions about the future.