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I would also note that the word _theory_ has a different meaning in mathematics than in science. In science a _theory_ is a well-tested hypothesis. In mathematics _theory_ means "the study of."

Thus Number Theory is simply the study of numbers. It is a collective name for all the mathematics relating to properties of integers and the operations of traditional arithmetic. Similarly Probability Theory is the study of probability. It is a collective name for the study of the mathematics of probabilities. Consistent with this view we could refer to the study of angles and lines and such as "Geometric Theory," but mathematicians stick with the simpler "Geometry."

In mathematics, then, a theory is not a proposition, not something to prove or disprove. Saying, "I have disproved number theory" is nonsensical, on the order of saying "I have disproved physics." This is quite different from science, in which a theory is indeed a proposition (namely a statement that is either true or false), specifically one that has a great deal of evidence supporting it.

Thus the author who says "we still count even though counting is part of number theory" by way of arguing that the word _theory_ does not always indicate uncertainty about truth (e.g., in the theory of evolution) is using the word _theory_ in two unrelated senses.

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