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People create facts rather than investigate them; people formulate mathematical concepts rather than discover them. But why can people design different mathematical concepts, and use different tools to change the reality? According to conventional wisdom, the relationship between P and NP must be one of two possibilities: either P=NP or P≠NP. Unlike traditional approaches that base mathematical concepts on equivalent transformations—and, by extension, on the principle that correspondence remains unchanged—my theory is founded on non-equivalent transformations. By constructing a special non-equivalent transformation, I will demonstrate that for a problem Pa in the complexity class P and its corresponding problem Pb in the complexity class NP, Pa is a P non-equivalent transformation of Pb, and Pb is an NP non-equivalent transformation of Pa. That is, the relationship between Pa and Pb is neither P=NP nor P≠NP.