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English: Ontology is a prerequisite for Physics, but not for Mathematics. It means Physics is ultimately concerned with descriptions of the real world, while mathematics is concerned with abstract patterns, even beyond the real world. Thus Physics statements are synthetic, while Mathematical statements are analytic. Mathematics contains hypotheses, while Physics contains theories. Mathematical statements have to be only logically true, while Physics statements must match observed and experimental data. The distinction is clear-cut, but not always obvious. Mathematical physics is the application of Mathematics to Physics. The problems in this field start with a "mathematical model of a physical situation" and a "mathematical description of a physical law". Every mathematical statement used for a solution has a hard-to-find physical meaning; the final mathematical solution has an easier-to-find meaning.