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1. 1. Mathematics As A Science Of Patterns

   

   This book argues that mathematics is fundamentally the systematic study of patterns: mathematical claims describe structures—configurations of relations and positions—that can be instantiated in many different systems. By treating mathematical entities as positions in patterns rather than as independently existing Platonic objects, the author offers a structuralist ontology that explains both the objectivity of mathematical truth and its powerful applicability in the empirical sciences; the work also examines how mathematical knowledge arises through abstraction, idealization, and the recognition of recurring structural features, and considers consequences for foundations, explanation, and the practice of mathematics.

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