The Riemann Legacy

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The book explores the profound impact of small domains on the entirety of Riemann surfaces and analytic manifolds, emphasizing Riemann's insights into meromorphic functions and their singularities. It discusses the ongoing relevance of Euclidean space, challenging the notion that it is the only "real" space, while acknowledging its comforting familiarity. The text highlights Riemann space as a unique geometrical framework that is locally Euclidean, making it significant in both mathematics and physics, particularly in applications like mechanics involving submanifolds.