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Hermann Guenther Grassmann was one of the most remarkable personalities in 19^th-century science. A "small-town genius", he developed a groundbreaking n-dimensional algebra of space and contributed to a revolution in the understanding of mathematics. His work fascinated great mathematicians such as W. R. Hamilton, J. W. Gibbs and A. N. Whitehead. This intellectual biography traces Grassmann's steps towards scientific brilliance by untangling a complicated web of influences: the force of unsolved problems in mathematics, Friedrich Schleiermacher's Dialectic, German Romanticism and life in 19^th-century Prussia. The book also introduces the reader to the details of Grassmann's mathematical work without neglecting his achievements in Sanskrit philology and physics. And, for the first time, it makes many original sources accessible to the English-language reader.