Hermann Grassmann

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Grassmann, Hermann


Born Apr. 15, 1809, in Stettin; died there Sept. 26, 1877. German mathematician. Also worked in physics and philology.

Grassmann’s work The Calculus of Extension (1844) gave the first systematic construction of the study of n-dimensional Euclidean space and led to the development of vector analysis and tensor calculus. However, because of the abstract exposition and unusual terminology, the work was difficult to understand. In A Textbook of Arithmetic, Grass-mann attempted a strict exposition of the arithmetic of integers and in the process explained the role of definition by induction. In physics, he wrote on acoustics and the magnetic interaction of currents. Grassmann’s general ideas about abstract vector spaces led him to the discovery of an important idea—the possibility of studying color sensations as three-dimensional vectors, which is the basis for the modern study of color. He established the laws (1853) of color mixing. Grassmann also compiled a comprehensive dictionary of the hymns of Rig Veda (a monument of ancient Indian literature).


Gesammelte mathematische und physikalische Werke, vols. 1–3. Leipzig, 1894–1911.


Klein. F. Lektsii o razvitii matematiki ν 19 stoletii, part I. Moscow-Leningrad, 1937. (Translated from German.) [7–755-l]
References in periodicals archive ?
The constructions of mathematics are a special instance of such synthetic activity, and in "On Construction in Philosophy" Schelling offered far reaching revisions of Kant's philosophy of mathematics based on this revised notion of construction, revisions which inspired the work of Justus and Hermann Grassmann.
Schleiermacher, the mathematicians Justus and Hermann Grassmann, the process metaphysicians C.
It is also shown here how Justus and Hermann Grassmann developed mathematics on the basis of Schelling's arguments against Kant.
Whitehead was deeply influenced by Hermann Grassmann whose work was the point of departure for Whitehead's first major work, A Treatise on Universal Algebra.
On the dialectic in Justus and Hermann Grassmann, see Albert C.
Hamilton [17], Hermann Grassmann [13], Giuseppe Peano [22] y Benjamin Peirce [23].