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).

WORKS

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

REFERENCE

Klein. F. Lektsii o razvitii matematiki ν 19 stoletii, part I. Moscow-Leningrad, 1937. (Translated from German.) [7–755-l]
References in periodicals archive ?
Schleiermacher, the mathematicians Justus and Hermann Grassmann, the process metaphysicians C.S.
It is also shown here how Justus and Hermann Grassmann developed mathematics on the basis of Schelling's arguments against Kant.
On the influence of this work on mathematics and the philosophy of mathematics, see Mircea Radu, "Justus Grassmann's Contributions to the Foundations of Mathematics: Mathematical and Philosophical Aspects", Historia Mathematica, 27 (2000): 4-35, Hans-Joachim Petsche, Hermann Grassmann: Biography, trans.
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.
Swabey (London: Dover, 2004), was strongly influenced by Schellingian thought through the influence on him of Hermann Grassmann.
(198) See Esposito, Schelling's Idealism and Philosophy of Nature, Heuser-Kessler, Die Produktivit'dt der Natur: Schellings Naturphilosophie und das neue Paradigma der Selbsorganization in den Naturwissenschaften and Marie-Luise Heuser, "The Significance of Naturphilosphe for Justus and Hermann Grassmann", From Past to Future: Grassmann's Work in Context, ed.
Petsche, H.-J.; Hermann Grassmann. Biography, Birkhauser, Basel, 2009, 306 pp.
Hamilton [17], Hermann Grassmann [13], Giuseppe Peano [22] y Benjamin Peirce [23].
12 Eight occurrences of krt- are listed in Hermann Grassmann, Worterbuch zum Rig-Veda (Wiesbaden: Otto Harrassowitz, 1964 [rpt.]), 346, most with the preverbs vi- or nis-.