Hermann Grassmann

Quotes

• “From the imputation of confounding axioms with assumed concepts Euclid himself, however, is free. Euclid incorporated the former among his postulates while he separated the latter as common concepts—a proceeding which even on the part of his commentators was no longer understood, and likewise with modern mathematicians, unfortunately for science, has met with little imitation. As a matter of fact, the abstract methods of mathematical science know no axioms at all.”
• “Geometry can in no way be viewed... as a branch of mathematics; instead, geometry relates to something already given in nature, namely, space. I... realized that there must be a branch of mathematics which yields in a purely abstract way laws similar to geometry.”
• “It is clear... that the concept of space can in no wise be generated by thought. ...Whoever maintains the contrary must undertake to derive the dimensions of space from the pure laws of thought—a problem which is at once seen to be impossible of solution.”
• “A work on tidal theory... led me to Lagrange's Mécanique analytique and thereby I returned to those ideas of analysis. All the developments in that work were transformed through the principles of the new analysis in such a simple way that the calculations often came out more than ten times shorter than in Lagrange's work.”
• “The concept of rotation led to geometrical exponential magnitudes, to the analysis of angles and of trigonometric functions, etc. I was delighted how thorough the analysis thus formed and extended, not only the often very complex and unsymmetric formulae which are fundamental in tidal theory, but also the technique of development parallels the concept.”
• “I feel entitled to hope that I have found in this new analysis the only natural method according to which mathematics should be applied to nature, and according to which geometry may also be treated, whenever it leads to general and to fruitful results.”

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Key facts

Born

( 1809-04-15 ) 15 April 1809, Stettin , Province of Pomerania , Kingdom of Prussia , (present-day Szczecin, Poland)

Died

26 September 1877 (1877-09-26) (aged 68), Stettin, Province of Pomerania , Kingdom of Prussia, German Empire

Alma mater

University of Berlin

Known for

Bivector Color space Grassmannian Grassmann algebra Grassmann number Grassmann's law Grassmann's laws

Awards

PhD (Hon) :, University of Tübingen (1876)

Institutions

Stettin Gymnasium

via Wikipedia infobox

Wikidata facts

Image

Hermann Graßmann.jpg

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