Hermann Grassmann

Hermann Grassmann was a German polymath, 1809-1877. Among many other accomplishments, an early inventor of linear algebra and notably of Grassmann algebra (exterior algebra, hence superalgebra), which he laid out in his book *Ausdehnungslehre*

From Drew Armstrong:

Perhaps owing to the abstraction of his work, he was not recognized by the mathematical community and was more famous during his lifetime for his work in philology (including a translation of the Rig Veda). Despite his failure to achieve mathematical success, Grassmann never doubted that his work was significant. Here’s a striking quote from the preface of the 1862 second edition of the

Ausdehnungslehre:I remain completely confident that the labour I have expended on the science presented here and which has demanded a significant part of my life as well as the most strenuous application of my powers, will not be lost. It is true that I am aware that the form which I have given the science is imperfect and must be imperfect. But I know and feel obliged to state (though I run the risk of seeming arrogant) that even if this work should again remain unused for another seventeen years or even longer, without entering into the actual development of science, still that time will come when it will be brought forth from the dust of oblivion and when ideas now dormant will bring forth fruit. I know that if I also fail to gather around me (as I have until now desired in vain) a circle of scholars, whom I could fructify with these ideas, and whom I could stimulate to develop and enrich them further, yet there will come a time when these ideas, perhaps in a new form, will arise anew and will enter into a living communication with contemporary developments. For truth is eternal and divine.

(Translation from Michael Crowe,

A History of Vector Analysis)

Grassmann’s ideas were then finally picked up by William Kingdon Clifford who turned Grassmann algebras into *Clifford algebras* in

- William Clifford,
*Applications of Grassmann’s extensive algebra*, American Journal of Mathematics 1 (4): 350–358. (1878). doi:10.2307/2369379.

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Last revised on March 4, 2015 at 11:44:49. See the history of this page for a list of all contributions to it.