"One may say without great exaggeration that Grassmann invented linear algebra and, with none at all, that he showed how properly to apply it to geometry. ...He ...anticipated in its most important aspects Peano's treatment of the natural numbers, published 28 years later. ...A feature of Grassmann's work, far in advance of the times, is the tendency towards the use of the implicit definition. ...The definition of a linear space (or vector space) came into mathematics, in the sense of becoming widely known, around 1920, when Hermann Weyl and others published formal definitions. ...Grassmann did not put down a formal definition—again, the language was not available—but there is no doubt that he had the concept."
Quote Details
Added by wikiquote-import-bot
Unverified quote
0 likes
PolymathsMathematicians from GermanyPhysicists from GermanyEducators from GermanyLinguists from Germany
Original Language: English
Available Languages (1)
Sources
Desmond Fearnley-Sander, "Hermann Grassmann and the Creation of Linear Algebra" (1979)
https://en.wikiquote.org/wiki/Hermann_Grassmann
Revision History
No revisions have been submitted for this quote.
Categories
Hermann Grassmann
Hermann Günther Grassmann (April 15, 1809 – September 26, 1877) was a German polymath, best known as a mathematician and linguist. His mathematical work was little noted until he was in his sixties. He was also a physicist, neohumanist, general scholar, and publisher.
19 quotes on TrueQuotesView all quotes by Hermann Grassmann →
Related Quotes
"As I was reading the extract from your paper in the geometric sum and difference... I was struck by the marvelous sim…"
"From the imputation of confounding axioms with assumed concepts Euclid himself, however, is free. Euclid incorporated…"
"Geometry can in no way be viewed... as a branch of mathematics; instead, geometry relates to something already given …"
"It is clear... that the concept of space can in no wise be generated by thought. ...Whoever maintains the contrary mu…"
"The first impulse came from the consideration of negatives in geometry; I was accustomed to viewing the distances AB …"
"While I was pursuing the concept of geometrical product, as this idea was established by my father... I concluded tha…"
"A work on tidal theory... led me to Lagrange's Mécanique analytique and thereby I returned to those ideas of analysis…"
"The concept of rotation led to geometrical exponential magnitudes, to the analysis of angles and of trigonometric fun…"
"I feel entitled to hope that I have found in this new analysis the only natural method according to which mathematics…"
"The concept of centroid as sum led me to examine Möbius' Barycentrische Calcul, a work of which until then I knew onl…"