Hermann Grassmann Quotes (10 quotes) | Quotes of famous people

Hermann Grassmann: 10 quotes10 likes

Famous Hermann Grassmann Quotes

“As I was reading the extract from your paper in the geometric sum and difference… I was struck by the marvelous similarity between your results and those discoveries which I made even as early as 1832…
I conceived the first idea of the geometric sum and difference of two or more lines and also of the geometric product of two or three lines in that year (1832). This idea is in all ways identical to that presented in your paper. But since I was for a long time occupied with entirely different pursuits, I could not develop this idea. It was only in 1839 that I was led back to that idea and pursued this geometrical analysis up to the point where it ought to be applicable to all mechanics. It was possible for me to apply this method of analysis to the theory of tides, and in this I was astounded by the simplicity of the calculations resulting from this method.”

Hermann Grassmann

Letter to Saint-Venant (1845) as quoted by Michael J. Crowe, A History of Vector Analysis: The Evolution of the Idea of a Vectorial System (1967)

“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.”

Hermann Grassmann

Ausdehnungslehre (1844)

“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.”

Hermann Grassmann

As quoted in "Diverse Topics: The Origin of Thought Forms," The Monist (1892) Vol. 2 https://books.google.com/books?id=8akLAAAAIAAJ&pg=PA120 ed., Paul Carus, citing The Open Court Vol. II. No. 77. A Flaw in the Foundation of Geometry by Hermann Grassmann, translated from his Ausdehnungslehre

“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.”

Hermann Grassmann

Forward, as quoted by Mario Livio, Is God a Mathematician? (2009)
Ausdehnungslehre (1844)

“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.”

Hermann Grassmann

the "ideas of analysis" to which he returned, are those quoted above.
Ausdehnungslehre (1844)

“While I was pursuing the concept of geometrical product, as this idea was established by my father… I concluded that not only rectangles, but also parallelograms, may be viewed as products of two adjacent sides, provided that the sides are viewed not merely as lengths, but rather as directed magnitudes. When I joined this concept of geometrical product with the previously established idea of geometrical sum the most striking harmony resulted. Thus when I multiplied the sum of two vectors by a third coplaner vector, the result coincided (and must always coincide) with the result obtained by multiplying separately each of the two original vectors by the third… and adding together (with due attention to positive and negative values) the two products. [Thus A(B + C) = AB + AC. ]
From this harmony I came to see a whole new area of analysis was opening up which could lead to important results.”

Hermann Grassmann

Ausdehnungslehre (1844)