# Zitate von Hermann Graßmann

## Hermann Graßmann

**Geburtstag:** 15. April 1809**Todesdatum:** 26. September 1877

Hermann Günther Graßmann war ein deutscher Mathematiker, Physiker und Sprachwissenschaftler. Er gilt als eigentlicher Begründer der Vektor- und Tensorrechnung.

### Zitate Hermann Graßmann

### „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 "ideas of analysis" to which he returned, are those quoted above.

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.“

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

### „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.“

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)

### „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.“

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

Ausdehnungslehre (1844)

### „I define as a unit any magnitude that can serve for the numerical derivation of a series of magnitudes, and in particular I call such a unit an original unit if it is not derivable from another unit. The unit of numbers, that is one, I call the absolute unit, all others relative.“

Zero can never be a unit.

Definition 3. Part 1. The Elementary Conjunctions of Extensive Magnitudes. Ch. 1. Addition, Subtraction, Multiples and Fractions of Extensive Magnitudes. 1. Concepts and laws of calculation. Extension Theory Hermann Grassman, History of Mathematics (2000) Vol. 19 Tr. Lloyd C. Kannenberg, American Mathematical Society, London Mathematical Society

Ausdehnungslehre (1844)