26 Facts About Hermann Grassmann

Hermann Grassmann's work preceded and exceeded the concept which is known as a vector space.

Hermann Grassmann introduced the Grassmannian, the space which parameterizes all k-dimensional linear subspaces of an n-dimensional vector space V In linguistics he helped free language history and structure from each other.

Hermann Grassmann was the third of 12 children of Justus Gunter Grassmann, an ordained minister who taught mathematics and physics at the Stettin Gymnasium, where Hermann was educated.

In 1834 Hermann Grassmann began teaching mathematics at the Gewerbeschule in Berlin.

One of the many examinations for which Hermann Grassmann sat required that he submit an essay on the theory of the tides.

Hermann Grassmann went on to develop those methods in his Die lineale Ausdehnungslehre, ein neuer Zweig der Mathematik and its later revision Die Ausdehnungslehre: Vollstandig und in strenger Form bearbeitet.

In 1844, Hermann Grassmann published his masterpiece commonly referred to as the Ausdehnungslehre, which translates as "theory of extension" or "theory of extensive magnitudes".

Hermann Grassmann then showed that once geometry is put into the algebraic form he advocated, the number three has no privileged role as the number of spatial dimensions; the number of possible dimensions is in fact unbounded.

Hermann Grassmann then develops the theory of linear independence in a way that is astonishingly similar to the presentation one finds in modern linear algebra texts.

Hermann Grassmann defines the notions of subspace, linear independence, span, dimension, join and meet of subspaces, and projections of elements onto subspaces.

When Hermann Grassmann submitted it to apply for a professorship in 1847, the ministry asked Ernst Kummer for a report.

In 1846, Mobius invited Hermann Grassmann to enter a competition to solve a problem first proposed by Leibniz: to devise a geometric calculus devoid of coordinates and metric properties.

Mobius, as one of the judges, criticized the way Hermann Grassmann introduced abstract notions without giving the reader any intuition as to why those notions were of value.

In 1853, Hermann Grassmann published a theory of how colors mix; his theory's four color laws are still taught, as Hermann Grassmann's laws.

In 1861, Hermann Grassmann laid the groundwork for Peano's axiomatization of arithmetic in his Lehrbuch der Arithmetik.

In 1862, Hermann Grassmann published a thoroughly rewritten second edition of A1, hoping to earn belated recognition for his theory of extension, and containing the definitive exposition of his linear algebra.

Hermann Grassmann then entered into a dispute with Grassmann about which of the two had thought of the ideas first.

Hermann Grassmann had published his results in 1844, but Saint-Venant claimed that he had first developed these ideas in 1832.

Hankel was the first to recognise the significance of Hermann Grassmann's long-neglected writings and was strongly influenced by them.

Comprehension of Hermann Grassmann awaited the concept of vector spaces, which then could express the multilinear algebra of his extension theory.

Hermann Grassmann wrote books on German grammar, collected folk songs, and learned Sanskrit.

Hermann Grassmann wrote a 2,000-page dictionary and a translation of the Rigveda.

In modern studies of the Rigveda, Hermann Grassmann's work is often cited.

Hermann Grassmann noticed and presented a phonological rule that exists in both Sanskrit and Greek.

Hermann Grassmann's discovery was revolutionary for historical linguistics at the time, as it challenged the widespread notion of Sanskrit as an older predecessor to other Indo-European languages.

Hermann Grassmann was elected to the American Oriental Society and in 1876 he received an honorary doctorate from the University of Tubingen.