Hermann Grassmann

Hermann Günther Grassmann (, ; 15 April 1809 – 26 September 1877) was a German polymath known in his day as a linguist and now also as a mathematician. He was also a physicist, general scholar, and publisher. His mathematical work was little noted until he was in his sixties. His work preceded and exceeded the concept which is now known as a vector space. He 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.

Biography

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

Grassmann was an undistinguished student until he obtained a high mark on the examinations for admission to Prussian universities. Beginning in 1827, he studied theology at the University of Berlin, also taking classes in classical languages, philosophy, and literature. He does not appear to have taken courses in mathematics or physics.

Although lacking university training in mathematics, it was the field that most interested him when he returned to Stettin in 1830 after completing his studies in Berlin. After a year of preparation, he sat the examinations needed to teach mathematics in a gymnasium, but achieved a result good enough to allow him to teach only at the lower levels. Around this time, he made his first significant mathematical discoveries, ones that led him to the important ideas he set out in his 1844 paper ''Die lineale Ausdehnungslehre, ein neuer Zweig der Mathematik'', here referred to as A1, later revised in 1862 as ''Die Ausdehnungslehre: Vollständig und in strenger Form bearbeitet'', here referred to as A2.

In 1834 Grassmann began teaching mathematics at the Gewerbeschule in Berlin. A year later, he returned to Stettin to teach mathematics, physics, German, Latin, and religious studies at a new school, the Otto Schule. Over the next four years, Grassmann passed examinations enabling him to teach mathematics, physics, chemistry, and mineralogy at all secondary school levels.

In 1847, he was made an "Oberlehrer" or head teacher. In 1852, he was appointed to his late father's position at the Stettin Gymnasium, thereby acquiring the title of Professor. In 1847, he asked the Prussian Ministry of Education to be considered for a university position, whereupon that Ministry asked Ernst Kummer for his opinion of Grassmann. Kummer wrote back saying that Grassmann's 1846 prize essay (see below) contained "commendably good material expressed in a deficient form." Kummer's report ended any chance that Grassmann might obtain a university post. This episode proved the norm; time and again, leading figures of Grassmann's day failed to recognize the value of his mathematics.

Starting during the political turmoil in Germany, 1848–49, Hermann and his brother Robert published a Stettin newspaper, '' Deutsche Wochenschrift für Staat, Kirche und Volksleben'', calling for German unification under a constitutional monarchy. (This eventuated in 1871.) After writing a series of articles on constitutional law, Hermann parted company with the newspaper, finding himself increasingly at odds with its political direction.

Grassmann had eleven children, seven of whom reached adulthood. A son, Hermann Ernst Grassmann, became a professor of mathematics at the University of Giessen.

Mathematician

One of the many examinations for which Grassmann sat required that he submit an essay on the theory of the tides. In 1840, he did so, taking the basic theory from Laplace's '' Traité de mécanique céleste'' and from Lagrange

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