Universidad hermann grassmann biography

In modern Rigvedic studies Grassmann's work is often cited. In the third edition of his dictionary to Rigveda was issued. Grassmann also discovered a sound law of Indo-European languages , which was named Grassmann's Law in his honor. Extensive online bibliography , revealing substantial contemporary interest in Grassmann's life and work.

References each chapter in Schubring. From Wikipedia, the free encyclopedia. For the surname, see Grassmann surname. Stettin, German Empire. Categories : births deaths People from Szczecin 19th-century German mathematicians Algebraists Linguists from Germany German mathematicians German physicists People from the Province of Pomerania Color scientists Humboldt University of Berlin alumni Translators from Sanskrit 19th-century translators.

Namespaces Article Talk. Views Read Edit View history. In other projects Wikimedia Commons Wikiquote. This page was last edited on 12 December , at UTC. By using this site, you agree to the Terms of Use and Privacy Policy. Prussia , Germany. University of Berlin. Multilinear algebra , Grassmannian , Exterior algebra. The definition of a linear space vector space In fact, such a definition had been given thirty years previously by Peano , who was thoroughly acquainted with Grassmann's mathematical work.

The plane is the system of the second step If one adds a third independent direction, then the whole infinite space system of the third step is produced One cannot here go further than up to three independent directions rules of change , while in the pure theory of extension their quantity can increase up to infinity. Grassmann invented what is now called exterior algebra.

This was joined to Hamilton 's quaternions by Clifford in References show. Biography in Encyclopaedia Britannica. Autographs and Unknown Documents. Text in German and English. G Schubring ed. Nauk No. L G Biryukova and B V Biryukov, Algorithmic problems in the 20 th century and the formation of axiomatics of fundamental algebraic structures : the contribution of Hermann and Robert Grassmann Russian , in Methodological analysis of the foundations of mathematics Russian 'Nauka', Moscow, , - Monthly 86 10 , - Monthly 89 3 , - I Grattan-Guinness, Where does Grassmann fit in the history of logic?

Second Kazakhstan Interuniv.

Universidad hermann grassmann biography

SSR, Alma-Ata, , -- 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 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.

In 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 , he was made an "Oberlehrer" or head teacher. In , he was appointed to his late father's position at the Stettin Gymnasium, thereby acquiring the title of Professor. In , 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 prize essay see below contained "commendably good material expressed in a deficient form.

This episode proved the norm; time and again, leading figures of Grassmann's day failed to recognize the value of his mathematics. This eventuated in 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.

One of the many examinations for which Grassmann sat required that he submit an essay on the theory of the tides. This essay, first published in the Collected Works of —, contains the first known appearance of what is now called linear algebra and the notion of a vector space. In , Grassmann published his masterpiece A1 commonly referred to as the Ausdehnungslehre , which translates as "theory of extension" or "theory of extensive magnitudes".

Since A1 proposed a new foundation for all of mathematics, the work began with quite general definitions of a philosophical nature. 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.

Fearnley-Sander describes Grassmann's foundation of linear algebra as follows: [ 1 ]. The definition of a linear space vector space [ In fact, such a definition had been given thirty years previously by Peano , who was thoroughly acquainted with Grassmann's mathematical work. Grassmann did not put down a formal definition — the language was not available — but there is no doubt that he had the concept.

Beginning with a collection of 'units' e 1 , e 2 , e 3 , He then develops the theory of linear independence in a way that is astonishingly similar to the presentation one finds in modern linear algebra texts. He defines the notions of subspace , linear independence , span , dimension , join and meet of subspaces, and projections of elements onto subspaces.

One should keep in mind that in Grassmann's day, the only axiomatic theory was Euclidean geometry , and the general notion of an abstract algebra had yet to be defined. For more details, see Exterior algebra. A1 was a revolutionary text, too far ahead of its time to be appreciated. When Grassmann submitted it to apply for a professorship in , the ministry asked Ernst Kummer for a report.

Kummer assured that there were good ideas in it, but found the exposition deficient and advised against giving Grassmann a university position. Over the next odd years, Grassmann wrote a variety of work applying his theory of extension, including his Neue Theorie der Elektrodynamik and several papers on algebraic curves and surfaces , in the hope that these applications would lead others to take his theory seriously.

In , Grassmann published a theory of how colors mix; his theory's four color laws are still taught, as Grassmann's laws. Disappointed at his inability to be recognized as a mathematician, Grassmann turned to historical linguistics. He wrote books on German grammar, collected folk songs, and learned Sanskrit. His dictionary and his translation of the Rigveda still in print were recognized among philologists.

He devised a sound law of Indo-European languages, named Grassmann's Law in his honor. Die lineare Ausdehnungslehre. Leipzig : Wiegand. English translation, , by Lloyd Kannenberg, A new branch of mathematics. Chicago: Open Court. This is A1. Berlin : Enslin. Die Ausdehnungslehre. Berlin: Enslin. English translation, , by Lloyd Kannenberg, Extension Theory.

American Mathematical Society. This is A2. Excerpt translated by D. Leipzig: Brockhaus. Translation in two vols. Gesammelte mathematische und physikalische Werke, in 3 vols. Friedrich Engel ed. Leipzig: B. Reprinted , New York: Johnson. Monthly