Hermann Grassmann

Early Life and Education

Hermann Günther Grassmann was born on April 15, 1809, in Stettin, Pomerania. He studied at the Gymnasium there and later went to the University of Jena and the University of Berlin. Grassmann became interested in many subjects, especially mathematics, physics, and languages.

Work in Mathematics

Grassmann made big contributions to mathematics, even though many people did not understand his work at first. His ideas were very new and ahead of their time. He created the idea of a vector space, which is important in modern math. He also developed something called the Grassmannian, which helps us understand patterns in math better.

Language Studies

Besides math, Grassmann was also known for his work on languages. He helped improve how we study and understand language history and structure. His work made these subjects stronger and clearer.

Later Life and Legacy

Grassmann worked as a teacher and a publisher. He kept studying math, physics, and languages all his life. Even though he did not get much recognition during his lifetime, his ideas later became very important in many areas of science. He passed away on September 26, 1877.

Biography

Hermann Grassmann was one of twelve children born to a teacher and minister in Stettin, a city in Germany. He went to school there and later studied theology in Berlin, though he did not study mathematics or physics formally.

Even without formal training, Grassmann grew to love mathematics and made important discoveries when he was young. He began teaching math in schools in Berlin and Stettin and eventually became a head teacher and a professor. Sadly, many experts at the time did not recognize the value of his ideas.

Grassmann also had a family. He married in 1849 and had eleven children, seven of whom grew up. One of his sons also became a mathematics professor.

Mathematician

In 1840, Hermann Grassmann wrote an essay about the tides. He used ideas from other scientists and special math methods he had thought about since 1832. This essay showed the first signs of what we now call linear algebra and vector spaces.

In 1844, Grassmann published a major work called Ausdehnungslehre, meaning "theory of extension." He wanted to create a new foundation for all mathematics. He showed that geometry could be built using algebra, and that space could have more than three dimensions. His work included early ideas that are important in modern math. Unfortunately, his ideas were too new and were not appreciated during his lifetime. He kept writing more papers hoping others would see the value in his work.

Response

In the 1840s, most mathematicians did not understand Grassmann's new ideas. Later, in the 1860s and 1870s, other mathematicians began thinking about similar concepts, but Grassmann was no longer interested in math.

One mathematician, Adhémar Jean Claude Barré de Saint-Venant, created a system close to Grassmann's in 1845. He and Grassmann argued about who first came up with the ideas.

Hermann Hankel was one of the first to see the value in Grassmann's work. In 1867, Hankel wrote about Grassmann's algebras and quaternions.

In 1872, Victor Schlegel published a book using Grassmann's methods to explain geometry. Felix Klein reviewed it but was not impressed.

It wasn’t until later that mathematicians fully understood Grassmann’s work, especially after the idea of vector spaces was introduced. In 1995, an English translation of some of Grassmann’s works was published. To learn more about how Grassmann’s ideas are used today, you can read The Road to Reality by Roger Penrose.

Linguist

Hermann Grassmann spent his later years studying languages. After his math work wasn’t popular, he focused on historical language studies and the language Sanskrit. He wrote books on German grammar, collected folk songs, and made a large dictionary and translation of the Rigveda, an ancient collection of poems. His work on the Rigveda is still used by scholars today.

Grassmann also found an important pattern in the sounds of Sanskrit and Greek, called Grassmann’s law. This discovery changed ideas about language family trees, showing that German could be seen as “older” in some ways than Sanskrit. For his language work, he was honored by groups like the American Oriental Society and received a special degree from the University of Tübingen.

Publications

Hermann Grassmann wrote many important books and papers. Some of his well-known works include:

• In 1844, he published Die Lineale Ausdehnungslehre in German.
• In 1847, he wrote Geometrische Analyse in German.
• In 1861, he created Lehrbuch der Mathematik für höhere Lehranstalten, a math book for schools.

His major work, Die Ausdehnungslehre, was completed in 1862. An English version called Extension Theory was published much later in 2000.

Grassmann also worked on ancient languages and published a dictionary for the Rig-Veda in 1873, followed by a translation of the Rig-Veda in 1876–1877.