Felix Christian Klein

In 1875, Klein married Anna Maria Carolina Hegel, the granddaughter of the noted philosopher, Georg Wilhelm Friedrich Hegel. The couple had three children; a son named Otto Klein and two daughters, Luise Süchtig nee Klein and Elisabeth Steiger nee Klein. According to some biographers, he had another daughter, whose name remains unknown.

Klein died on 22 June 1925 in Göttingen, at the age of 76.

Concepts like Klein bottle and Beltrami–Klein model continue to carry his legacy.

Felix Christian Klein was born on 25 April 1849 in Düsseldorf, at that time the capital city of Rhine Province under the Kingdom of Prussia, now the capital city of North Rhine-Westphalia state of Germany. Both his parents, Casper Klein and Sophie Elise Klein née Kayser, were Prussians.

Beginning his elementary education at home with his mother, he was enrolled at a private school at the age of six, studying there for two and half years. Later in 1857, he was shifted to the Gymnasium in Düsseldorf, from where he graduated in 1865.

Although traditionally gymnasiums paid more importance to the teachings of classics, the one he went to also laid equal stress on mathematics and science. Here under the guidance of several qualified teachers, he gained in-depth knowledge in mathematics, doing quite well in the final examination.

After graduating from the Gymnasium, he entered the University of Bonn in the winter semester of 1865-1866, wanting to become a physicist. Here he studied mathematics and natural sciences, attending ‘Seminar für die gesamten Naturwissenschaften’ consisting of physics, chemistry, geology, botany and zoology.

Although he earned distinction in botany and zoology he was especially good in physics. From the very beginning, his abilities in theoretical and experimental physics earned him praise from Julius Plücker, professor of mathematics and experimental physics.

On 22 May 1868, before Klein received his doctoral degree, Julius Plücker passed away, leaving his work on the foundations of line geometry, ‘Neue Géometrie des Raumes’ incomplete. Klein, being his closest assistant, was asked to complete the work by Alfred Clebsch, Professor of Mathematics at the University of Göttingen.

In January 1869, Felix Christian Klein left for University of Göttingen, studying there with Alfred Clebsch until August 1869. Thereafter, he moved to Berlin, where he studied until April 1870, attending Mathematisches Seminar and lectures by Kronecker. Here, he also met Norwegian mathematician Sophus Lie, and formed a close partnership with him.

Working together, Klein and Lie discovered the fundamental properties of the asymptotic lines on the Kummer surface. Later they worked on W-curves, curves invariant under a group of projective transformations.

In April 1870, Klein and Lie left for Paris, intending to study recent developments in French mathematics. But the Franco Prussian War, which broke out in July 1870, forced Klein to abandon the idea.

Volunteering for the army, he served as the medical orderly in the Prussian Army; but very shortly, on being infected with typhus, he was released from the army. While recovering from his ailments, he started preparing for his habilitation, obtaining his degree in January 1871.

In early 1871, soon after receiving his degree, Felix Christian Klein began his career as a Privatdozent at the University of Göttingen. All along, he continued with his research work, publishing two important papers on Euclidean and non-Euclidean geometry.

In October 1872, on Clebsch’s recommendation, Klein was appointed professor of mathematics at the University of Erlangen, Bavaria. Although he was only 23 years old, he had by then become known for his publications on geometry.

Traditionally, a professor, on assuming his chair, had to submit a scientific paper. Going by the custom, he published ‘Vergleichende Betrachtungen über neuere geometrische Forschungen’, which was the continuation of his earlier work on Euclidean geometry. The paper led to the formation of ‘Erlangen Program’.

To his disappointment, Klein had very few students at Erlangen. That is mainly because mathematics was being just developed in Bavaria and therefore not many students were interested in it. However, the period was not totally uneventful.

Clebsch, who was not only the cofounder, but also one of the editors of a mathematical journal called ‘Mathematische Annalen’, passed away a month after Klein joined Erlangen. In 1874, Klein entered the journal’s editorial team, subsequently overtaking the leadership of the Clebsch School.