1912 - Copley medal

Felix Christian Klein is appreciated and well-known for his significant works in the field of Geometry. He obtained his Doctorate degree from the University of Bonn in 1868 under the supervision of Julius Plücker. He served as a professor in many prestigious universities like University of Gottingen, University of Erlangen and also at Technische Hochschule (Institute of Technology) in Munich. He set up a mathematical research center at Göttingen, which became the most respected mathematical centers in the world. His works on Geometry brought a breakthrough in his career. One of his famous contributions includes the ‘Erlanger Programm’. Functional theory was also one his major works and became widely accepted all over the world. His discovery on non-Euclidean geometry was one of the best researches that contributed immensely in the field of Mathematics. Klein also devised mathematical curriculums in secondary schools, which were accepted worldwide. In 1885, he was elected as a Fellow of the ‘Royal Society’. Read on to know more about this great mathematician.

**Childhood And Early Life**

**Education And Career**

In 1865, Klein joined the University of Bonn to study Physics and Mathematics. He was appointed as a laboratory assistant to Julius Plücker in 1866, while continuing his studies at the university. Initially, he wanted to pursue a career as a physicist but after being influenced by the great Mathematician Julius Plücker, he chose a career in the field of Mathematics. Under the supervision of Plücker, Klein received his Doctorate from the University of Bonn in 1868.

Unfortunately, Plücker died that year, leaving behind his important work on the foundations of geometry. It was Klein, who finished Plücker’s incomplete work. Klein worked as a medical orderly for a short period of time until 1871, and was appointed as a lecturer at Göttingen soon after. There he worked with the geometer, Alfred Clebsch, who was the head of the mathematics department at the University of Göttingen. In 1872, he was appointed as professor of mathematics at Erlangen on Clebsch’s recommendation. He then accepted a post at Technische Hochschule (Institute of Technology) in Munich in 1875. In 1880, Klein was appointed as professor at the University of Leipzig. He then joined at the University of Göttingen in 1886 and taught subjects like Mechanics and Potential Theory until his retirement in 1913.

**Researches**

- With the help of Weierstrass’ theory of elementary divisors, Klein established the second degree line complexes.
- While he was at the University of Erlangen, he represented his views from his ‘Erlanger Programm’ in 1872. His synthesis of geometry that included the study of the properties of a space, is invariant under a given group of transformations gave rise to the ‘Erlanger Programm’. His approach to geometry was accepted widely as the standard view.
- He also combined his ideas on W-curves with the Norwegian Mathematician, Sophus Lie. Together they also discovered the fundamental properties of the asymptotic lines present on the Kummer surface.
- Klein published two papers on non-Euclidean geometry in the year 1871. He proved that Non-Euclidean geometry was consistent, if and only if Euclidean geometry was consistent. This discovery enabled non-Euclidean geometry to become similar to Euclidean geometry.
- His major contribution to Mathematics was his work on functional theory. In 1882, he presented a paper on the basis of treating functional theory in the geometric way by connecting conformal mappings and potential theory. Using fluid dynamics, he was able to incorporate physical ideas into his work.
- Klein worked on solving general equations of the fifth degree by using transcendental methods. He applied views of Charles Hermite and Leopold Kronecker into his methods and solved the problems with the icosahedron group. This research led him to work on elliptic modular functions.
- Klein connected geometric and algebraic results in order to develop the theory of automorphic functions, which he published in his book on icosahedron, in 1884.
- In 1900, Klein took to advocating in modernizing mathematic instructions.
- In 1905, he introduced the rudiments of calculus and the functional concepts in the secondary schools in Germany. Under Klein’s direction, the German branch of the commission published several volumes for teaching mathematics at all levels of Germany.

**Publications**

**Achievements**

**Personal Life**

**Death**

FELIX CHRISTIAN KLEIN TIMELINE

Klein was born on 25 April.

Klein joined the University of Bonn.

He became a laboratory assistant to Julius Plücker.

Klein received his Ph. D from the University of Bonn.

He represented his views from the ‘Erlanger Programm’.

He became the editor of ‘Mathematische Annalen’ or ‘Annals of Mathematics’.

Klein married Anne Hegel. He also accepted the chair at the Institute of Technology in Munich.

He became the professor at the University of Leipzig.

He was elected as a Fellow of the ‘Royal Society’.

Klein accepted a chair at the University of Göttingen.

He began to supervise the ‘Encyklopädie der mathematischen Wissenschaften mit Einschluss iher Anwendungen’ or ‘Encyclopedia of Pure and Applied Mathematics’.

He was made the Chairman of the ‘International Commission on Mathematical Instruction’ at the Rome ‘International Congress of Mathematicians’.

He was awarded the ‘Copley Medal of the Society’.

Klein retired from the University of Göttingen.

Klein died on 22 June.

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