Mathematical developments involving the Christoffel symbols provided the essential framework for tensor calculus and, ultimately, the general theory of relativity. Born in 1829 in Monschau, Kingdom of Prussia, Elwin Bruno Christoffel spent his career navigating the academic landscapes of Germany and Switzerland, bridging the nineteenth-century transition toward rigorous, modern differential geometry through his deep engagement with complex analysis and potential theory.
Early Education and Research
Christoffel attended the Dreikönigsgymnasium and the Friedrich-Wilhelm-Gymnasium before enrolling at the Frederick William University in Berlin in 1850. Under the guidance of Gustav Dirichlet, Martin Ohm, Ernst Kummer, and Heinrich Gustav Magnus, he refined his expertise in physics and mathematics. Following his 1856 doctorate, he spent three years in isolation at Monschau, where he studied the works of Augustin-Louis Cauchy and Bernhard Riemann while publishing his initial papers on differential geometry.
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In 1859, he returned to the University of Berlin as a lecturer. He accepted a chair at ETH Zurich in 1862, establishing a new mathematics institute. His career included a brief tenure at the Royal College for Vocational Studies in Berlin beginning in 1869, followed by a move to the University of Strasbourg in 1872. He remained at Strasbourg until his retirement in 1892, where he cultivated a robust mathematics department and mentored students.
Contributions to Geometry and Analysis
His primary influence on mathematics stems from his 1869 paper in Crelle’s Journal, which introduced covariant differentiation and the components known as Christoffel symbols. He also formalized the Christoffel–Darboux formula for orthogonal polynomials and extended Gaussian quadrature methods. In complex analysis, the Schwarz–Christoffel mapping stands as a constructive application of the Riemann mapping theorem, finding utility in elliptic functions and physics.
Fast facts
- Born: 1829, Monschau
- Died: 1900, Strasbourg
- Citizenship: Kingdom of Prussia
- Education: Frederick William University Berlin
- Key fields: Differential geometry, complex analysis
- Notable work: Christoffel symbol
- Religion: Catholicism
- Languages: German
Questions readers ask
What is the primary mathematical legacy of Elwin Bruno Christoffel?
He developed the Christoffel symbols and covariant differentiation, which became the mathematical foundation for tensor calculus and the general theory of relativity.
Did Christoffel hold positions at multiple universities?
Yes, he held academic roles at the University of Berlin, ETH Zurich, the Royal College for Vocational Studies, and the University of Strasbourg.
Achievements
- Notable work: Christoffel symbol
- Notable work: Christoffel–Darboux formula
- Notable work: Schwarz–Christoffel mapping
- Held posts at Royal College for Vocational Studies, ETH Zurich and Frederick William University Berlin
- Fields: differential geometry
