Person: Halphen, George Henri
George-Henri Halphen was a French mathematician who worked on the singularity theory of algebraic curves as well as invariant theory and projective differential geometry.
Mathematical Profile (Excerpt):
- Political events determined the course of the next few years for Halphen and work for his doctorate would have to wait until after the Franco-Prussian war.
- Halphen served in the French army in the conflict.
- Halphen, however, had served his country with great distinction.
- Also in 1872 Halphen was appointed as répétiteur at the École Polytechnique and he was soon making major contributions.
- Halphen showed that Chasles was essentially correct, but that restrictions on the kinds of singularity were necessary.
- Halphen's solution was ingenious ...
- Halphen took a different view on the problems of enumeration from his contemporaries.
- Halphen was well ahead of his time in the ideas which he brought to these problems.
- Halphen and Schubert engaged in a heated debate on whether an enumerative formula should be allowed to count degenerate solutions along with the nondegenerate solutions.
- Next Halphen classified singular points of algebraic closed curves thus extending the work of Riemann.
- A characterisation of such invariant differential equations appeared in Halphen's doctoral dissertation On differential invariants which he presented in 1878.
- Halphen made major contributions to linear differential equations and algebraic space curves.
- This last result appeared in a paper Halphen published in the Proceedings of the London Mathematical Society in 1878.
- In 1884 Halphen was made an examinateur at the École Polytechnique, then two years later he was elected to the Académie des Sciences.
- A major figure in his time, much of Halphen's work was in areas which have fallen out of favour.
- Perhaps with its inevitable revival, analytic geometry will restore Halphen to the eminence he earned.
Born 30 October 1844, Rouen, France. Died 23 May 1889, Versailles, France.
View full biography at MacTutor
Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive