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.
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References
Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive
