Person: Laurent, Pierre
Pierre Laurent was a French mathematician best-known for his study of the so-called Laurent Series in Complex analysis.
Mathematical Profile (Excerpt):
- Pierre Alphonse entered the École Polytechnique in Paris in 1830, in the year of the July Revolution which forced King Charles X from the throne and led to the rule of Louis-Philippe.
- Laurent graduated from the École Polytechnique in 1832, being one of the best students in his year, and entered the engineering corps as second lieutenant.
- The French decided to send forces against these resistance leaders and Laurent took part in two of these expeditions.
- Laurent had returned to France from Algeria around 1840 and spent six years directing operations for the enlargement of the port of Le Havre on the English Channel coast.
- Rouen had been the main French port up to the nineteenth century but the hydraulic construction projects on which Laurent worked in Le Havre turned it into France's main seaport.
- It is clear that Laurent was a good engineer, putting his deep theoretical knowledge to good practical use.
- Pierre Georges, born in the Military District of Le Havre, was educated in the schools in Avesnes and Douai, studied in Paris at the École Polytechnique from 1861 to 1863 and became a military engineer.
- It was while Laurent was working on the construction project at Le Havre that he began to write his first mathematical papers.
- Cauchy reported on Laurent's entry Mémoire sur le calcul des variations Ⓣ(Memoir on the calculus of variations), which contains the Laurent series for a complex function, on 20 May 1843.
- There exist functions, such as certain Bessel functions, which cannot be expanded into Taylor series, and Laurent's theorem would be applicable to these functions.
- Being late, the memoir was never seriously considered for the Grand Prix, which was won by Pierre Frédéric Sarrus (1798-1861), a mathematician working at Strasbourg, with Charles Delaunay's entry receiving an honourable mention, but Cauchy and Liouville were asked to review Laurent's paper and consider it for publication.
- They proposed that Laurent's memoir should be approved and published in the Recueil des savants étrangers Ⓣ(Reports of foreign scientists).
- The Academy of Sciences published the entries of Sarrus and Delaunay but they ignored Cauchy and Liouville's recommendation concerning Laurent and his memoir was not published.
- Only on 30 October did he present his (and Liouville's) report on Laurent's memoir to the Academy.
- Cauchy then went on to argue that the main theorem in Laurent's paper could be deduced from a theorem he (Cauchy) had stated in 1840.
- To support his claims Cauchy added to the report a note of his own to show that "the easiest way" to obtain Laurent's theorem was by reformulating the results in his 1840 paper.
- Given Cauchy's attempt to claim the result of Laurent's paper it is not surprising the Academy of Sciences chose not to publish it but, despite this, the theorem and series are named for Laurent.
- However, even if we ignore Cauchy's attempt to claim the theorem, Laurent was not the first to prove the result we today call Laurent's theorem.
- A second paper by Laurent, Extension du théorème de M Cauchy relatif à la convergence du développement d'une fonction suivant les puissances ascendantes de la variable Ⓣ(Extension of Cauchy's theorem on the convergence of the expansion of a function according to the ascending powers of the variable), submitted to the Academy of Sciences around the same time was also considered by Cauchy.
- This paper presented an extension of one of Cauchy's theorems and again Cauchy proposed that Laurent's memoir should be approved and published in the Recueil des savants étrangers Ⓣ(Reports of foreign scientists).
- After this Laurent, disappointed that his papers had not been accepted for publication, decided that he had better change the topic of his research.
- Laurent died at the young age of 41 probably as a consequence of overwork over many years when he was carrying out a demanding job yet producing a large number of mathematical papers at the same time.
- Examen de la théorie de la lumière dans le système des ondes Ⓣ(Review of the theory of light in the wave system) was considered by Cauchy who proposed that Laurent's memoir should be approved and published in the Recueil des savants étrangers Ⓣ(Reports of foreign scientists) but again it was never published.
Born 18 July 1813, Paris, France. Died 2 September 1854, Paris, 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