Up until 1830 Algeria was an autonomous province of the Ottoman Empire. France had in the couple of years up to 1830 tried to control the country using various political moves and a naval blockade. However they decided early in 1830 to invade and French troops landed in Algeria on 5 July 1830. They won quick victories since the Algerian people detested their rulers and there was no united forces to oppose the French invasion. However the July Revolution in France led to a period when desire for foreign conquests vanished but they retained the foothold in Algeria that they had established. Two leaders, Ahmad Bey and Abdelkader, established themselves rallying support aganist the French invaders. The French decided to send forces against these resistance leaders and Laurent took part in two of these expeditions. One was to Tlemcen, in northwestern Algeria near the Moroccan border, the other was the Tafna expedition against Abdelkader which led to the French signing the Treaty of Tafna in 1837.
Laurent 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. Itard writes :-
His superiors considered him a promising officer; they admired his sure judgement and his extensive practical training.It was while Laurent was working on the construction project at Le Havre that he began to write his first mathematical papers. He submitted a memoir for the Grand Prize of the Academy of Sciences of 1842, unfortunately after the final date for submission in 1843. The topic proposed was (see for example ):-
Find the limiting equations that must be joined to the indefinite equations in order to determine completely the maxima and minima of multiple integrals.Cauchy reported on Laurent's entry Mémoire sur le calcul des variations Ⓣ, which contains the Laurent series for a complex function, on 20 May 1843. Being late, the memoir was never seriously considered for the Grand Prix, which was won by Pierre Frédéric Sarrus with Delaunay's entry receiving an honourable mention, but Cauchy proposed that Laurent's memoir should be approved and published in the Recueil des savants étrangers Ⓣ. The Academy of Sciences published the entries of Sarrus and Delaunay but they ignored Cauchy's recommendation concerning Laurent and his memoir was not published. A second paper by Laurent 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 Ⓣ. Again the Academy of Sciences decided not to publish the work and it has been lost and is now only known through Cauchy's report.
After this Laurent, disappointed that his papers had not been accepted for publication, decided that he better change the topic of his research. He began to study the theory of light waves, in particular examining the theory of polarisation. He published a number of papers on the topic and Cauchy proposed him for a vacant position in the Academy of Sciences in 1846. However he was not elected and soon after this he was promoted to major and sent to Paris to become a member of a committee set up to look at the problems of fortification. He continued to undertake research into applied mathematical topics.
Laurent was married and had three children. He died at the young age of 41 and after his death his widow arranged for two more of his memoirs to be presented to the Academy. One was considered by Cauchy who proposed that Laurent's memoir should be approved and published in the Recueil des savants étrangers Ⓣ but again it was never published. The second Mémoire sur la théorie des imaginaires, sur l'équilibre des températures et sur l'équilibre d'élasticité Ⓣ was published in Journal de l'École Polytechnique in 1863.
Article by: J J O'Connor and E F Robertson