The Academy was founded in Paris in 1666 by Jean-Baptiste Colbert. He was at that time controller general of finance in France and his programme of economic reconstruction was largely responsible for making France the leading power in Europe. Colbert was in a position to give the new Academy the support it needed and he arranged for it to meet in the royal library. Right from the beginning the Academy contained foreign members and, for example, Huygens was one of the founding members. The excellent financial position of the Academy is illustrated by the fact that it was able to grant Huygens a large pension and an apartment in its building.
In 1699 the Academy was reorganized under the royal patronage of Louis XIV and transferred to meet in the Louvre. It was seen as a forum for the development of science but, as a state institution, it had wide consultation responsibilities, in particular for patents and technology. It had a small active membership consisting of 56 scientists who were divided into subject disciplines. There were two main categories, namely Mathematical Sciences and Physical Sciences. These in turn were each divided into three, with geometry, mechanics and astronomy being the three Mathematical Sciences, while chemistry, botany and anatomy were the three Physical Sciences. Note that 'geometry' was used at this time in the sense we would use 'mathematics' today. This was clearly a classification based on Aristotle. Administratively the Academy was run by the Perpetual Secretary, who undertook the assignment of duties, annual reports on the achievements of the Academy, obituaries of members etc.
The Academy established a system of prizes in 1721. These had a major impact on the development of mathematics and other sciences as they directed work towards important areas. One of the earliest prizes was awarded to Maclaurin for his work on the impact of bodies.
The Academy set up a committee consisting of leading experts to judge each Grand Prix. Let us give some details of the Grand Prix competitions with information extracted from our archive. In 1727 Bouguer and Camus shared the Grand Prix for their submissions on masts of ships. Euler also submitted an entry which was placed third. In 1729 Bouguer again won the Grand Prix, this time with an essay on observing the altitudes of stars at sea. In 1731 Bouguer won his third Grand Prix from the Académie for his work on the observation of the magnetic declination at sea. Euler shared the Grand Prize in 1738 and again in 1740. Coulomb shared the 1777 prize with a memoir on the magnetic compass. Coulomb's major work on friction Théorie des machines simples won him the Grand Prix from the Académie in 1781.
A major reform of the Academy's structure was undertaken by Lavoisier and introduced in 1785. The broad structure of Mathematical Sciences and Physical Sciences was retained but each was now split into four. To geometry, mechanics and astronomy in the Mathematical Sciences was added 'general physics'. This was to include topics such as optics, electricity, magnetism, acoustics and heat which were still largely experimental subjects at this time but were beginning to become more mathematical in nature. The classification was a good one for it correctly anticipated these subjects becoming applied mathematics (and in a small way contributed to this trend). The three Physical Sciences of chemistry, botany and anatomy became four subjects: chemistry and metallurgy; mineralogy and natural history; botany and agriculture; and anatomy.
The French Revolution began with the storming of the Bastille on 14 July 1789 and this would have a major impact on the Academy. In 1793 the Reign of Terror commenced and the Academy, along with the other learned societies, was abolished on 8 August of that year. As a Royal institution it was an obvious target of the Revolution and although some argued that it served a useful purpose for the nation and should be exempted, even some of its members accepted that it was undemocratic and approved of its abolition. Lavoisier was arrested and subsequently executed. In 1795 more moderate republicans then in power in France established the National Institute and the functions of the Academy were assumed by a branch of the new Institute. The National Convention ratified the creation of the Institut National des Sciences et des Arts on 22 August 1795. The First Class of the Institute was Science with 60 members (and effectively the old Academy), the Second Class was Moral and Political Sciences with 36 members, the Third Class was literature and fine arts with 48 members.
The 60 members of the First Class were divided into ten sections with six members each. There was still the division into two categories, Mathematical Sciences and Physical Sciences, as had existed before. Mathematical Sciences now consisted of: mathematics; mechanical arts; astronomy; and experimental physics. Physical Sciences now consisted of: chemistry; natural history and mineralogy; botany and vegetable physics; anatomy and zoology; medicine and surgery; and rural economy and veterinary medicine.
On 9 November 1799 Napoleon and two others seized power in a coup and a new government, the Consulate, was set up. Napoleon became 1st Consul in 1800 and then Emperor in 1804. Even before he became Emperor, however, Napoleon had become dissatisfied with the National Institute, of which he made himself President in 1801, and he reorganised it in 1803. His particular displeasure with "the salon politics of liberal intellectuals" was directed at the Second Class which he abolished. However, some of its work was retained in a new geography section which was added to the First Class and new historical sections were added to the Third Class. The two categories of Mathematical Sciences and Physical Sciences were retained for the First Class with Mathematical Sciences now divided into five: geometry; mechanics; astronomy; geography and navigation; and general physics. Delambre was made its perpetual secretary.
Following the Restoration of King Louis XVIII in 1816, the name of the Academy was restored but it remained part of the Institute of France. However, even before its name was restored, the Academy was again motivating important contributions with its annual announcement of the Grand Prix topic.
Poisson won the 1812 prize on electricity. To show how precise the prize questions were worded, here is the text of the 1812 prize question:-
To determine by calculation and to confirm by experiment the manner in which electricity is distributed at the surface of electrical bodies considered either in isolation or in the presence of each other - for example at the surface of two electrified spheres in the presence of each other. In order to simplify the problem, the Class asks only for an examination of cases where the electricity spread on each surface remains always of the same kind.In 1816 Cauchy won the Grand Prix of the Academy for a memoir on waves. Fresnel won the Grand Prix for 1819 which was awarded for the best work on diffraction. Abel and Jacobi won the Grand Prix in 1830. This was the famous occasion when Galois submitted an entry to Fourier (who was at that time perpetual secretary), but after Fourier's death the submission was not found and so Galois's memoir was never considered for the prize. The 1825 prize on the compressibility of water was not awarded and was set again in the following year when it was won by Sturm and Colladon with a joint submission.
The 1857 prize was offered for a solution to Fermat's Last Theorem and, not surprisingly, no solutions were submitted even when the deadline was extended. The prize was awarded to Kummer, even although he had not entered! The 1858 Grand Prix was awarded half to Dupré with a paper on Legendre's theory of numbers. In 1859 Bonnet, Bour and Codazzi submitted entries for the prize 'to find all surfaces of a given linear element'. The 1860 prize on group theory was not awarded despite submissions from Kirkman, Emile Mathieu and Jordan. The 1861 topic was on polyhedra. In 1862 Jonquières was awarded two-thirds of the Prize for his work on fourth order plane curves. In 1880 Halphen won the Grand Prix for his work on linear differential equations.
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