A Manuscript by Joseph Fourier and Five Autographs by François Arago Enter the Collections of the École polytechnique

Two autograph groups that we were offering have just been acquired by the library of the École polytechnique: a leaf of calculations in the hand of Joseph Fourier and a file of five political pieces by François Arago. Two professors of the X who, two centuries apart, return to their own school.

The Fourier leaf: a page “14” without the thirteen that came before it

A single quarto leaf, numbered “14” at the head, covered in a tight hand in brown ink. On it Fourier deals, for a curve of equation y = f(x), with the calculation of the tangent, the normal and the subnormal, then moves on to the case of an implicit function F(x, y) = 0 and, in the last surviving lines, to three variables F(x, y, z) = 0. It reads:

« Lorsque on a y = f(x), on a pour sous tg, PT = ydx/dy, pour la sous normale, Pn = ydy/dx, pour la tangente [...] »

No title, no date, no signature: the page number alone tells us that this leaf belonged to a continuous exposition, the rest of which is lost or scattered. The hand and the subject matter — differential calculus as it was then taught — point to the late eighteenth century, that is, the years when Fourier was teaching at the still-young École polytechnique: assistant instructor in analysis in 1795, Lagrange's successor to the chair of analysis and mechanics in 1797, before leaving for Egypt in 1798 with Monge, Berthollet and some twenty students.

This point matters: the lessons given by Fourier at the X in 1795–1796 were never printed — Arago already regretted this in his Éloge — and are known only through students' notes. Those of Charles-Louis Donop (X1797) are held at the library of the Accademia dei Lincei in Rome, in the collection of the mathematician and bibliophile Vito Volterra; a more complete manuscript, in the hand of an unidentified student, was located in 2023 among the papers of Joseph Bertrand at the Institut de France. Any autograph page by Fourier from this period is therefore a piece of extreme rarity.

Arago as deputy: five pieces on the X, the École navale and scholarship students

François Arago (1786-1853) entered the X in 1803, became professor of analysis and geodesy there in 1810, and taught there until 1830. It is the later Arago — the deputy, the committee man — that the five pieces now transferred document.

Two of them concern the system of scholarship students, at the École polytechnique (“chapter 14”) and at the École des Arts et Métiers (“chapter 19”). For the X, Arago wants a table to be distributed to the Chambers at the opening of each session, giving the scholarship students' order of admission and « les noms, demeures et professions de leurs parents » : a measure of transparency against favouritism, very characteristic of him. For the Arts et Métiers, the same table was also to record « les diverses natures de machines, d'appareils, de meubles et d'ustensiles exécutés par les élèves et leurs prix moyens », whether the students were admitted « soit à Angers, soit à Châlons ».

A third, entitled Amendement à l'article 4 du projet de loi relatif à l'avancement dans l'armée navale, sets out the place of the X in the recruitment of naval officers: « Le nombre de places d'élèves de la marine réservé chaque année à l'École polytechnique sera égal au dixième du nombre de candidats sortant la même année de l'École navale avec le titre d'élèves de première classe. » The question of the respective share of the two schools was, at the time, agitating the officer corps. The file also includes a second amendment on promotion in the navy, written on paper headed by the Questure of the Chamber of Deputies and presented in the name of Alexandre de Laborde, deputy for the Seine, as well as a letter dated 30 November 1847 in which Arago, president of the Conseil général de la Seine, asks the minister to receive a deputation from the Council.

Fourier, Arago, and the Académie between them

The two groups echo one another. On Fourier's death in 1830, it was Arago who succeeded him as permanent secretary of the Académie des sciences for the mathematical sciences; in 1833 he delivered the Éloge historique de Joseph Fourier, which remains the first biography of the mathematician. Here they are reunited a second time, on the shelves of the X.

Why this destination delights us

The Centre de ressources historiques de l'École polytechnique has preserved, since 1794, the School's archives, its instruments, its iconographic collections and the papers of its former students and professors. A leaf by Fourier and a file by Arago are now at home there: accessible to researchers, and no longer scattered.

Other letters and manuscripts by scholars can be found in our collection of autographs.

We are always looking for letters and manuscripts by scholars: Monge, Laplace, Ampère, Fourier, Arago… If you own any, we would be delighted to examine them and to have a piece of your collection appraised.

Further reading

• F. Arago, Éloge historique de Joseph Fourier, read at the Académie des sciences on 18 November 1833; reprinted in the Œuvres complètes, vol. I — available on Gallica.
• J. Dhombres and J.-B. Robert, Joseph Fourier (1768-1830), créateur de la physique mathématique, Belin, 1998.
• A. Juhel, « Fourier à Polytechnique, an IV : un cours retrouvé », study day Pour un bicentenaire prospectif de la Théorie analytique de la chaleur, CNRS, 8 December 2023 — summary of the paper.
• Bibliothèque de l'École polytechnique, « Don à l'École polytechnique de lettres de Joseph Fourier », 19 June 2017.
• Bibliothèque de l'École polytechnique, Centre de ressources historiques (CRH).