Jean-Baptiste Joseph Fourier (1768 - 1830) was a French mathematician and physicist whose study of heat conduction produced one of the most widely used tools in mathematics and engineering. [1] His decomposition of functions into trigonometric series, set out in Théorie analytique de la chaleur, underlies modern signal processing, acoustics and quantum theory. [2] He was also an administrator under Napoleon and an early student of the Earth's temperature balance.
Early life and education
Fourier was born on 21 March 1768 in Auxerre, the son of a tailor, and was orphaned before the age of ten. [1] He was educated at the local military school attached to the Royal Abbey of Saint-Germain d'Auxerre and later at the Benedictine abbey of Fleury, where he considered entering religious orders before mathematics prevailed.
The French Revolution interrupted these plans. Fourier joined a local revolutionary committee, was arrested during the Terror and narrowly escaped execution. [3] In 1795 he entered the newly founded École Normale in Paris, studying under Joseph-Louis Lagrange and Pierre-Simon Laplace, and soon afterwards took up a teaching post at the École Polytechnique.
Egypt and public administration
In 1798 Fourier accompanied Napoleon Bonaparte's expedition to Egypt as a scientific adviser. He served as permanent secretary of the Institut d'Égypte in Cairo and contributed the historical preface to the monumental Description de l'Égypte compiled from the expedition's surveys. [2]
On his return he was appointed prefect of the department of Isère, based at Grenoble, a post he held for more than a decade. Administrative duties included draining marshland and overseeing road construction, but it was in Grenoble that he carried out the research on heat that made his scientific reputation. [3] He also encouraged the young Jean-François Champollion, later the decipherer of Egyptian hieroglyphs.
The analytical theory of heat
Fourier presented a first memoir on heat propagation to the Institut de France in 1807. The work was criticised by Lagrange and others for its treatment of convergence, but a revised version won the Academy's Grand Prix des Sciences Mathématiques in 1811. [1] The mature statement appeared in 1822 as Théorie analytique de la chaleur.
The book introduced the partial differential equation governing heat diffusion and the method of solving it by expanding an arbitrary function into an infinite series of sine and cosine terms. [2] The claim that essentially any function could be so represented was contentious, and the effort to make it rigorous drove much of nineteenth-century analysis, including work by Dirichlet, Riemann and Cantor on convergence, integration and set theory.
Later years and legacy
Fourier was elected to the Académie des Sciences and became its permanent secretary in 1822; he was also elected a Foreign Member of the Royal Society and made an Officer of the Legion of Honour. [1] In papers of the 1820s he argued that the Earth's atmosphere retains heat that would otherwise escape to space, an early formulation of what later became known as the greenhouse effect. [3]
He died in Paris on 16 May 1830. His name is among the seventy-two inscribed on the Eiffel Tower, and Fourier series and the Fourier transform remain standard equipment in mathematics, physics and engineering, from the analysis of sound and images to the solution of differential equations. [2]
