Jean-Baptiste Joseph Fourier (; ; 21 March 1768 – 16 May 1830) was a

French French (french: français(e), link=no) may refer to: * Something of, from, or related to France ** French language, which originated in France, and its various dialects and accents ** French people, a nation and ethnic group identified with Franc ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

and

physicist A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate cau ...

born in Auxerre and best known for initiating the investigation of

Fourier series A Fourier series () is a summation of harmonically related sinusoidal functions, also known as components or harmonics. The result of the summation is a periodic function whose functional form is determined by the choices of cycle length (or '' ...

, which eventually developed into Fourier analysis and

harmonic analysis Harmonic analysis is a branch of mathematics concerned with the representation of functions or signals as the superposition of basic waves, and the study of and generalization of the notions of Fourier series and Fourier transforms (i.e. an ex ...

, and their applications to problems of

heat transfer Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy ( heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conducti ...

and

vibration Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. The word comes from Latin ''vibrationem'' ("shaking, brandishing"). The oscillations may be periodic, such as the motion of a pendulum—or random, su ...

s. The

Fourier transform A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed ...

and Fourier's law of conduction are also named in his honour. Fourier is also generally credited with the discovery of the

greenhouse effect The greenhouse effect is a process that occurs when energy from a planet's host star goes through the planet's atmosphere and heats the planet's surface, but greenhouse gases in the atmosphere prevent some of the heat from returning directly ...

Biography

Fourier was born at Auxerre (now in the Yonne

département In the administrative divisions of France, the department (french: département, ) is one of the three levels of government under the national level (" territorial collectivities"), between the administrative regions and the communes. Ninety ...

of France), the son of a

tailor A tailor is a person who makes or alters clothing, particularly in men's clothing. The Oxford English Dictionary dates the term to the thirteenth century. History Although clothing construction goes back to prehistory, there is evidence of ...

. He was orphaned at the age of nine. Fourier was recommended to the Bishop of Auxerre and, through this introduction, he was educated by the

Benedictine Order , image = Medalla San Benito.PNG , caption = Design on the obverse side of the Saint Benedict Medal , abbreviation = OSB , formation = , motto = (English: 'Pray and Work') , foun ...

of the Convent of St. Mark. The commissions in the scientific corps of the army were reserved for those of good birth, and being thus ineligible, he accepted a military lectureship on mathematics. He took a prominent part in his own district in promoting the

French Revolution The French Revolution ( ) was a period of radical political and societal change in France that began with the Estates General of 1789 and ended with the formation of the French Consulate in November 1799. Many of its ideas are conside ...

, serving on the local Revolutionary Committee. He was imprisoned briefly during the Terror but, in 1795, was appointed to the '' École Normale'' and subsequently succeeded

Joseph-Louis Lagrange Joseph-Louis Lagrange (born Giuseppe Luigi LagrangiaÉcole Polytechnique École may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, Savoi ...

''. Fourier accompanied

Napoleon Bonaparte Napoleon Bonaparte ; it, Napoleone Bonaparte, ; co, Napulione Buonaparte. (born Napoleone Buonaparte; 15 August 1769 – 5 May 1821), later known by his regnal name Napoleon I, was a French military commander and political leader wh ...

on his Egyptian expedition in 1798, as scientific adviser, and was appointed secretary of the Institut d'Égypte. Cut off from France by the British fleet, he organized the workshops on which the French army had to rely for their munitions of war. He also contributed several mathematical papers to the Egyptian Institute (also called the Cairo Institute) which Napoleon founded at

Cairo Cairo ( ; ar, القاهرة, al-Qāhirah, ) is the capital of Egypt and its largest city, home to 10 million people. It is also part of the largest urban agglomeration in Africa, the Arab world and the Middle East: The Greater Cairo metr ...

, with a view of weakening British influence in the East. After the British victories and the capitulation of the French under General Menou in 1801, Fourier returned to France. Legendre and Fourier (1820)

In 1801,

Napoleon Napoleon Bonaparte ; it, Napoleone Bonaparte, ; co, Napulione Buonaparte. (born Napoleone Buonaparte; 15 August 1769 – 5 May 1821), later known by his regnal name Napoleon I, was a French military commander and political leader wh ...

appointed Fourier

Prefect Prefect (from the Latin ''praefectus'', substantive adjectival form of ''praeficere'': "put in front", meaning in charge) is a magisterial title of varying definition, but essentially refers to the leader of an administrative area. A prefect's ...

(Governor) of the Department of Isère in Grenoble, where he oversaw road construction and other projects. However, Fourier had previously returned home from the Napoleon expedition to Egypt to resume his academic post as professor at

École Polytechnique École may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, Savoi ...

when

decided otherwise in his remark Hence being faithful to Napoleon, he took the office of Prefect. It was while at Grenoble that he began to experiment on the propagation of heat. He presented his paper ''On the Propagation of Heat in Solid Bodies'' to the Paris Institute on December 21, 1807. He also contributed to the monumental '' Description de l'Égypte''. In 1822, Fourier succeeded Jean Baptiste Joseph Delambre as Permanent Secretary of the

French Academy of Sciences The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. It was at ...

. In 1830, he was elected a foreign member of the

Royal Swedish Academy of Sciences The Royal Swedish Academy of Sciences ( sv, Kungliga Vetenskapsakademien) is one of the royal academies of Sweden. Founded on 2 June 1739, it is an independent, non-governmental scientific organization that takes special responsibility for prom ...

. Fourier never married. In 1830, his diminished health began to take its toll: Shortly after this event, he died in his bed on 16 May 1830. Fourier was buried in the Père Lachaise Cemetery in Paris, a tomb decorated with an Egyptian motif to reflect his position as secretary of the Cairo Institute, and his collation of ''Description de l'Égypte''. His name is one of the 72 names inscribed on the Eiffel Tower. A bronze statue was erected in Auxerre in 1849, but it was melted down for armaments during World War II.

Joseph Fourier University Joseph Fourier University (UJF, french: Université Joseph Fourier, also known as Grenoble I) was a French university situated in the city of Grenoble and focused on the fields of sciences, technologies and health. It is now part of the Univers ...

in Grenoble is named after him.

''The Analytic Theory of Heat''

In 1822, Fourier published his work on heat flow in ''Théorie analytique de la chaleur'' (''The Analytical Theory of Heat''), in which he based his reasoning on Newton's law of cooling, namely, that the flow of heat between two adjacent molecules is proportional to the extremely small difference of their temperatures. This book was translated, with editorial 'corrections',Truesdell, C.A. (1980). ''The Tragicomical History of Thermodynamics, 1822–1854'', Springer, New York, , page 52. into English 56 years later by Freeman (1878). The book was also edited, with many editorial corrections, by Darboux and republished in French in 1888. There were three important contributions in this work, one purely mathematical, two essentially physical. In mathematics, Fourier claimed that any function of a variable, whether

continuous Continuity or continuous may refer to: Mathematics * Continuity (mathematics), the opposing concept to discreteness; common examples include ** Continuous probability distribution or random variable in probability and statistics ** Continuous g ...

or discontinuous, can be expanded in a series of

sines Sines () is a city and a municipality in Portugal. The municipality, divided into two parishes, has around 14,214 inhabitants (2021) in an area of . Sines holds an important oil refinery and several petrochemical industries. It is also a popular ...

of multiples of the variable. Though this result is not correct without additional conditions, Fourier's observation that some discontinuous functions are the sum of infinite series was a breakthrough. The question of determining when a Fourier series converges has been fundamental for centuries.

Joseph-Louis Lagrange Joseph-Louis Lagrange (born Giuseppe Luigi LagrangiaPeter Gustav Lejeune Dirichlet was the first to give a satisfactory demonstration of it with some restrictive conditions. This work provides the foundation for what is today known as the

. One important physical contribution in the book was the concept of dimensional homogeneity in equations; i.e. an equation can be formally correct only if the dimensions match on either side of the equality; Fourier made important contributions to dimensional analysis. The other physical contribution was Fourier's proposal of his

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to h ...

for conductive diffusion of heat. This equation is now taught to every student of mathematical physics.

Real roots of polynomials

Grenoble - ancien évêché - Joseph Fourier

Fourier left an unfinished work on determining and locating real roots of polynomials, which was edited by Claude-Louis Navier and published in 1831. This work contains much original matter—in particular, Fourier's theorem on polynomial real roots, published in 1820. François Budan, in 1807 and 1811, had published independently his

theorem In mathematics, a theorem is a statement that has been proved, or can be proved. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of t ...

(also known by the name of Fourier), which is very close to Fourier's theorem (each theorem is a corollary of the other). Fourier's proof is the one that was usually given, during 19th century, in textbooks on the theory of equations. A complete solution of the problem was given in 1829 by Jacques Charles François Sturm.

Discovery of the greenhouse effect

Père-Lachaise - Division 18 - Joseph Fourier 03

In the 1820s, Fourier calculated that an object the size of the Earth, and at its distance from the Sun, should be considerably colder than the planet actually is if warmed by only the effects of incoming solar radiation. He examined various possible sources of the additional observed heat in articles published in 1824 and 1827. While he ultimately suggested that interstellar radiation might be responsible for a large portion of the additional warmth, Fourier's consideration of the possibility that the Earth's atmosphere might act as an insulator of some kind is widely recognized as the first proposal of what is now known as the

, although Fourier never called it that. In his articles, Fourier referred to an experiment by de Saussure, who lined a vase with blackened cork. Into the cork, he inserted several panes of transparent glass, separated by intervals of air. Midday sunlight was allowed to enter at the top of the vase through the glass panes. The temperature became more elevated in the more interior compartments of this device. Fourier concluded that gases in the atmosphere could form a stable barrier like the glass panes. This conclusion may have contributed to the later use of the metaphor of the "greenhouse effect" to refer to the processes that determine atmospheric temperatures.. Fourier noted that the actual mechanisms that determine the temperatures of the atmosphere included

convection Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the c ...

, which was not present in de Saussure's experimental device.

Works

* * ** * *
Translation by W M Connolley
* * * * *

References

External links

* *
Fourier, J. B. J., 1824, Remarques Générales Sur Les Températures Du Globe Terrestre Et Des Espaces Planétaires., in Annales de Chimie et de Physique, Vol. 27, pp. 136–167 – translation by Burgess (1837).

Université Joseph Fourier, Grenoble, France
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MathsBank.co.uk
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Joseph Fourier – Œuvres complètes, tome 2
Gallican-Math * {{DEFAULTSORT:Fourier, Jean Baptiste Joseph 1768 births 1830 deaths 18th-century French mathematicians 19th-century French mathematicians Barons of the First French Empire Burials at Père Lachaise Cemetery Commission des Sciences et des Arts members Fluid dynamicists Foreign Members of the Royal Society French physicists Honorary members of the Saint Petersburg Academy of Sciences Mathematical analysts Members of the Académie Française Members of the French Academy of Sciences Members of the Royal Swedish Academy of Sciences Officers of the French Academy of Sciences People from Auxerre Prefects of Isère French Roman Catholics