Born: 21 March 1768 in Auxerre, Bourgogne, France

Died: 16 May 1830 in Paris, France

Joseph Fourier ‘s male parent was a seamster in Auxerre. After the decease of his first married woman, with whom he had three kids, he remarried and Joseph was the 9th of the 12 kids of this 2nd matrimony. Joseph ‘s female parent died went he was nine old ages old and his male parent died the undermentioned twelvemonth.

His first schooling was at Pallais ‘s school, run by the music maestro from the cathedral. There Joseph studied Latin and French and showed great promise. He proceeded in 1780 to the & # 201 ; cole Royale Militaire of Auxerre where at foremost he showed endowments for literature but really shortly, by the age of 13, mathematics became his existent involvement. By the age of 14 he had completed a survey of the six volumes of B & # 233 ; zout ‘s Cours de mathematique. In 1783 he received the first award for his survey of Bossut ‘s M & # 233 ; chanique en g & # 233 ; n & # 233 ; ral.

In 1787 Fourier decided to develop for the priesthood and entered the Benedictine abbey of St Benoit-sur-Loire. His involvement in mathematics continued, nevertheless, and he corresponded with C L Bonard, the professor of mathematics at Auxerre. Fourier was diffident if he was doing the right determination in preparation for the priesthood. He submitted a paper on algebra to Montucla in Paris and his letters to Bonard suggest that he truly wanted to do a major impact in mathematics. In one missive Fourier wrote

Yesterday was my twenty-first birthday, at that age Newton and Pascal had already acquired many claims to immortality.

Fourier did non take his spiritual vows. Having left St Benoit in 1789, he visited Paris and read a paper on algebraic equations at the Acad & # 233 ; mie Royale diethylstilbestrols Sciences. In 1790 he became a instructor at the Benedictine college, & # 201 ; cole Royale Militaire of Auxerre, where he had studied. Up until this clip there had been a struggle indoors Fourier about whether he should follow a spiritual life or one of mathematical research. However in 1793 a 3rd component was added to this struggle when he became involved in political relations and joined the local Revolutionary Committee. As he wrote: –

As the natural thoughts of equality developed it was possible to gestate the empyreal hope of set uping among us a free authorities exempt from male monarchs and priests, and to liberate from this dual yoke the long-usurped dirt of Europe. I readily became enamoured of this cause, in my sentiment the greatest and most beautiful which any state has of all time undertaken.

Surely Fourier was unhappy about the Terror which resulted from the Gallic Revolution and he attempted to vacate from the commission. However this proved impossible and Fourier was now steadfastly entangled with the Revolution and unable to retreat. The revolution was a complicated matter with many cabals, with loosely similar purposes, violently opposed to each other. Fourier defended members of one cabal while in Orl & # 233 ; autonomic nervous systems. A missive depicting events relates: –

Citizen Fourier, a immature adult male full of intelligence, fluency and ardor, was sent to Loiret. … It seems that Fourier… got up on certain popular platforms. He can speak really good and if he put frontward the positions of the Society of Auxerre he has done nil blameworthy…

This incident was to hold serious effects but after it Fourier returned to Auxerre and continued to work on the radical commission and continued to learn at the College. In July 1794 he was arrested, the charges associating to the Orl & # 233 ; autonomic nervous systems incident, and he was imprisoned. Fourier feared the he would travel to the closure by compartment but, after Robespierre himself went to the closure by compartment, political alterations resulted in Fourier being freed.

Subsequently in 1794 Fourier was nominated to analyze at the & # 201 ; cole Normale in Paris. This establishment had been set up for preparation instructors and it was intended to function as a theoretical account for other teacher-training schools. The school opened in January 1795 and Fourier was surely the most able of the students whose abilities ranged widely. He was taught by Lagrange, who Fourier described as

the first among European work forces of scientific discipline,

and besides by Laplace, who Fourier rated less extremely, and by Monge who Fourier described as

holding a loud voice and is active, clever and really learned.

Fourier began learning at the Coll & # 232 ; ge de France and, holding first-class dealingss with Lagrange, Laplace and Monge, began farther mathematical research. He was appointed to a place at the & # 201 ; cole Centrale des Travaux Publiques, the school being under the way of Lazare Carnot and Gaspard Monge, which was shortly to be renamed & # 201 ; cole Polytechnique. However, reverberations of his earlier apprehension remained and he was arrested once more imprisoned. His release has been put down to a assortment of different causes, supplications by his students, supplications by Lagrange, Laplace or Monge or a alteration in the political clime. In fact all three may hold played a portion.

By 1 September 1795 Fourier was back learning at the & # 201 ; cole Polytechnique. In 1797 he succeeded Lagrange in being appointed to the chair of analysis and mechanics. He was renowned as an outstanding lector but he does non look to hold undertaken original research during this clip.

In 1798 Fourier joined Napoleon ‘s ground forces in its invasion of Egypt as scientific advisor. Monge and Malus were besides portion of the expeditionary force. The expedition was at first a great success. Malta was occupied on 10 June 1798, Alexandria taken by storm on 1 July, and the delta of the Nile rapidly taken. However, on 1 August 1798 the Gallic fleet was wholly destroyed by Nelson ‘s fleet in the Battle of the Nile, so that Napoleon found himself confined to the land that he was busying. Fourier acted as an decision maker as Gallic type political establishments and disposal was set up. In peculiar he helped set up educational installations in Egypt and carried out archeological geographic expeditions.

While in Cairo Fourier helped establish the Cairo Institute and was one of the 12 members of the mathematics division, the others included Monge, Malus and Napoleon Bonaparte. Fourier was elected secretary to the Institute, a place he continued to keep during the full Gallic business of Egypt. Fourier was besides put in charge of collating the scientific and literary finds made during the clip in Egypt.

Bonaparte abandoned his ground forces and returned to Paris in 1799, he shortly held absolute power in Franc

e. Fourier returned to France in 1801 with the remains of the expeditionary force and resumed his station as Professor of Analysis at the Ecole Polytechnique. However Napoleon had other thoughts about how Fourier might function him and wrote: –

… the Prefect of the Department of Is & # 232 ; rhenium holding late died, I would wish to show my assurance in citizen Fourier by naming him to this topographic point.

Fourier was non happy at the chance of go forthing the academic universe and Paris but could non decline Napoleon ‘s petition. He went to Grenoble where his responsibilities as Prefect were many and varied. His two greatest accomplishments in this administrative place was supervising the operation to run out the swamps of Bourgoin and to supervise the building of a new main road from Grenoble to Turin. He besides spent much clip working on the Description of Egypt which was non completed until 1810 when Napoleon made alterations, rewriting history in topographic points, to it before publication. By the clip a 2nd edition appeared every mention to Napoleon would hold been removed.

It was during his clip in Grenoble that Fourier did his of import mathematical work on the theory of heat. His work on the subject began around 1804 and by 1807 he had completed his of import memoir On the Propagation of Heat in Solid Bodies. The memoir was read to the Paris Institute on 21 December 1807 and a commission dwelling of Lagrange, Laplace, Monge and Lacroix was set up to describe on the work. Now this memoir is really extremely regarded but at the clip it caused contention.

There were two grounds for the commission to experience unhappy with the work. The first expostulation, made by Lagrange and Laplace in 1808, was to Fourier ‘s enlargements of maps as trigonometrical series, what we now call Fourier series. Further elucidation by Fourier still failed to convert them. As is pointed out in: –

All these are written with such model lucidity – from a logical as opposed to calligraphic point of position – that their inability to carry Laplace and Lagrange… provides a good index of the originality of Fourier ‘s positions.

The 2nd expostulation was made by Biot against Fourier ‘s derivation of the equations of transportation of heat. Fourier had non made mention to Biot ‘s 1804 paper on this subject but Biot ‘s paper is surely wrong. Laplace, and subsequently Poisson, had similar expostulations.

The Institute set as a award competition subject the extension of heat in solid organic structures for the 1811 mathematics prize. Fourier submitted his 1807 memoir together with extra work on the chilling of infinite solids and tellurian and beaming heat. Merely one other entry was received and the commission set up to make up one’s mind on the award of the award, Lagrange, Laplace, Malus, Ha & # 252 ; Y and Legendre, awarded Fourier the award. The study was non nevertheless wholly favorable and provinces: –

… the mode in which the writer arrives at these equations is non exempt of troubles and that his analysis to incorporate them still leaves something to be desired on the mark of generalization and even cogencies.

With this instead assorted study there was no move in Paris to print Fourier ‘s work.

When Napoleon was defeated and on his manner to expatriate in Elba, his path should hold been through Grenoble. Fourier managed to avoid this hard confrontation by directing word that it would be unsafe for Napoleon. When he learnt of Napoleon ‘s flight from Elba and that he was processing towards Grenoble with an ground forces, Fourier was highly disquieted. He tried to carry the people of Grenoble to oppose Napoleon and give their commitment to the King. However as Napoleon marched into the town Fourier left in hastiness.

Bonaparte was angry with Fourier who he had hoped would welcome his return. Fourier was able to speak his manner into favor with both sides and Napoleon made him Prefect of the Rh & # 244 ; Ne. However Fourier shortly resigned on having orders, perchance from Carnot, that the was to take all decision makers with royalist understandings. He could non hold wholly fallen out with Napoleon and Carnot, nevertheless, for on 10 June 1815, Napoleon awarded him a pension of 6000 francs, collectible from 1 July. However Napoleon was defeated on 1 July and Fourier did non have any money. He returned to Paris.

Fourier was elected to the Acad & # 233 ; mie diethylstilbestrols Sciences in 1817. In 1822 Delambre, who was the Secretary to the mathematical subdivision of the Acad & # 233 ; mie diethylstilbestrols Sciences, died and Fourier together with Biot and Arago applied for the station. After Arago withdrew the election gave Fourier an easy win. Shortly after Fourier became Secretary, the Academy published his award winning essay Th & # 233 ; orie analytique de la chaleur in 1822. This was non a piece of political manoeuvring by Fourier nevertheless since Delambre had arranged for the printing before he died.

During Fourier ‘s eight last old ages in Paris he resumed his mathematical researches and published a figure of documents, some in pure mathematics while some were on applied mathematical subjects. His life was non without jobs nevertheless since his theory of heat still provoked contention. Biot claimed precedence over Fourier, a claim which Fourier had small trouble demoing to be false. Poisson, nevertheless, attacked both Fourier ‘s mathematical techniques and besides claimed to hold an alternate theory. Fourier wrote Historical Pr & # 233 ; Commonwealth of Independent States as a answer to these claims but, although the work was shown to assorted mathematicians, it was ne’er published.

Fourier ‘s positions on the claims of Biot and Poisson are given in the undermentioned, see: –

Having contested the assorted consequences [ Biot and Poisson ] now recognise that they are exact but they protest that they have invented another method of elaborating them and that this method is first-class and the true 1. If they had illuminated this subdivision of natural philosophies by of import and general positions and had greatly perfected the analysis of partial differential equations, if they had established a chief component of the theory of heat by all right experiments… they would hold the right to judge my work and to rectify it. I would subject with much pleasance.. But one does non widen the bounds of scientific discipline by showing, in a signifier said to be different, consequences which one has non found oneself and, above all, by preventing the true writer in publication.

Fourier ‘s work provided the drift for ulterior work on trigonometric series and the theory of maps of a existent variable.

J J O’Connor and E F Robertson