The mathematician and physicist of the highest level, Joseph Fourier, with his researches, revolutionized the scientific world.

###### Childhood and early years

Joseph Fourier, born in Auxerre, France, was a descendant of a modest family. Orphaned at an early age, Joseph receives primary education at the Cathedral School, which is run by a church music teacher. After this, Fourier continues his studies at the Royal Military School of Auxerre. The boy exhibits remarkable literary abilities, but at the age of 15 these talents outshine the penchant for mathematics, which he enjoys with all his heart. To his fourteen years, Joseph finishes studying the “Course of Mathematics” Bezu, and the next year receives his first award for an essay to the book Bossu “Fundamentals of Mechanics.” In 1787, Fourier became a novice in the Benedictine Abbey of St. Benoît-sur-Loire, intending to later be tonsured in the monks. However, he suddenly changes his plans, sending his scientific notes on algebra to Paris, Jean Monette, and even declaring in a letter addressed to Bonar his desire to make a significant contribution to the development of mathematics. Such actions reveal Fourier’s doubts as to whether he really wants to depart from worldly life. In 1789, Fourier went to Paris, where he presented his article on the subject of algebraic equations at the Royal Academy of Sciences.

The following year, Fourier holds the position of junior instructor

To the dilemma, whether to devote one’s life to the service of God or to seriously engage in mathematics, politics is added, when Fourier joins the ranks of the local Revolutionary Committee. Returning to his native Auxerre, Joseph teaches in college and works on the committee. In 1794 he was arrested, but soon released. A year later, he is sent to study in the Higher Normal School of Paris – an educational institution that prepares teachers – where, of course, he is the most capable among students. Joseph learns from the best teachers of his time – Lagrange, Laplace and Monge. Later, Fourier himself becomes a teacher at the College de France. With his teachers, he maintains good relations and, with their help, begins his journey to great mathematical achievements. Fourier quickly moves up the career ladder, receiving a teaching position at the Central School of Public Works, which will later be renamed the Polytechnic School. However, in his old criminal case, new circumstances are opened, as a result of which Fourier is arrested again and imprisoned. It will not last long, and very soon he will again be free.

###### Late period

September 1, 1795 Fourier again begins to teach at the Polytechnic School. Two years later, in 1797, he replaced Lagrange as head of the Department of Analysis and Mechanics. Despite the fact that Fourier had established himself as an outstanding lecturer, he will only undertake serious research work now. In 1798, during the invasion of Egypt, Fourier is a scientific adviser to the army of Napoleon. Although at first this military company was extremely successful, on August 1 the French fleet suffers a complete defeat. Napoleon is surrounded in the country he captured. With the help of Fourier, he establishes here a typical French political structure and administration. Fourier is also engaged in the opening of educational institutions in Egypt and the organization of archaeological excavations. In Cairo, the scientist not only helps to found the Cairo Institute, but also becomes one of the twelve members of his mathematical department, along with Monge, Malius and Napoleon himself. In view of the weakening English influence in the East, he even writes a number of mathematical articles. Later, Fourier becomes the scientific secretary of the Institute, and will remain in this post all the time of the French occupation of Egypt. In his charge are also all scientific achievements and literary works.

In 1801, Fourier returned to Paris and holds his former post of head of the Department of Analysis at the Polytechnic School. However, Napoleon had his own plans for him. Fourier goes to Grenoble, where he is appointed prefect of the department of Ysera. The scientist is engaged in a number of projects, including the supervision of the operation to drain the bogs of Burguin and the control of the construction of a new road from Grenoble to Turin. It is here that Fourier begins his experiments with “the spread of heat.” On December 21, 1816, at the Paris Institute, he will present his article “Thermal conductivity of solids” to the scientific public, which will be included in the monumental French edition “Description of Egypt”. In the same year, he will go to England, returning from which six years later,

###### Fourier’s Proceedings

In 1822, Fourier presented his article on the topic of heat flow called “Théorie analytique de la chaleur”. Based on Newton’s law of cooling, Fourier concludes that the heat flux between two adjacent molecules is directly proportional to the extremely small difference in their temperatures. There were three aspects in the work: one mathematical and two physical. From a mathematical point of view, Fourier proves that any function with a variable, whether continuous or discontinuous, can be expanded into a series of sines multiples of the variable. Although this assertion was incorrect, the idea that some deliberately discontinuous functions are given by formulas, if the latter include infinite series, has become a discovery of great importance. Among the physical conclusions of the paper was the theory of uniformity of the dimensions of the equation, according to which the equation can formally be correct only if the dimensions in both sides of the equation coincide. Another significant contribution of Fourier to the development of physics was the proposal of a partial differential equation for heat conduction. To this day, every student who studies mathematical physics knows this equation.

To all of the above, we can add also the unfinished Fourier’s work on the equations containing determinants, which Claude-Louis Navier completed and published in 1831. In this paper we present the Fourier theorem for determining the number of real roots of an algebraic equation. In addition to mathematical discoveries, Fourier first proposed the theory of the greenhouse effect. Having made the necessary calculations, he deduces that if the Earth was heated only by solar radiation, then, taking into account its dimensions and distance to the Sun, on our planet it should be much colder. Proceeding from this, the scientist comes to the conclusion that a significant portion of additional heat the planet receives thanks to interstellar radiation. His idea that the Earth’s atmosphere acts as an insulating layer was the first theory of the phenomenon in history, which is now known to us under the name of the greenhouse effect. Referring to the experience carried out by Ferdinand de Saussure, Fourier suggests that gases in the atmosphere can create a reliable barrier, like the glass frames of a greenhouse, which lays the foundations for a modern theory of the greenhouse effect.

###### Death and heritage

In 1830, Fourier’s health deteriorated sharply. The first symptoms of an aneurysm of the heart are evident during his stay in Egypt and Grenoble, but with the return to Paris, the attacks of suffocation are becoming increasingly difficult. All this complicates the fall of Fourier from the stairs, which happened on May 4, 1830. A few days later, on May 16, 1830, Fourier died. The scientist was buried at the Pere Lachaise cemetery in Paris. His grave is decorated in the Egyptian style as a sign that he was the secretary of the Cairo Institute, and also as a reminder of his contribution to the publication “Description of Egypt.” Fourier’s name is on the list of 72 two names of outstanding people of France, immortalized on the first floor of the Eiffel Tower.