Joseph-Louis Lagrange was an Italian-French mathematician and astronomer, who excelled in all fields of analysis and number theory and analytical and celestial mechanics. His contributions to math and the sciences were vast and much of his work in researching helped create a foundation for others to build upon. He received many awards and commendations for his work while also serving as a teacher who helped guide others towards the learned path.
Background
Ethnicity:
Joseph-Louis Lagrange was of Italian and French descent.
Joseph-Louis Lagrange was born as Giuseppe Lodovico Lagrangia on January 25, 1736, in Turin, Piedmont-Sardinia (now Italy). Lagrange was from a well-to-do family of French origin on his father’s side. His father, Giuseppe Francesco Lodovico Lagrangia, worked as a Treasurer in the Office of Public Works and Fortifications in Turin. His mother, Teresa Grosso, was the daughter of a doctor from the nearby town of Cambiano. Lagrange was the eldest of his parent’s two surviving children.
Despite the official position held by the father - who had engaged in some unsuccessful financial speculations - the family lived very modestly. Lagrange himself declared that if he had had money, he probably would not have made mathematics his vocation. He remained with his family until his departure to Berlin in 1766.
His family was, through the male members, of French origin, as stated in the marriage contract of 1792. His great-grandfather, a cavalry captain, had passed from the service of France to that of Charles Emmanuel II, Duke of Savoy, and had married a Conti, from a Roman family whose members included Pope Innocent XIII.
Lagrange always leaned towards his French ancestry, for as a youth he would sign himself Lodovico LaGrange or Luigi Lagrange, using the French form of his family name.
Education
Young Joseph was intended to be a lawyer and attended the University of Turin with that goal. Initially, he did not show much interest in mathematics. In fact, he found Greek geometry rather dull and was more interested in Classic Latin. It wasn't until the age of 17 that he became interested in mathematics. His interest was piqued by a paper he came across by the astronomer Edmond Halley, and, entirely on his own, Lagrange dove into mathematics. Once his interest was piqued, he traveled down the path of being a very accomplished mathematician.
Career
On July 23, 1754, Lagrange published his first mathematical work in the form of a letter written to Italian mathematician Giulio Fagnano. In this work, he drew an analogy between the binomial theorem and the successive derivatives of the product of functions. Unfortunately, a month after the paper was published, he realized that the work had already appeared in correspondence between Johann Bernoulli and Leibniz. Lagrange was greatly upset about this as he thought he would now be accused of plagiarism. He now started working even harder so as to produce genuine results.
Over time, Lagrange's expertise led him to become the director of mathematics at the Prussian Academy of Sciences. The discovery of this new interest in mathematics was one that emerged by accident. Working on the problem of tautochrone, he made some important discoveries, which in later years contributed to the study of the calculus of variations. Lagrange had read a paper by Edmund Halley on the subject and then became so interested in it that he launched himself into a great deal of study. On August 12, 1755, he sent the result of his work to Euler. In a very short time, he would go on and become a very skilled and visionary mathematician.
Although he was still only 19 years old, Lagrange was appointed professor of mathematics at the Royal Artillery School in Turin on 28 September 1755. It was well deserved for the young man had already shown the world of mathematics the originality of his thinking and the depth of his great talents. In 1756 Lagrange sent Euler results that he had obtained on applying the calculus of variations to mechanics. These results generalized results which Euler had himself obtained and Euler consulted Maupertuis, the president of the Berlin Academy, about this remarkable young mathematician.
Not only was Lagrange an outstanding mathematician but he was also a strong advocate for the principle of least action so Maupertuis had no hesitation but to try to entice Lagrange to a position in Prussia. He arranged with Euler that he would let Lagrange know that the new position would be considerably more prestigious than the one he held in Turin. However, Lagrange did not seek greatness, he only wanted to be able to devote his time to mathematics, and so he shyly but politely refused the position.
Despite the refusal, Lagrange was elected to the Berlin Academy on September 2, 1756. In 1757, Lagrange formed a scientific society in Turin, which later came became known as the Royal Academy of Sciences of Turin. Lagrange’s work during this period covered a variety of topics, such as calculus of variations, calculus of probabilities, and foundations of dynamics. Later, he also worked on fluid mechanics, linear differential equations, and propagation of sound as well as on orbits of planets like Jupiter and Saturn.
By 1761 Lagrange was already recognized as one of the greatest living mathematicians. In 1766, Lagrange became the director of mathematics at the Prussian Academy of Sciences, located in Berlin. He stayed there for more than 20 years. During his time there, LaGrange created a large body of works and he won many prizes from the French Academy of Sciences. In 1781, he was invited to take up the position of the Director of Philosophy at the Naples Academy by the Count of Naples. However, Lagrange wanted to concentrate only on mathematics and the Berlin Academy gave him ample opportunity so he refused the offer.
In 1786, King Frederick the Great died, and with that Lagrange’s position at the Berlin, Academy became less comfortable as many of his colleagues had always envied him for he became a director at such a young age. Many Italian states now tried to lure him back to Italy. Around that time, he received an offer from Académie des Sciences, Paris, which exempted him from teaching. On May 18, 1787, he left Berlin for Paris and subsequently became a member of the Académie and remained there for the rest of his career.
The Revolution, which began in 1789, pressed Lagrange into work on the committee to reform the metric system. In May 1790, Lagrange was made a member of the committee, whose job was to standardize weights and measures. When the École Centrale des Travaux Publics (later École Polytechnique) was opened in 1794, he became Gaspard Monge, its leading professor of mathematics. Thereafter Lagrange continued in a teaching position and at the same time continued publishing important papers. His last major work, Leçonssur le calcul des fonctions, was published in 1800.
Many incorrectly consider Joseph-Louis Lagrange to mainly be a mathematician. He was actually very accomplished in the field of astronomy as evidenced in the body of work he completed. What would eventually be known as the Lagrangian points originated out of a problem-solving endeavor centering on the three-body problem. Through the problem-solving process, he made the discovery of two constant-pattern solutions: the equilateral and the collinear.
He also wrote a paper about the moon. In particular, he delved into the topic of the secular equation of the moon. The paper he had written was extremely complex and highly detailed and well thought out. Various themes covered in the paper revolved around examinations of mass, distance, and attraction in varied directions. The material in this paper would continue to be built upon for many years.
Other papers would examine the orbits of comets and planets as well as the elements of planets and their relationship to secular and periodic variations. Three papers were written on the subject of the method of interpolation. Some of the material in these three papers has not been built upon since Lagrange originally wrote the material.
Lagrange is best known for his contribution to the development of the metric system. As a President of la Commission des Poids et Mesures, he played a decisive role in taking up the unit system of meter and kilogram as well as their decimal subdivisions. He is also considered one of the founders of the calculus of variations. While working on the problem of tautochrone, he discovered a method of maximizing and minimizing functional, which led to the development of the calculus of variation.
Napoleon honored the aging mathematician, making him a senator and a count of the empire, but he remained the quiet, unobtrusive academician, a venerable figure wrapped in his thoughts.
Joseph-Louis Lagrange was raised as a Roman Catholic, but later on, became an agnostic.
Politics
In the late 18th century, there was a great deal of political upheaval in the nation. Lagrange did have concerns about his safety and became a citizen of France.
Views
Quotations:
"As long as algebra and geometry proceeded along separate paths, their advance was slow and their applications limited. But when these sciences joined company, they drew from each other fresh vitality and thenceforward marched on at a rapid pace toward perfection."
"Newton was the greatest genius that ever existed, and the most fortunate, for we cannot find more than once a system of the world to establish."
Membership
Before leaving Turin, Joseph-Louis Lagrange and friends founded the Turin Private Society, an organization intended to support pure research. The Society soon began publishing its own journal and, in 1783, it became the Turin Royal Academy of Sciences.
Joseph-Louis Lagrange was a founding member of the Bureau des Longitudes. Lagrange was elected a Fellow of the Royal Society of Edinburgh in 1790. He was also a Fellow of the Royal Society and a foreign member of the Royal Swedish Academy of Sciences since 1806.
Bureau des Longitudes
1795
Royal Society of Edinburgh
1790
Royal Society
Royal Swedish Academy of Sciences
1806
Turin Royal Academy of Sciences
Personality
Joseph-Louis Lagrange was known for his personality and his overall demeanor. People would talk about his nervousness and his timidity. He also let people take credit for some of the things he did simply to avoid any potential controversy.
Interests
Astronomy
Philosophers & Thinkers
Edmond Halley, Isaac Newton
Connections
In September 1767 Lagrange married his cousin Vittoria Conti. They did not have any children. From his letters to d'Alembert, some scholars have deduced that he did not wish to have any. In 1783, Vittoria died after years of illness, leaving Lagrange very depressed. In 1792, he married 24-year-old Renee-Francoise-Adelaide Le Monnier, the daughter of his colleague, Pierre Charles Le Monnier. It is said that she insisted that he marry her and was very devoted until his death on April 10, 1813, in Paris.
At the age of 19, Lagrange wrote to Leonhard Euler, the world's greatest mathematician, describing his new ideas for calculus. Euler was so impressed that he recommended Lagrange for membership in the Berlin Academy at the extraordinarily young age of 20. Euler and Lagrange continued their correspondence and, as a result, the two collaborated on developing the calculus of variations.
