Joseph-Louis Lagrange Biography

Comte Joseph-Louis Lagrange is considered by many historians to be the foremost mathematician of 18th century Europe. He invented the calculus of variations, laid the foundation for modern mechanics, and made major contributions to the fields of algebra and number theory. He is also credited with establishing the standard of the metric system, now in widespread use throughout the world. Lagrange is highly regarded both for the originality of his work and the rigor and generality of his mathematical proofs.

Lagrange was born in Turin, Italy, on January 25, 1736. His father, a Frenchman, served as Treasurer of War in Sardinia, and his mother, Marie-Therese Gros, was the daughter of a wealthy Italian physician. Lagrange was the youngest of 11 children and the only one to survive past infancy. His early schooling focused on the classics, and although he read the works of Euclid and Archimedes, Lagrange displayed little initial interest in mathematics. It was not until he came across an article about calculus and its superiority over ancient Greek geometry that his interest was kindled. Its author, English astronomer and mathematician Edmund Halley, was cited years later by Lagrange as the individual who had most influenced his decision to pursue mathematics. By the time Lagrange was 16 years old, he had mastered so much of the subject that he was appointed as a professor of mathematics at the Artillery School in Turin.

At the age of 19, Lagrange began working on a solution to several isoperimetric problems that were then under discussion among the leading European mathematicians of the era. In the course of deriving his proofs, Lagrange developed what was to become his most important intellectual achievement, the creation of the calculus of variations. In 1756, he sent a letter describing his work to Leonhard Euler, then the director of the mathematics division at the Berlin Academy of Sciences. Euler praised and encouraged Lagrange, realizing at once the significance of his results, and the two mathematicians began a long correspondence. By 1759, through Euler's influence, Lagrange was elected to the Berlin Academy.

Lagrange continued teaching in Turin. Pulling together his most talented students, he organized a research society that evolved into the Turin Academy of Sciences. In 1759, the Academy published its first volume of memoirs. Lagrange contributed three papers, one introducing his calculus of variations, another on the application of differential calculus to the field of probability, and a third regarding the theory of sound. In this last paper, he provided a mathematical description of string vibration, using a partial differential equation. His result settled an ongoing controversy about the subject between Euler and French mathematician Jean le Rond d'Alembert, favoring Euler's position.

Throughout 18th century Europe, the learned academies encouraged research in celestial mechanics, frequently offering the incentive of a prize, since knowledge in this area was valuable to navigation. In 1764, Lagrange entered a competition sponsored by the French Académie Royale des Sciences to determine the gravitational forces that caused the moon to present a relatively consistent face to earth. For his calculations he received the Grand Prize. Two years later Lagrange again won the Grand Prize from the Académie, this time for deriving a partial solution to a more complicated gravitational problem involving the planet Jupiter, its four then-known satellites, and the sun. That same year, Lagrange received an invitation from King Frederick of Prussia to become director of mathematics at the Berlin Academy, replacing Euler, who had departed for St. Petersburg. Accepting the appointment in November of 1766, Lagrange entered a prolific period, composing memoirs nearly every month on subjects ranging from probability to the theory of equations.

In 1767, Lagrange published On the Solution of Numerical Equations, a treatise in which he explored universal methods for reducing equations from higher to lower degree. This work would help set the stage for the development of modern algebra. Lagrange also made early contributions to number theory, solving several of Fermat's theorems. He continued his investigation of gravitational interactions among planetary bodies, winning, in 1772, his third Grand Prize from the French Académie for a memoir on attractions among the sun, moon, and Earth. In 1774 and in 1778 he again won Grand Prizes, first for work related to lunar movement, then for a study of the perturbations of comets.

During his tenure at the Berlin Academy, Lagrange worked steadily on the topic of mechanical analysis, employing his calculus of variations. Through his efforts, the study of fluid and solid mechanics was to be unified. His Mecanique Analytique, finally published in 1788, applied calculus to the mechanics of rigid bodies and contained the general equations for describing motion in mechanical systems. This work is universally considered his most important masterpiece. Ironically, Lagrange lost interest in the subject, and in mathematics in general, in the years before its publication. He began suffering from depression around 1780. When Frederick the Great died in 1786 an indifference toward science and a resentment toward foreigners arose in Berlin. Lagrange sought and obtained a position with the French Académie, where he was well-received. In Paris, his depression worsened. He was known to stare out the window for long periods of time and he hardly spoke. In letters to his friends and colleagues he wrote that mathematics was no longer important.

It was not until after the French Revolution that Lagrange finally began to emerge from his apathy and end his ambivalence toward mathematics. The monarchy had fallen and the Académie lost its royal patronage. Many of Lagrange's colleagues were beheaded, but Lagrange himself had managed to remain a politically neutral figure. He was granted a pension by the revolutionists and eventually appointed to a government committee that was charged with establishing standards for weights and measures. It was in this position that he persuaded the French to adopt the metric system. In 1795, Lagrange became a professor of mathematics at the newly formed École Normale and when it closed two years later, he assumed a professorship at the École Polytechnique. In an attempt to clarify the topic of calculus for his students he wrote Theory of Analytic Functionsin 1797 and Lessons on the Calculus of Functionsin 1801. In these texts Lagrange attempted to reduce calculus to an algebraic system and was unsuccessful. Still, the works proved valuable as a catalyst to 19th century mathematicians who would refine his ideas and develop a more coherent calculus.

When Lagrange reached his seventies, he began revising and extending his Mecanique Analytique, completing a second edition. The long hours of work diminished his strength and energy and he suffered increasingly from fainting spells. On April 10, 1813, Lagrange died. His body was brought to rest in the Pantheon, as a tribute to the contributions he made to France.

Lagrange was known for his gentle demeanor and his diplomatic skills. At the Berlin Academy, he fell into favor with Frederick the Great, who had been highly critical of Lagrange's predecessor, Leonhard Euler. When Lagrange arrived at the French Académie he was doted upon by Queen Marie-Antoinette, yet he also managed to remain on good terms with leaders of the French Revolution, Napoleon Bonaparte, who made Lagrange a Senator, a Count of the Empire, and a Grand Officer of the Legion of Honor, consulted him frequently on philosophical and technical matters. Shortly after accepting his appointment at the Berlin Academy in 1766, Lagrange married a young woman to whom he was related. In his correspondence with his friend and colleague d'Alembert, he referred to the marriage as "inconsequential" and one of convenience. Nonetheless, when his wife took ill and died a few years later, Lagrange was reportedly heartbroken. He did not marry again until he was living in Paris and suffering from his depression. Then, at the age of 56 he took as his second wife the teenage daughter of his friend, astronomer Pierre-Charles Lemonnier. His new bride was devoted to him, and it is said she helped Lagrange regain his interest in mathematics. Neither marriage resulted in children.