Biography of Joseph Louis Lagrange, Mathematician

Joseph Louis Lagrange (1736–1813) is considered to be one of the greatest mathematicians in history. Born in Italy, he made his home in France before, during, and after the French Revolution. His most important contributions to modern mathematics related to number theory and celestial mechanics, and analytic mechanics; his 1788 book "Analytic Mechanics" is the foundation for all later work in the field.

Early Life

Joseph Louis Lagrange was born in Turin, the capital of the kingdom of Piedmont-Sardinia, to a well-to-do family on January 25, 1736. His father was treasurer of the Office of Public Works and Fortifications in Turin, but he lost his fortune as a result of bad investments.

Young Joseph was intended to be a lawyer and attended the University of Turin with that goal; 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. In just a year, his course of self-study was so successful that he was appointed to be an assistant professor of mathematics at the Royal Military Academy. There, he taught courses in calculus and mechanics until it became clear that he was a poor educator (though a highly talented theorist).

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.

Before leaving Turin, 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. During his time at the Society, Lagrange began applying his new ideas to several areas of mathematics:

• The theory of sound propagation.
• The theory and notation of the calculus of variations, solutions to dynamics problems, and deduction of the principle of least action.
• Solutions to dynamics problems such as the motion of three bodies mutually attracted by gravity.

Work in Berlin

Leaving Turin in 1766, Lagrange went to Berlin to fill a position recently vacated by Euler. The invitation came from Frederick the Great, who believed Lagrange to be "the greatest mathematician in Europe."

Lagrange spent 20 years living and working in Berlin. Though his health was sometimes precarious, he was extremely prolific. During this time he developed new theories about the three-body problem in astronomy, differential equations, probability, mechanics, and the stability of the solar system. His groundbreaking 1770 publication, "Reflections on the Algebraic Resolution of Equations” launched a new branch of algebra.

Work in Paris

When his wife passed away and his patron Frederick the Great died, Lagrange accepted an invitation to Paris extended by Louis XVI. The invitation included luxurious rooms at the Louvre as well as every type of financial and professional support. Depressed because of his wife's death, he soon found himself married again to a much younger woman who found the gentle mathematician fascinating.

While in Paris, LaGrange published "Analytical Mechanics," an astonishing treatise and a still-classic mathematics text, which synthesized 100 years of research in mechanics since Newton, and led to the Lagrangian equations, which detailed and defined the differences between kinetic and potential energies.

Lagrange was in Paris when the French Revolution began in 1789. Four years later, he became the head of the revolutionary weights and measures commission and helped establish the metric system. While Lagrange continued as a successful mathematician, the chemist Lavoisier (who had worked on the same commission) was guillotined. As the revolution came to a close, Lagrange became a professor of mathematics at the École Centrale des Travaux Publics (later renamed the École Polytechnique), where he continued his theoretical work on calculus.

When Napoleon came into power, he, too honored Lagrange. Before his death, the mathematician became a senator and count of the empire.

Contributions Most Significant Contributions and Publications

• Lagrange's most important publication was The "Mécanique Analytique," his monumental work in pure math.
• His most prominent influence was his contribution to the metric system and his addition of a decimal base, which is in place largely due to his plan. Some refer to Lagrange as the founder of the Metric System.
• Lagrange is also known for doing a great deal of work on planetary motion. He was responsible for developing the groundwork for an alternate method of writing Newton's Equations of Motion, referred to as "Lagrangian Mechanics." In 1772, he described the Lagrangian points, the points in the plane of two objects in orbit around their common center of gravity at which the combined gravitational forces are zero and where a third particle of negligible mass can remain at rest. This is why Lagrange is referred to as an astronomer/mathematician.
• The Lagrangian Polynomial is the easiest way to find a curve through points.

Death

Lagrange died in Paris in 1813 during the process of revising "Analytical Mechanics." He was buried in the Panthéon in Paris. 

Legacy

Lagrange left behind an incredible array of mathematical tools, discoveries, and ideas which have had a profound impact on modern theoretical and applied calculus, algebra, mechanics, physics, and astronomy.

Sources

• ." Joseph Louis Lagrange | A Short Account of the History of Mathematics"University of South Florida.
• "Joseph-Louis Lagrange." Famous Scientists.
• Joseph-Louis Lagrange." Stetson.edu.
• Struik, Dirk Jan. “Joseph-Louis Lagrange, Comte De L'Empire.” Encyclopædia Britannica, 18 Apr. 2019.