Joseph-Louis Lagrange facts for kids

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Quick facts for kids Joseph-Louis Lagrange

Born	Giuseppe Lodovico Lagrangia (1736-01-25)25 January 1736 Turin, Kingdom of Sardinia
Died	10 April 1813(1813-04-10) (aged 77) Paris, First French Empire
Citizenship	Sardinia French Empire
Alma mater	University of Turin
Known for	(see list) Analytical mechanics Calculus of variations Celestial mechanics Mathematical analysis Number theory Theory of equations
Scientific career
Fields	Mathematics Astronomy Mechanics
Institutions	École Normale École Polytechnique
Academic advisors	Leonhard Euler (epistolary correspondent) Giovanni Battista Beccaria
Notable students	Joseph Fourier Giovanni Plana Siméon Poisson
Influences	Leonhard Euler
Influenced	Évariste Galois

Joseph-Louis Lagrange was a brilliant Italian and later French scientist. He was a mathematician, physicist, and astronomer. He made huge contributions to many areas of science. These included analysis, number theory, and the study of how things move (called classical and celestial mechanics).

In 1766, Lagrange became the head of mathematics at the Prussian Academy of Sciences in Berlin. He stayed there for over twenty years. During this time, he wrote many important works and won several awards. His book, Mécanique analytique, published in 1788, was a major step forward in understanding how things move. It built on the work of Newton.

In 1787, at age 51, he moved to Paris, France. He joined the French Academy of Sciences. He helped create the metric system. He also became a professor at the École Polytechnique in 1794. He was a very important figure in science during his lifetime.

Amazing Discoveries and Contributions

Lagrange was a pioneer in a field called calculus of variations. This is a way to find the best possible shape or path for something. He also created the method of Lagrange multipliers. This helps solve problems with certain limits or conditions.

He found new ways to solve differential equations. He also used differential calculus to study probabilities. Lagrange proved that every natural number can be written as the sum of four squares. His work also helped lay the groundwork for group theory. This is a key area of modern mathematics.

In calculus, he improved methods for interpolation and Taylor's theorem. He studied the three-body problem involving the Earth, Sun, and Moon. He also looked at the movement of Jupiter's moons. In 1772, he found special solutions to this problem. These are now known as Lagrangian points. Lagrange is famous for changing Newtonian mechanics into a branch of analysis. This new way of looking at mechanics is called Lagrangian mechanics.

Life Story of a Genius

Portrait of Joseph-Louis Lagrange (18th-century)

Early Life and Education

Joseph-Louis Lagrange was born Giuseppe Lodovico Lagrangia in Turin. He was the first of eleven children. His family had both Italian and French roots. His father was a lawyer. He wanted Lagrange to become a lawyer too.

At first, Lagrange wasn't very interested in mathematics. He found Ancient Greek geometry a bit boring. But when he was seventeen, he found a paper by Edmond Halley. This paper sparked his interest in math. He taught himself mathematics and became very skilled in just one year.

In 1755, he became a math assistant professor at the Royal Military Academy in Turin. He taught calculus and mechanics there. This made him the first person to teach calculus in an engineering school.

Founding Variational Calculus

Starting in 1754, Lagrange worked on a problem called the tautochrone. He found a new way to solve problems by finding the maximum or minimum of certain mathematical expressions. This led to the Euler–Lagrange equations. These equations are very important in calculus of variations.

He wrote letters to the famous mathematician Leonhard Euler about his discoveries. Euler was very impressed by Lagrange's work. Lagrange published his new method in 1762.

Early Writings and Discoveries

In 1758, Lagrange helped start a scientific society. It later became the Turin Academy of Sciences. Many of his early writings were published there. These included papers on:

The theory of how sound travels.
The problem of a vibrating string.
Probabilities.
The calculus of variations.

He also solved several problems in dynamics. He used his new calculus of variations for this. He worked on Fermat's problem about finding numbers. He also studied the general equations for the motion of three bodies attracting each other.

In 1764, he wrote about the libration of the Moon. This explained why we always see the same side of the Moon. His solution was important because it hinted at his later ideas about general equations of motion.

Years in Berlin

In 1766, Frederick the Great invited Lagrange to Berlin. Frederick wanted "the greatest mathematician in Europe" at his court. Lagrange accepted and spent the next twenty years in Prussia. During this time, he wrote many papers and his huge book, the Mécanique analytique. In 1767, he married his cousin, Vittoria Conti.

Lagrange was a favorite of the king. He worked very hard and planned his studies carefully. He tried to find out how much work he could do before getting tired. He usually wrote his papers without any mistakes or corrections.

However, Lagrange's health was not good in Berlin. His wife, Vittoria, was also very ill and died in 1783. This made Lagrange very sad. In 1786, Frederick II died. Lagrange felt it was time to leave Berlin.

Life in Paris

In 1786, Lagrange moved to Paris, France. King Louis XVI welcomed him. He was given special apartments in the Louvre palace. He became a member of the French Academy of Sciences. At first, he felt a bit down. He didn't even open his Mécanique analytique book for two years.

The French Revolution started to stir his interest. But he soon became worried as the revolution grew more intense. In 1792, he married Renée-Françoise-Adélaïde Le Monnier. She was 24 and the daughter of his friend. She was a very loving wife.

During the Reign of Terror (1793-1794), many scientists were in danger. But Lagrange was protected. Even Napoleon later honored him. Lagrange believed in following the laws of the country he lived in. This might have helped keep him safe. In 1796, the French government honored his father in Italy. They praised Lagrange for his genius. Napoleon made him a senator in 1799. Lagrange became a French citizen.

Helping with the Metric System

Lagrange played a big part in creating the metric system in the 1790s. He was asked to lead the committee for weights and measures. After the death of Antoine Lavoisier in 1794, Lagrange greatly influenced the choice of the metre and kilogram units. He also helped set up the Bureau des Longitudes in 1795.

Teaching at New Schools

In 1795, Lagrange became a math professor at the new École Normale. His lectures were simple. They were published so that many people could read them.

In 1794, he also became a professor at the École Polytechnique. Students who attended his lectures said they were almost perfect. He taught them to use general methods in a clear way. However, he wasn't always seen as a successful teacher. Joseph Fourier said Lagrange's voice was weak and he had a strong Italian accent.

Later Years and Legacy

Lagrange's tomb in the crypt of the Panthéon

In 1810, Lagrange began to update his Mécanique analytique. But he only finished about two-thirds of it before he died in Paris in 1813. Napoleon honored him with a special award just two days before his death. He was buried in the Panthéon in Paris. This is a special place for honored French people.

Important Works in Berlin

Lagrange was very busy during his twenty years in Berlin. He wrote his Mécanique analytique. He also wrote over a hundred papers for various academies. These papers were all of very high quality. He usually wrote about one paper a month.

Some of his most important papers were:

His work on how to combine astronomical observations to get the most accurate results (1771).
Papers on how fluids move and how to use infinite series in math (1784-1785).

Many papers sent to Paris were about astronomy. These included his work on the Jovian system (1766). He also wrote about the problem of three bodies (1772). He won prizes for these works.

Lagrangian Mechanics

Between 1772 and 1788, Lagrange changed how Newtonian mechanics was understood. He made the formulas simpler and easier to use. This new way of looking at mechanics is now called Lagrangian mechanics.

Algebraic Discoveries

Many of his papers in Berlin were about algebra.

He studied how to represent numbers using quadratic forms (1769-1770).
He worked on the Theory of Elimination (1770).
He proved Lagrange's theorem in group theory. This theorem states that the size of a subgroup always divides the size of the main group.
His papers from 1770 and 1771 showed a general way to solve algebraic equations. This method was very important for the development of Galois theory.
In 1773, he looked at a special kind of determinant called a Jacobian. He also found a formula for the volume of a tetrahedron.

Number Theory Breakthroughs

Lagrange also made big steps in number theory.

He was the first European to prove that Pell's equation always has a solution (1766–1769).
He proved every positive integer is the sum of four squares (1770). This was a famous problem.
He proved Wilson's theorem (1771). This theorem helps tell if a number is a prime.
He proved several results that Fermat had stated but not proved (1773, 1775, 1777).
His work Recherches d'Arithmétique (1775) developed a general theory for quadratic forms.
He also helped develop the theory of continued fractions.

Other Math Work

He wrote many articles on analytical geometry. In 1792 and 1793, he simplified the equations of quadrics (3D shapes).

From 1772 to 1785, he wrote many papers that helped create the science of partial differential equations.

Astronomy Studies

Lagrange also wrote many papers on problems in astronomy.

He tried to solve the three-body problem. This led to his discovery of the Lagrangian points (1772). These are special spots in space where objects can stay stable.
He studied the attraction of ellipsoids (1773).
He worked on the Moon's motion (1773). Here, he first introduced the idea of the "potential." This idea is very important in physics.
He studied the stability of planetary orbits (1776).
He found a way to figure out a comet's orbit from just three observations (1778, 1783).
He calculated the long-term changes in the planets' orbits (1781–1784).
He wrote about the method of interpolation (1783, 1792, 1793).

His Main Book: Mécanique analytique

Lagrange's most important book was the Mécanique analytique. In this book, he showed how all of mechanics (the study of motion) could be understood from one basic principle. He used the calculus of variations to do this.

The book's goal was to show that all of mechanics is connected to a single idea. It provided general formulas to solve any problem. He used a method called "generalised coordinates." This was a brilliant idea. Instead of tracking each part of a system, he showed that you could describe its position with a few variables. Then, you could find the equations of motion by simple calculations.

Lagrange was very proud that his book had no diagrams. He said mechanics was like a geometry of four dimensions (time and three space coordinates). At first, no one wanted to publish the book. But Legendre helped him find a publisher. It was finally released in 1788.

Work in France

Calculus and Functions

Lagrange's lectures on differential calculus at École Polytechnique became his book Théorie des fonctions analytiques (1797). This book tried to explain calculus using algebraic functions and Taylor's theorem. He wanted to avoid the confusing ideas of "infinitely large" and "infinitely small" numbers.

Another book, Leçons sur le calcul des fonctions (1804), further developed these ideas. In this book, he clearly explained his famous method of Lagrange multipliers. These works were a starting point for later mathematicians like Cauchy and Jacobi.

1813 copy of "Theorie des fonctions analytiques"
Title page to "Theorie des fonctions analytiques"
Introduction to "Theorie des fonctions analytiques"
First page of "Theorie des fonctions analytiques"

Title page of volume I of Lagrange's "Mécanique Analytique" (1811)

Using Infinitesimals

Later in his life, Lagrange changed his mind. He started to use infinitesimals (infinitely small quantities) again. In the second edition of Mécanique Analytique (1811), he said that infinitesimals are a good way to simplify proofs. He believed they were useful once you understood their spirit.

Solving Equations

His book Résolution des équations numériques (1798) came from his lectures. In it, he showed how to find the real solutions of an equation using continued fractions. He also explained how Fermat's little theorem could be used to solve certain equations.

Planetary Motion

Lagrange had already studied planetary motion in Berlin. In 1806, Poisson showed that Lagrange's formulas predicted limits for the stability of orbits. Lagrange then revisited the topic. In 1808, he explained how to determine the changes in the orbits of interacting bodies.

Awards and Honors

Lagrange received many honors during his life.

He was elected to the Berlin Academy in 1756.
He became a Fellow of the Royal Society of Edinburgh in 1790.
He was also a member of the Royal Society and the Royal Swedish Academy of Sciences in 1806.
In 1808, Napoleon made him a Grand Officer of the Legion of Honour. He also became a Count of the Empire.
Just two days before he died in 1813, he received the Grand Croix of the Ordre Impérial de la Réunion.
He was buried in the Panthéon in Paris.

Lagrange won the French Academy of Sciences prize several times.

In 1764, for his work on the Moon's libration.
In 1766, for his work on the motion of Jupiter's satellites.
He also shared or won prizes in 1772, 1774, and 1778.

Lagrange is one of the 72 prominent French scientists honored on the Eiffel Tower. A street in Paris, Rue Lagrange, is named after him. In Turin, Italy, the street where he was born is called via Lagrange. The lunar crater Lagrange on the Moon and the asteroid 1006 Lagrangea are also named in his honor.