Adrien-Marie Legendre

Adrien was a man who loved math.

He lived in France a long time ago. He wrote many books. One book helped people learn shapes.

He also found ways to study how things move. He used math to look at paths in the sky. His work helps us understand stars and comets. His name is even on the Eiffel Tower! Even a crater on the moon has his name.

Adrien-Marie Legendre was a famous math expert from France. He was born in Paris in 1752. He loved to solve hard puzzles with numbers and shapes. One of his best books was about geometry.

This book helped students learn for a very long time. He also studied how objects move through the air. This helped people understand the paths of comets in space.

Legendre found a special way to work with data. We call this the least squares method. It helps find the best fit for a group of numbers. Many people use this math today to study patterns. He also worked on a hard problem called Fermat's Last Theorem. He found a way to prove it for the number five. Many math ideas now carry his name. We see his name on the Eiffel Tower. A crater on the moon is named after him, too. He died in 1833 after being sick for a long time.

Adrien-Marie Legendre was a brilliant mathematician from France. He lived from 1752 to 1833. He spent his life studying patterns and numbers. Many math ideas today carry his name. These include the Legendre polynomials and the Legendre transformation. He also created the Legendre symbol in number theory. His work helps scientists understand many things in nature. It even helps engineers with things like electrostatics.

One of his most famous ideas is the least squares method. This is a way to find the best fit for a group of numbers. It helps people see patterns in data. He first published this idea in 1806. He used it to study the paths of comets. This method is still used today in many ways. It helps with things like statistics and signal processing. It is a very useful tool for finding the middle of many different observations.

Legendre grew up in a wealthy family in Paris. He went to school at the Collège Mazarin. In 1770, he finished his studies in math and physics. He taught at the École Militaire for several years. He also worked with the Bureau des Longitudes. In 1782, the Berlin Academy gave him a prize. This prize was for his work on how objects move through the air. His hard work caught the attention of other great thinkers.

Legendre wrote many important books during his life. His book on geometry was published in 1794. It was used as a main textbook for about 100 years. He also wrote three volumes on calculus between 1811 and 1819. In these books, he shared new ideas about special math functions. He also worked on a very hard problem called Fermat's Last Theorem. In 1830, he proved it for the number five. He was a very busy and productive scientist.

We can still see Legendre's impact on our world today. His name is one of 72 names on the Eiffel Tower. There is even a crater on the moon named after him. An asteroid in space also carries his name. He was a very respected member of many science groups. In 1831, he became an officer of the Légion d'Honneur. He lived in the village of Auteuil for a time. He is remembered as a great person in the history of math.

Adrien-Marie Legendre was a prolific French mathematician. He lived from 1752 to 1833. His work touched many different fields of science. These included number theory, geometry, and classical mechanics. Many mathematical concepts today carry his name. Examples include the Legendre polynomials and the Legendre transformation. He also created the Legendre symbol. His discoveries continue to influence physics and engineering.

One of his most significant contributions is the method of least squares. This technique helps find the best fit for a set of data points. It is used to determine the most probable middle value among different observations. Legendre first published this method in 1806. He included it as an appendix to his book on comet paths. While Carl Friedrich Gauss had discovered it earlier, Legendre was the first to officially publish it. Today, the term is a translation of the French "méthode des moindres carrés." It is essential for linear regression, statistics, and signal processing.

Legendre also made massive strides in the study of calculus. His three-volume work, *Exercices de Calcul Intégral*, was published between 1811 and 1819. In the first volume, he introduced properties of beta functions and gamma functions. He used the symbol Γ for the gamma function. He also provided a normalization where Γ(n+1) equals n factorial. The second volume explored applications in mechanics. This included studying the rotation of the Earth and the attraction of ellipsoids. His work on elliptic functions was also very deep. He worked on the classification of elliptic integrals. Later, the mathematician Niels Henrik Abel built upon this work using Jacobi's functions.

In the field of number theory, Legendre was a pioneer. He worked extensively on the distribution of prime numbers. In 1798, he made a conjecture regarding the prime number theorem. This conjecture was eventually proven by Jacques Hadamard and Charles Jean de la Vallée-Poussin in 1896. He also conjectured the quadratic reciprocity law. This law was later proven by Gauss. To this discovery, the Legendre symbol is closely linked. Furthermore, Legendre provided a proof for Fermat's Last Theorem for the exponent n = 5 in 1830. This followed a similar proof by Lejeune Dirichlet in 1828.

Legendre's early life was spent in Paris. He was born on 18 September 1752 to a wealthy family. He studied at the Collège Mazarin. In 1770, he defended his thesis in physics and mathematics. He taught at the École Militaire from 1775 to 1780. He also taught at the École Normale starting in 1795. In 1782, the Berlin Academy awarded him a prize. This was for his treatise on projectiles in resistant media. This achievement brought him to the attention of the mathematician Lagrange.

His professional life was marked by both success and hardship. He assisted with the Anglo-French Survey between 1784 and 1790. This used trigonometry to find the distance between the Paris Observatory and the Royal Greenwich Observatory. During this time, he visited London and Dover. He met with Pierre Méchain and the comte de Cassini. He also met with William Herschel, who discovered Uranus. However, the French Revolution caused him to lose his private fortune in 1793. In that same year, he married Marguerite-Claudine Couhin. She helped him manage his affairs during difficult times.

Legendre's influence is visible in many places today. His name is one of 72 names inscribed on the Eiffel Tower. There is a crater on the Moon named Legendre. A main-belt asteroid, 26950 Legendre, also bears his name. In 1831, he was made an officer of the Légion d'Honneur. He died in Paris on 9 January 1833. He suffered from a long and painful illness. His widow carefully preserved his belongings to memorialize him. She is buried next to him in the village of Auteuil.

Interestingly, historians discovered an error regarding his appearance. For two centuries, many books showed a profile portrait of a politician named Louis Legendre. This error happened because a sketch was simply labeled "Legendre." It was placed in books alongside other famous mathematicians. A true portrait was only rediscovered in 2008. This portrait was found in an 1820 book by the artist Julien-Léopold Boilly. This discovery corrected a long-standing mistake in his visual history.