**Joseph-Louis, comte de Lagrange, born Giuseppe Lodovico Lagrangia (**

**January 25**

**,**

**1736**

**Turin**

**,**

**Kingdom of Sardinia**

**-**

**April 10**

**,**

**1813**

**Paris**

**) was an**

**Italian**

**/**

**French**

**mathematician**

**and**

**astronomer**

**who made important contributions to all fields of**

**analysis**

**and**

**number theory**

**and to**

**classical**

**and**

**celestial mechanics**

**as arguably the greatest mathematician of the**

**18th century**

**. It is said that he was able to write out his papers complete without a single correction required. Before the age of 20 he was professor of**

**geometry**

**at the royal artillery school at Turin. By his mid-twenties he was recognized as one of the greatest living mathematicians because of his papers on**

**wave propagation**

**and the maxima and minima of curves. His greatest work, Mécanique Analytique (**

**Analytical Mechanics**

**) (4. ed., 2 vols. Paris: Gauthier-Villars et fils, 1888-89. First Edition:**

**1788**

**), was a mathematical masterpiece and the basis for all later work in this field. On the recommendation of**

**Euler**

**and**

**D'Alembert**

**, Lagrange succeeded the former as the director of mathematics at the**

**Prussian Academy of Sciences**

**in**

**Berlin**

**. Under the**

**First French Empire**

**, Lagrange was made both a**

**senator**

**and a**

**count**

**; he is buried in the**

**Panthéon**

**.**

It was Lagrange who created the

It was Lagrange who created the

**calculus of variations**

**which was later expanded by**

**Weierstrass**

**, solved the**

**isoperimetrical problem**

**on which the variational calculus is in part based, and made some important discoveries on the**

**tautochrone**

**which would contribute substantially to the then newly formed subject. Lagrange established the theory of**

**differential equations**

**, and provided many new solutions and theorems in number theory, including**

**Wilson's theorem**

**. Lagrange's classic Theorie des fonctions analytiques laid some of the foundations of**

**group theory**

**, anticipating**

**Galois**

**. Lagrange developed the**

**mean value theorem**

**which led to a proof of the**

**fundamental theorem of calculus**

**, and a proof of**

**Taylor's theorem**

**. Lagrange also invented the method of solving differential equations known as**

**variation of parameters**

**, applied**

**differential calculus**

**to the**

**theory of probabilities**

**and attained notable work on the solution of**

**equations**

**. He studied the**

**three-body problem**

**for the Earth, Sun, and Moon (**

**1764**

**) and the movement of Jupiter’s satellites (**

**1766**

**), and in**

**1772**

**found the special-case solutions to this problem that are now known as**

**Lagrangian points**

**. But above all he impressed on mechanics, having transformed**

**Newtonian mechanics**

**into a branch of analysis,**

**Lagrangian mechanics**

**as it is now called, and exhibited the so-called mechanical "principles" as simple results of the variational calculus.**

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