Joseph-Louis Lagrange(1736 — 1813)
Joseph-Louis Lagrange
France, royaume de Sardaigne
8 min read
Franco-Sardinian mathematician and astronomer (1736–1813), considered one of the greatest mathematicians of the 18th century. He revolutionized mechanics with his analytical formulation and founded the calculus of variations.
Frequently asked questions
Famous Quotes
« Algebra is generous; she often gives more than is asked of her.»
Key Facts
- Born in Turin in 1736, he developed the calculus of variations at the age of 19
- Published the Mécanique analytique in 1788, reformulating all of Newton's mechanics without geometric figures
- Director of the Berlin Academy of Sciences from 1766 to 1787, succeeding Euler
- Contributed to the creation of the decimal metric system in France from 1790
- Died in Paris in 1813, having been made a count of the Empire by Napoleon
Works & Achievements
Lagrange's absolute masterpiece, this work reformulates all of classical mechanics in terms of algebraic equations, without a single diagram. The “Lagrange equations” it contains are still taught today in advanced university-level physics and mathematics courses.
A founding paper in the calculus of variations, a discipline largely invented by Lagrange. This branch of mathematics, which seeks the optimal form of a curve, is used today in quantum physics and robotics.
By analyzing why classical methods fail to solve fifth-degree equations, Lagrange laid the groundwork for what would become group theory — work that Galois and Abel would develop fifty years later.
Lagrange attempts to eliminate infinitesimals from differential calculus by grounding it entirely in power series. Although this approach would eventually be superseded, it deeply influenced the development of rigorous analysis in the 19th century.
A series of papers on the perturbations of planetary orbits, the oscillations of the Moon, and the three-body problem. This work led in particular to the discovery of libration points, now known as “Lagrange points.”
A systematic treatise on the approximate solution of algebraic equations, which contributed to the standardization of numerical methods used by astronomers and engineers.
Anecdotes
At just 19 years old, Lagrange sent Euler a letter outlining a new mathematical method for solving certain problems involving curves. Euler, deeply impressed, immediately recognized the young man's genius and delayed publishing his own work on the subject so that all the credit would go to Lagrange.
When Frederick II of Prussia sought a successor to Euler at the Berlin Academy, Euler himself recommended Lagrange in these words: 'The greatest king in Europe ought to have the greatest mathematician in Europe at his court.' Lagrange joined Berlin in 1766 and spent twenty fruitful years there.
During the French Revolution, nearly all foreign scholars were expelled from France, but Lagrange was explicitly protected thanks to the intervention of Lavoisier and his colleagues at the Academy. He played a key role in the creation of the decimal metric system, serving on the committee on weights and measures.
Napoleon held a deep admiration for Lagrange and heaped honors upon him: Count of the Empire, senator, Grand Cross of the Legion of Honor. He described him as the 'lofty pyramid of the mathematical sciences.' Lagrange died just a few days after revising for the last time the new edition of his *Mécanique analytique*.
Lagrange sometimes suffered from bouts of melancholy that prevented him from working for months at a time. In Berlin, he wrote to d'Alembert that he found mathematics 'exhausted.' Yet each time he bounced back with a groundbreaking memoir, as though the creative crisis had forced him to deepen his thinking.
Primary Sources
No figures will be found in this work. The methods I set forth require neither constructions nor geometrical or mechanical reasoning, but solely algebraic operations subjected to a regular and uniform procedure.
I have found a general method for solving all problems of this kind, without needing to resort to any particular geometrical construction, and assuming only the rules of differential and integral calculus.
The aim of this work is to give the principles of differential calculus, free from any consideration of infinitely small or vanishing quantities, of limits or fluxions, and reduced to the algebraic analysis of finite quantities.
I communicate to you, Sir, a new method for determining curves that enjoy certain properties of maximum or minimum. This method seems to me simpler and more general than those employed hitherto.
The problem of solving algebraic equations has not yet been resolved in its full generality… I propose here to examine the various known methods for this resolution, and to seek their true principles.
Key Places
Lagrange's birthplace, where he studied and taught at the Royal School of Artillery from 1755 to 1766. He co-founded the scientific society that became the Royal Academy of Sciences of Turin.
Lagrange headed its mathematics class from 1766 to 1787, producing his most groundbreaking memoirs on the calculus of variations, celestial mechanics, and number theory.
Lagrange joined the Academy in 1787 at the invitation of Louis XVI. After the Revolution, he continued to serve within its successor, the Institut national, until his death in 1813.
Founded in 1794, the École Polytechnique counted Lagrange among its first professors of analysis. His teaching there shaped generations of French scientists and engineers.
Appointed senator under the Napoleonic Empire, Lagrange sat in the Conservative Senate housed at the Palais du Luxembourg — a symbol of the honors Napoleon bestowed upon him.
