**Joseph-Louis Lagrange** was an Italian-born French mathematician who excelled in all fields of analysis and number theory and analytical and celestial mechanics.

- They certainly have some justification in this claim since Lagrange was born in Turin and baptised in the name of Giuseppe Lodovico Lagrangia.
- Turin had been the capital of the duchy of Savoy, but became the capital of the kingdom of Sardinia in 1720, sixteen years before Lagrange's birth.
- Lagrange's interest in mathematics began when he read a copy of Halley's 1693 work on the use of algebra in optics.
- Perhaps most surprising was the name under which Lagrange wrote this paper, namely Luigi De la Grange Tournier.
- This work was no masterpiece and showed to some extent the fact that Lagrange was working alone without the advice of a mathematical supervisor.
- Before writing the paper in Italian for publication, Lagrange had sent the results to Euler, who at this time was working in Berlin, in a letter written in Latin.
- The month after the paper was published, however, Lagrange found that the results appeared in correspondence between Johann Bernoulli and Leibniz.
- Lagrange was greatly upset by this discovery since he feared being branded a cheat who copied the results of others.
- However this less than outstanding beginning did nothing more than make Lagrange redouble his efforts to produce results of real merit in mathematics.
- Lagrange sent Euler his results on the tautochrone containing his method of maxima and minima.
- His letter was written on 12 August 1755 and Euler replied on 6 September saying how impressed he was with Lagrange's new ideas.
- Although he was still only 19 years old, Lagrange was appointed professor of mathematics at the Royal Artillery School in Turin on 28 September 1755.
- In 1756 Lagrange sent Euler results that he had obtained on applying the calculus of variations to mechanics.
- Not only was Lagrange an outstanding mathematician but he was also a strong advocate for the principle of least action so Maupertuis had no hesitation but to try to entice Lagrange to a position in Prussia.
- He arranged with Euler that he would let Lagrange know that the new position would be considerably more prestigious than the one he held in Turin.
- However, Lagrange did not seek greatness, he only wanted to be able to devote his time to mathematics, and so he shyly but politely refused the position.
- Euler also proposed Lagrange for election to the Berlin Academy and he was duly elected on 2 September 1756.
- The following year Lagrange was a founding member of a scientific society in Turin, which was to become the Royal Academy of Sciences of Turin.
- Lagrange was a major contributor to the first volumes of the Mélanges de Turin volume 1 of which appeared in 1759, volume 2 in 1762 and volume 3 in 1766.
- The papers by Lagrange which appear in these transactions cover a variety of topics.
- In a work on the foundations of dynamics, Lagrange based his development on the principle of least action and on kinetic energy.
- In the Mélanges de Turin Lagrange also made a major study on the propagation of sound, making important contributions to the theory of vibrating strings.
- Lagrange used a discrete mass model for his vibrating string, which he took to consist of nnn masses joined by weightless strings.
- His different route to the solution, however, shows that he was looking for different methods than those of Euler, for whom Lagrange had the greatest respect.
- In papers which were published in the third volume, Lagrange studied the integration of differential equations and made various applications to topics such as fluid mechanics (where he introduced the Lagrangian function).
- Lagrange entered the competition, sending his entry to Paris in 1763 which arrived there not long before Lagrange himself.
- Lagrange arrived in Paris shortly after his entry had been received but took ill while there and did not proceed to London with the ambassador.
- D'Alembert was upset that a mathematician as fine as Lagrange did not receive more honour.
- Returning to Turin in early 1765, Lagrange entered, later that year, for the Académie des Sciences prize of 1766 on the orbits of the moons of Jupiter.
- By March 1766 d'Alembert knew that Euler was returning to St Petersburg and wrote again to Lagrange to encourage him to accept a post in Berlin.
- Lagrange succeeded Euler as Director of Mathematics at the Berlin Academy on 6 November 1766.
- Lagrange was greeted warmly by most members of the Academy and he soon became close friends with Lambert and Johann(III) Bernoulli.
- However, not everyone was pleased to see this young man in such a prestigious position, particularly Castillon who was 32 years older than Lagrange and considered that he should have been appointed as Director of Mathematics.
- However, for 20 years Lagrange worked at Berlin, producing a steady stream of top quality papers and regularly winning the prize from the Académie des Sciences of Paris.
- Although Lagrange had made numerous major contributions to mechanics, he had not produced a comprehensive work.
- Caraccioli, who was by now in Sicily, would have liked to see Lagrange return to Italy and he arranged for an offer to be made to him by the court of Naples in 1781.
- Offered the post of Director of Philosophy of the Naples Academy, Lagrange turned it down for he only wanted peace to do mathematics and the position in Berlin offered him the ideal conditions.
- She died in 1783 after years of illness and Lagrange was very depressed.
- The offer which was most attractive to Lagrange, however, came not from Italy but from Paris and included a clause which meant that Lagrange had no teaching.
- The Mécanique analytique Ⓣ(Analytical mechanics) which Lagrange had written in Berlin, was published in 1788.
- With this work Lagrange transformed mechanics into a branch of mathematical analysis.
- Lagrange was made a member of the committee of the Académie des Sciences to standardise weights and measures in May 1790.
- The weights and measures commission was the only one allowed to continue and Lagrange became its chairman when others such as the chemist Lavoisier, Borda, Laplace, Coulomb, Brisson and Delambre were thrown off the commission.
- Lavoisier intervened on behalf of Lagrange, who certainly fell under the terms of the law, and he was granted an exception.
- On 8 May 1794, after a trial that lasted less than a day, a revolutionary tribunal condemned Lavoisier, who had saved Lagrange from arrest, and 27 others to death.
- Lagrange was its first professor of analysis, appointed for the opening in 1794.
- Lagrange taught courses on elementary mathematics there.
- We mentioned above that Lagrange had a 'no teaching' clause written into his contract but the Revolution changed things and Lagrange was required to teach.
- Lagrange published two volumes of his calculus lectures.
- The second work of Lagrange on this topic Leçons sur le calcul des fonctions Ⓣ(Lessons on calculating functions) appeared in 1800.
- Napoleon named Lagrange to the Legion of Honour and Count of the Empire in 1808.

Born 25 January 1736, Turin, Sardinia-Piedmont (now Italy). Died 10 April 1813, Paris, France.

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