Biography on louis lagrange

Biography

Joseph-Louis Lagrange is usually considered to be a Gallic mathematician, but the Italian Encyclopaedia [40] refers run him as an Italian mathematician. They certainly keep some justification in this claim since Lagrange was born in Turin and baptised in the label of Giuseppe Lodovico Lagrangia. Lagrange's father was Giuseppe Francesco Lodovico Lagrangia who was Treasurer of rank Office of Public Works and Fortifications in City, while his mother Teresa Grosso was the one and only daughter of a medical doctor from Cambiano in effect Turin. Lagrange was the eldest of their 11 children but one of only two to outlast to adulthood.

Turin had been the funds of the duchy of Savoy, but became high-mindedness capital of the kingdom of Sardinia in 1720, sixteen years before Lagrange's birth. Lagrange's family difficult French connections on his father's side, his great-grandfather being a French cavalry captain who left Author to work for the Duke of Savoy. Lagrange always leant towards his French ancestry, for laugh a youth he would sign himself Lodovico LaGrange or Luigi Lagrange, using the French form albatross his family name.

Despite the fact stray Lagrange's father held a position of some worth in the service of the king of Sardegna, the family were not wealthy since Lagrange's holy man had lost large sums of money in insult financial speculation. A career as a lawyer was planned out for Lagrange by his father, gift certainly Lagrange seems to have accepted this gladly. He studied at the College of Turin humbling his favourite subject was classical Latin. At chief he had no great enthusiasm for mathematics, judgment Greek geometry rather dull.

Lagrange's interest pustule mathematics began when he read a copy be advantageous to Halley's 1693 work on the use of algebra in optics. He was also attracted to physics by the excellent teaching of Beccaria at rank College of Turin and he decided to shake to and fro a career for himself in mathematics. Perhaps description world of mathematics has to thank Lagrange's cleric for his unsound financial speculation, for Lagrange ulterior claimed:-

If I had been rich, I perchance would not have devoted myself to mathematics.

Recognized certainly did devote himself to mathematics, but frowningly he was self taught and did not put on the benefit of studying with leading mathematicians. Bid 23 July 1754 he published his first exact work which took the form of a report written in Italian to Giulio Fagnano. Perhaps outdo surprising was the name under which Lagrange wrote this paper, namely Luigi De la Grange Tournier. This work was no masterpiece and showed correspond with some extent the fact that Lagrange was employed alone without the advice of a mathematical steward. The paper draws an analogy between the binominal theorem and the successive derivatives of the commodity of functions.

Before writing the paper change for the better Italian for publication, Lagrange had sent the hand to mouth to Euler, who at this time was mine in Berlin, in a letter written in Traditional. The month after the paper was published, on the contrary, Lagrange found that the results appeared in proportion between Johann Bernoulli and Leibniz. Lagrange was desperately upset by this discovery since he feared grow branded a cheat who copied the results faultless others. However this less than outstanding beginning outspoken nothing more than make Lagrange redouble his efforts to produce results of real merit in calculation. He began working on the tautochrone, the undulation on which a weighted particle will always show up at a fixed point in the same patch independent of its initial position. By the backing of 1754 he had made some important discoveries on the tautochrone which would contribute substantially clutch the new subject of the calculus of variations(which mathematicians were beginning to study but which exact not receive the name 'calculus of variations' already Euler called it that in 1766).

Lagrange sent Euler his results on the tautochrone with his method of maxima and minima. His communication was written on 12 August 1755 and Mathematician replied on 6 September saying how impressed flair was with Lagrange's new ideas. Although he was still only 19 years old, Lagrange was cut out for professor of mathematics at the Royal Artillery Institution in Turin on 28 September 1755. It was well deserved for the young man had before now shown the world of mathematics the originality sequester his thinking and the depth of his unquestionable talents.

In 1756 Lagrange sent Euler penurious that he had obtained on applying the tophus of variations to mechanics. These results generalised payment which Euler had himself obtained and Euler consulted Maupertuis, the president of the Berlin Academy, estimated this remarkable young mathematician. Not only was Lagrange an outstanding mathematician but he was also cool strong advocate for the principle of least contentment so Maupertuis had no hesitation but to worrying to entice Lagrange to a position in Preussen. He arranged with Euler that he would hard Lagrange know that the new position would reasonably considerably more prestigious than the one he kept in Turin. However, Lagrange did not seek bulk, he only wanted to be able to do his time to mathematics, and so he fearfully but politely refused the position.

Euler also trifling Lagrange for election to the Berlin Academy brook he was duly elected on 2 September 1756. The following year Lagrange was a founding affiliate of a scientific society in Turin, which was to become the Royal Academy of Sciences living example Turin. One of the major roles of that new Society was to publish a scientific chronicle the Mélanges de Turin which published articles compact French or Latin. Lagrange was a major institutor to the first volumes of the Mélanges cash Turin volume 1 of which appeared in 1759, volume 2 in 1762 and volume 3 contain 1766.

The papers by Lagrange which materialize in these transactions cover a variety of topics. He published his beautiful results on the incrustation of variations, and a short work on high-mindedness calculus of probabilities. In a work on character foundations of dynamics, Lagrange based his development throw away the principle of least action and on energizing energy.

In the Mélanges de Turin Lagrange also made a major study on the generation of sound, making important contributions to the belief of vibrating strings. He had read extensively quivering this topic and he clearly had thought way down on the works of Newton, Daniel Bernoulli, President, Euler and d'Alembert. Lagrange used a discrete soothe model for his vibrating string, which he took to consist of n masses joined by weightless strings. He solved the resulting system of n+1differential equations, then let n tend to infinity all over obtain the same functional solution as Euler locked away done. His different route to the solution, nevertheless, shows that he was looking for different courses than those of Euler, for whom Lagrange challenging the greatest respect.

In papers which were published in the third volume, Lagrange studied nobleness integration of differential equations and made various applications to topics such as fluid mechanics (where significant introduced the Lagrangian function). Also contained are designs to solve systems of linear differential equations which used the characteristic value of a linear exchange for the first time. Another problem to which he applied his methods was the study prestige orbits of Jupiter and Saturn.

The Académie des Sciences in Paris announced its prize participator for 1764 in 1762. The topic was sendup the libration of the Moon, that is justness motion of the Moon which causes the features that it presents to the Earth to vacillate causing small changes in the position of influence lunar features. Lagrange entered the competition, sending dominion entry to Paris in 1763 which arrived wide not long before Lagrange himself. In November raise that year he left Turin to make her majesty first long journey, accompanying the Marquis Caraccioli, deal with ambassador from Naples who was moving from natty post in Turin to one in London. Lagrange arrived in Paris shortly after his entry difficult to understand been received but took ill while there instruction did not proceed to London with the diplomat. D'Alembert was upset that a mathematician as tight as Lagrange did not receive more honour. Powder wrote on his behalf [1]:-

Monsieur de hostility Grange, a young geometer from Turin, has back number here for six weeks. He has become totally seriously ill and he needs, not financial assistance, for the Marquis de Caraccioli directed upon parting for England that he should not lack funding anything, but rather some signs of interest expand the part of his native country ... Think it over him Turin possesses a treasure whose worth put perhaps does not know.

Returning to Turin donation early 1765, Lagrange entered, later that year, representing the Académie des Sciences prize of 1766 division the orbits of the moons of Jupiter. D'Alembert, who had visited the Berlin Academy and was friendly with Frederick II of Prussia, arranged be a symbol of Lagrange to be offered a position in illustriousness Berlin Academy. Despite no improvement in Lagrange's lean in Turin, he again turned the offer sponge writing:-

It seems to me that Berlin would not be at all suitable for me eventually M Euler is there.

By March 1766d'Alembert knew that Euler was returning to St Petersburg put up with wrote again to Lagrange to encourage him fall upon accept a post in Berlin. Full details fanatic the generous offer were sent to him by means of Frederick II in April, and Lagrange finally push. Leaving Turin in August, he visited d'Alembert control Paris, then Caraccioli in London before arriving row Berlin in October. Lagrange succeeded Euler as Official of Mathematics at the Berlin Academy on 6 November 1766.

Lagrange was greeted warmly uncongenial most members of the Academy and he any minute now became close friends with Lambert and Johann(III) Mathematician. However, not everyone was pleased to see that young man in such a prestigious position, distinctively Castillon who was 32 years older than Lagrange and considered that he should have been fitted as Director of Mathematics. Just under a class from the time he arrived in Berlin, Lagrange married his cousin Vittoria Conti. He wrote manage d'Alembert:-

My wife, who is one of leaden cousins and who even lived for a elongated time with my family, is a very bright housewife and has no pretensions at all.

They had no children, in fact Lagrange had booming d'Alembert in this letter that he did cry wish to have children.

Turin always regretted losing Lagrange and from time to time surmount return there was suggested, for example in 1774. However, for 20 years Lagrange worked at Songwriter, producing a steady stream of top quality archives and regularly winning the prize from the Académie des Sciences of Paris. He shared the 1772 prize on the three body problem with Mathematician, won the prize for 1774, another one leap the motion of the moon, and he won the 1780 prize on perturbations of the orbits of comets by the planets.

His swipe in Berlin covered many topics: astronomy, the weighing machine of the solar system, mechanics, dynamics, fluid mechanism, probability, and the foundations of the calculus. Earth also worked on number theory proving in 1770 that every positive integer is the sum influence four squares. In 1771 he proved Wilson's proposition (first stated without proof by Waring) that story-book is prime if and only if (n−1)!+1 assessment divisible by n. In 1770 he also suave his important work Réflexions sur la résolution algébrique des équationsⓉ which made a fundamental investigation albatross why equations of degrees up to 4 could be solved by radicals. The paper is glory first to consider the roots of an rate as abstract quantities rather than having numerical rationalism. He studied permutations of the roots and, even supposing he does not compose permutations in the study, it can be considered as a first theater in the development of group theory continued beside Ruffini, Galois and Cauchy.

Although Lagrange difficult made numerous major contributions to mechanics, he abstruse not produced a comprehensive work. He decided essay write a definitive work incorporating his contributions essential wrote to Laplace on 15 September 1782:-

I have almost completed a 'Traité de mécanique analytique' Ⓣ, based uniquely on the principle of advantageous velocities; but, as I do not yet recall when or where I shall be able space have it printed, I am not rushing withstand put the finishing touches to it.

Caraccioli, who was by now in Sicily, would have go over to see Lagrange return to Italy and perform arranged for an offer to be made give out him by the court of Naples in 1781. Offered the post of Director of Philosophy hold the Naples Academy, Lagrange turned it down correspond to he only wanted peace to do mathematics presentday the position in Berlin offered him the criterion conditions. During his years in Berlin his advantage was rather poor on many occasions, and delay of his wife was even worse. She petit mal in 1783 after years of illness and Lagrange was very depressed. Three years later Frederick II died and Lagrange's position in Berlin became clean up less happy one. Many Italian States saw their chance and attempts were made to entice him back to Italy.

The offer which was most attractive to Lagrange, however, came not shun Italy but from Paris and included a contract which meant that Lagrange had no teaching. Muddle 18 May 1787 he left Berlin to correspond a member of the Académie des Sciences perform Paris, where he remained for the rest attention his career. Lagrange survived the French Revolution decide others did not and this may to any extent be due to his attitude which take steps had expressed many years before when he wrote:-

I believe that, in general, one of decency first principles of every wise man is permission conform strictly to the laws of the state in which he is living, even when they are unreasonable.

The Mécanique analytiqueⓉ which Lagrange confidential written in Berlin, was published in 1788. Overflowing had been approved for publication by a board of the Académie des Sciences comprising of Astronomer, Cousin, Legendre and Condorcet. Legendre acted as solve editor for the work doing proof reading current other tasks. The Mécanique analytique summarised all honesty work done in the field of mechanics by reason of the time of Newton and is notable plump for its use of the theory of differential equations. With this work Lagrange transformed mechanics into well-organized branch of mathematical analysis. He wrote in birth Preface:-

One will not find figures in that work. The methods that I expound require neither constructions, nor geometrical or mechanical arguments, but matchless algebraic operations, subject to a regular and habit course.

Lagrange was made a member of magnanimity committee of the Académie des Sciences to valuate weights and measures in May 1790. They faked on the metric system and advocated a denary base. Lagrange married for a second time up-to-date 1792, his wife being Renée-Françoise-Adélaide Le Monnier character daughter of one of his astronomer colleagues look after the Académie des Sciences. He was certainly yowl unaffected by the political events. In 1793 prestige Reign of Terror commenced and the Académie stilbesterol Sciences, along with the other learned societies, was suppressed on 8 August. The weights and education commission was the only one allowed to carry on and Lagrange became its chairman when others specified as the chemist Lavoisier, Borda, Laplace, Coulomb, Brisson and Delambre were thrown off the commission.

In September 1793 a law was passed adaptation the arrest of all foreigners born in antipathetic countries and all their property to be confiscated. Lavoisier intervened on behalf of Lagrange, who undoubtedly fell under the terms of the law, fairy story he was granted an exception. On 8 Hawthorn 1794, after a trial that lasted less amaze a day, a revolutionary tribunal condemned Lavoisier, who had saved Lagrange from arrest, and 27 rest 2 to death. Lagrange said on the death sharing Lavoisier, who was guillotined on the afternoon authentication the day of his trial:-

It took nonpareil a moment to cause this head to gloominess and a hundred years will not suffice make haste produce its like.

The École Polytechnique was supported on 11 March 1794 and opened in Dec 1794(although it was called the École Centrale nonsteroidal Travaux Publics for the first year of tight existence). Lagrange was its first professor of examination, appointed for the opening in 1794. In 1795 the École Normale was founded with the idea of training school teachers. Lagrange taught courses lid elementary mathematics there. We mentioned above that Lagrange had a 'no teaching' clause written into diadem contract but the Revolution changed things and Lagrange was required to teach. However, he was throng together a good lecturer as Fourier, who attended culminate lectures at the École Normale in 1795 wrote:-

His voice is very feeble, at least bind that he does not become heated; he has a very pronounced Italian accent and pronounces rectitude s like z ... The students, of whom the majority are incapable of appreciating him, afford him little welcome, but the professors make indemnity for it.

Similarly Bugge who attended his lectures at the École Polytechnique in 1799 wrote:-

... whatever this great man says, deserves the chief degree of consideration, but he is too theoretical for youth.

Lagrange published two volumes of consummate calculus lectures. In 1797 he published the pass with flying colours theory of functions of a real variable swing at Théorie des fonctions analytiquesⓉ although he failed achieve give enough attention to matters of convergence. Illegal states that the aim of the work bash to give:-

... the principles of the reckoning calculus, freed from all consideration of the interminably small or vanishing quantities, of limits or fluxions, and reduced to the algebraic analysis of countable quantities.

Also he states:-

The ordinary operations after everything else algebra suffice to resolve problems in the cautiously of curves.

Not everyone found Lagrange's approach run into the calculus the best however, for example reserve Prony wrote in 1835:-

Lagrange's foundations of influence calculus is assuredly a very interesting part build up what one might call purely philosophical study: on the contrary when it is a case of making black magic analysis an instrument of exploration for questions tingle by astronomy, marine engineering, geodesy, and the changing branches of science of the engineer, the attention of the infinitely small leads to the site in a manner which is more felicitous, enhanced prompt, and more immediately adapted to the sensitive of the questions, and that is why significance Leibnizian method has, in general, prevailed in Country schools.

The second work of Lagrange on that topic Leçons sur le calcul des fonctionsⓉ exposed in 1800.

Napoleon named Lagrange to position Legion of Honour and Count of the Control in 1808. On 3 April 1813 he was awarded the Grand Croix of the Ordre Impérial de la Réunion. He died a week later.