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Joseph-Louis Lagrange | HearLore
Joseph-Louis Lagrange
Giuseppe Luigi Lagrangia, born the 25th of January 1736 in Turin, was destined to be a lawyer, not a mathematician. His father, a wealthy doctor of law, had planned a career in jurisprudence for his firstborn, and the young Lagrange seemed to accept this fate with quiet resignation. He studied at the University of Turin, where his heart lay not with numbers but with classical Latin. Greek geometry, the foundation of the mathematical world, appeared to him as dull and tedious. It was not until he was seventeen years old that a single accident of fate changed the trajectory of human history. He stumbled upon a paper by Edmond Halley from 1693, and in that moment, the boy who had no enthusiasm for mathematics became an accomplished mathematician within a year of incessant toil. Alone and unaided, he threw himself into the subject, proving that a single page of text could alter the course of civilization.
The King and The Greatest Mathematician
By 1756, the mathematical community in Berlin had taken notice of the shy Italian prodigy. Leonhard Euler and Pierre Louis Maupertuis, giants of the field, tried to persuade Lagrange to leave Turin for Prussia, but he refused. He was too shy, and perhaps too aware of his own limitations compared to the established masters. In 1765, Jean le Rond d'Alembert interceded on his behalf, asking him to leave Turin for a more prestigious position. Lagrange turned down the offer again, stating that Berlin would not be suitable for him while Euler was there. It was only in 1766, after Euler departed for Saint Petersburg, that Frederick the Great himself wrote to Lagrange. The King of Prussia, who called himself the greatest king in Europe, expressed a wish to have the greatest mathematician in Europe resident at his court. Lagrange was finally persuaded. He spent the next twenty years in Prussia, producing a long series of papers and composing his monumental work, the Mécanique analytique. During this time, he was a favorite of the king, who frequently lectured him on the advantages of perfect regularity of life. Lagrange accepted the lesson, studying his mind and body as though they were machines, experimenting to find the exact amount of work he could do before exhaustion. Every night he set himself a definite task for the next day, and on completing any branch of a subject, he wrote a short analysis to see what points in the demonstrations were capable of improvement.
A Life of Solitude and Sorrow
Despite his professional triumphs, the years in Berlin were marred by personal tragedy and poor health. Lagrange's wife, Vittoria Conti, whom he had married in 1767, suffered from years of illness and died in 1783, leaving him very depressed. The death of Frederick II in 1786 made the climate of Berlin difficult for the grieving mathematician. In 1786, following the King's death, Lagrange received similar invitations from states including Spain and Naples, but he accepted the offer of Louis XVI to move to Paris. In France, he was received with every mark of distinction, and special apartments in the Louvre were prepared for his reception. At the beginning of his residence in Paris, he was seized with an attack of melancholy, and even the printed copy of his Mécanique analytique, on which he had worked for a quarter of a century, lay for more than two years unopened on his desk. It was curiosity as to the results of the French Revolution that first stirred him out of his lethargy, a curiosity which soon turned to alarm as the revolution developed. In 1792, the unaccountable sadness of his life and his timidity moved the compassion of Renée-Françoise-Adélaïde Le Monnier, the twenty-four-year-old daughter of his friend, the astronomer Pierre Charles Le Monnier. She insisted on marrying him, and proved a devoted wife to whom he became warmly attached.
Giuseppe Luigi Lagrangia was born on the 25th of January 1736 in Turin. He was originally destined to be a lawyer rather than a mathematician.
Why did Joseph-Louis Lagrange move to Berlin in 1766?
Joseph-Louis Lagrange moved to Berlin in 1766 after Leonhard Euler departed for Saint Petersburg. Frederick the Great invited him to Prussia to serve as the greatest mathematician in Europe.
How did Joseph-Louis Lagrange survive the Reign of Terror in France?
Joseph-Louis Lagrange survived the Reign of Terror because Antoine Lavoisier secured his exemption from the decree ordering all foreigners to leave France. He remained in Paris despite the danger to his life as a foreigner.
What major mathematical theorem did Joseph-Louis Lagrange prove in 1770?
Joseph-Louis Lagrange proved the four-square theorem in 1770, which states that every positive integer is the sum of four squares. This result became a cornerstone of number theory.
When did Joseph-Louis Lagrange die and where was he buried?
Joseph-Louis Lagrange died in Paris on the 10th of April 1813 at 128 rue du Faubourg Saint-Honoré. He was buried in the Panthéon in Paris the same year.
The French Revolution brought terror to the gates of Paris, and Lagrange found himself in a precarious position as a foreigner. In September 1793, the Reign of Terror began. Under the intervention of Antoine Lavoisier, Lagrange was specifically exempted by name in the decree of October 1793 that ordered all foreigners to leave France. On the 4th of May 1794, Lavoisier and twenty-seven other tax farmers were arrested and sentenced to death. They were guillotined on the afternoon after the trial. Lagrange said on the death of Lavoisier that it took only a moment to cause this head to fall, and a hundred years would not suffice to produce its like. Though Lagrange had been preparing to escape from France while there was yet time, he was never in any danger. Different revolutionary governments, and at a later time Napoleon, gave him honours and distinctions. This safety may to some extent be due to his life attitude, which he expressed many years before: I believe that, in general, one of the first principles of every wise man is to conform strictly to the laws of the country in which he is living, even when they are unreasonable. He was instrumental in the decimalisation process in Revolutionary France, and was offered the presidency of the Commission for the reform of weights and measures. After Lavoisier's death in 1794, it was largely Lagrange who influenced the choice of the metre and kilogram units with decimal subdivision, by the commission of 1799.
The Silent Teacher and The Perfect Book
In 1794, Lagrange was appointed professor of the École Polytechnique, and his lectures there were described by mathematicians who had the good fortune to be able to attend them as almost perfect both in form and matter. Beginning with the merest elements, he led his hearers on until, almost unknown to themselves, they were themselves extending the bounds of the subject. Above all, he impressed on his pupils the advantage of always using general methods expressed in a symmetrical notation. However, Lagrange does not seem to have been a successful teacher in the eyes of the students. Fourier, who attended his lectures in 1795, wrote that his voice was very feeble, at least in that he did not become heated, and he had a very marked Italian accent and pronounced the s like z. The students, of whom the majority were incapable of appreciating him, gave him little welcome, but the professeurs made amends for it. His fundamental treatise, the Mécanique analytique, was issued in 1788 under the supervision of Laplace, Cousin, Legendre, and Condorcet. Lagrange remarked that mechanics was really a branch of pure mathematics analogous to a geometry of four dimensions, namely, the time and the three coordinates of the point in space. It is said that he prided himself that from the beginning to the end of the work there was not a single diagram. Sir William Rowan Hamilton said the work could be described only as a scientific poem.
The Four Squares and The Five Roots
Lagrange's contributions to number theory were as profound as his work in mechanics, yet they remain less celebrated by the general public. In 1770, he proved the theorem, stated by Bachet without justification, that every positive integer is the sum of four squares. This result, known as Lagrange's four-square theorem, was a cornerstone of number theory. He also proved Wilson's theorem that for any integer, the factorial of that integer plus one is a multiple of the integer if and only if the integer is a prime. His papers of 1773, 1775, and 1777 gave demonstrations of several results enunciated by Fermat, and not previously proved. In 1770 and 1771, he worked on the general process for solving an algebraic equation of any degree via the Lagrange resolvents. This method fails to give a general formula for solutions of an equation of degree five and higher because the auxiliary equation involved has a higher degree than the original one. The significance of this method is that it exhibits the already known formulas for solving equations of second, third, and fourth degrees as manifestations of a single principle, and was foundational in Galois theory. He also made contributions to the theory of continued fractions and proved that Pell's equation has a nontrivial solution in the integers for any non-square natural number.
The Stars and The Senate
Lagrange's work in astronomy was equally groundbreaking, particularly his study of the three-body problem for the Earth, Sun, and Moon. In 1772, he found the special-case solutions to this problem that yield what are now known as Lagrangian points. These points are locations in space where the gravitational forces of two large bodies balance the centrifugal force felt by a smaller object, allowing it to remain in a stable position relative to the two larger bodies. He also worked on the motion of Jupiter's satellites in 1766 and the secular equation of the Moon in 1773. In 1808, he explained how, by the variation of arbitrary constants, the periodical and secular inequalities of any system of mutually interacting bodies could be determined. His determination of the secular and periodic variations of the elements of the planets, from 1781 to 1784, agreed closely with those obtained later by Le Verrier. In 1799, he was appointed senator, and he was the first signer of the Sénatus-consulte which in 1802 annexed his fatherland Piedmont to France. He acquired French citizenship in consequence. The French claimed he was a French mathematician, but the Italians continued to claim him as Italian. Napoleon, when he attained power, warmly encouraged scientific studies in France, and was a liberal benefactor of them.
The Final Poem and The Pantheon
In 1810, Lagrange started a thorough revision of the Mécanique analytique, but he was able to complete only about two-thirds of it before his death in Paris in 1813, in 128 rue du Faubourg Saint-Honoré. Napoleon honoured him with the Grand Croix of the Ordre Impérial de la Réunion just two days before he died. He was buried that same year in the Panthéon in Paris. The inscription on his tomb reads in translation: Joseph Louis Lagrange. Senator. Count of the Empire. Grand Officer of the Legion of Honour. Grand Cross of the Imperial Order of the Reunion. Member of the Institute and the Bureau of Longitude. Born in Turin on the 25th of January 1736. Died in Paris on the 10th of April 1813. Lagrange is one of the 72 prominent French scientists who were commemorated on plaques at the first stage of the Eiffel Tower when it first opened. Rue Lagrange in the 5th Arrondissement in Paris is named after him. In Turin, the street where the house of his birth still stands is named via Lagrange. The lunar crater Lagrange and the asteroid 1006 Lagrangea also bear his name. He left behind a legacy that transformed Newtonian mechanics into a branch of analysis, creating a foundation for the development of mathematical physics in the nineteenth century and beyond.