Joseph-Louis Lagrange

• 1. A Turin Boy And A Halley Paper

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  Giuseppe Luigi Lagrangia was born in Turin on the 25th of January 1736. He grew up as the firstborn of eleven children in a family that had lost most of its wealth before he reached adulthood. His father held a position as Treasurer of Public Works, yet financial ruin shadowed their household. The young Giuseppe initially showed no interest in mathematics or Greek geometry. He found classical Latin to be his favorite subject instead. At age seventeen, an accidental discovery changed everything. He came across a paper by Edmond Halley from 1693 regarding the tautochrone problem. This single document ignited a passion that would consume him for the rest of his life. Alone and unaided, he threw himself into mathematical studies with relentless intensity. Within one year of incessant toil, he became an accomplished mathematician. Charles Emmanuel III appointed him to teach calculus at the Royal Military Academy in 1755. There he taught courses in mechanics to support the Piedmontese army's adoption of ballistics theories.

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• 2. The Berlin Years And Euler

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  Leonhard Euler and Pierre Louis Maupertuis tried to persuade Lagrange to move to Berlin as early as 1756. He shyly refused the offer twice because he did not want to work while Euler was still there. In 1765, Jean le Rond d'Alembert interceded on his behalf with Frederick II of Prussia. Frederick wrote directly to Lagrange expressing the wish of the greatest king in Europe to have the greatest mathematician resident at his court. Lagrange finally accepted this invitation in 1766 after Euler left for Saint Petersburg. He spent the next twenty years producing papers at the rate of about one per month. His health remained poor during these decades, and his wife Vittoria Conti suffered even worse illness before dying in 1783. Despite personal tragedy, he produced a long series of papers published in both Turin and Berlin transactions. Some of these were treatises of high order of excellence without exception. He contributed between one and two hundred papers to various academies during this period. The most important included discussions on combining astronomical observations to give the most probable result in 1771. Other significant works covered fluid pressure, integration by infinite series, and problems proposed by the Académie française.

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• 3. Mécanique Analytique And Pure Math

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  Lagrange composed his monumental work Mécanique analytique over a quarter of a century while living in Berlin. The book was first published in Paris in 1788 under the supervision of Laplace and Legendre. It offered the most comprehensive treatment of classical mechanics since Isaac Newton wrote his Principia. Lagrange laid down the law of virtual work as a single fundamental principle from which all mechanics could be deduced. He used generalized coordinates to express kinetic and potential energies in terms of variables representing degrees of freedom. This method replaced the consideration of individual parts with general equations now written as T minus V equals zero. Sir William Rowan Hamilton later described the work as a scientific poem due to its elegance. Lagrange remarked that mechanics was really a branch of pure mathematics analogous to a geometry of four dimensions. He prided himself that from beginning to end there was not a single diagram in the entire text. No printer could initially be found who would publish the book until Legendre persuaded a Paris firm to undertake it. The treatise formed a basis for the development of mathematical physics throughout the nineteenth century.

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• 4. Flight From Terror And A New Life

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  Frederick II died in 1786, making the climate of Berlin difficult for Lagrange to endure. He received similar invitations from states including Spain and Naples but accepted Louis XVI's offer to move to Paris instead. In France he was received with every mark of distinction and special apartments were prepared in the Louvre. At the beginning of his residence he suffered an attack of melancholy. The printed copy of his Mécanique lay unopened on his desk for more than two years. Curiosity about the French Revolution stirred him out of this lethargy before turning to alarm. In September 1793 the Reign of Terror began when Antoine Lavoisier was thrown out of the academy along with many other scholars. 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 guillotined. 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 preparing to escape while there was yet time, he was never in any danger.

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• 5. The Metric System And Polytechnic

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  Lagrange became involved in the development of the metric system during the 1790s. He was offered the presidency of the Commission for the reform of weights and measures when preparing to escape from France. After Lavoisier's death in 1794, Lagrange largely influenced the choice of the metre and kilogram units with decimal subdivision through the commission of 1799. He also served as one of the founding members of the Bureau des Longitudes established in 1795. In 1794 he was appointed professor at the École Polytechnique upon its opening. His lectures there were described by mathematicians who attended them as almost perfect both in form and matter. Beginning with merest elements, he led his hearers until they extended the bounds of the subject themselves. Fourier noted that Lagrange had a very feeble voice and marked Italian accent that pronounced s like z. The students gave him little welcome but the professeurs made amends for it. In 1795 he took a mathematical chair at the newly established École Normale which enjoyed only four months existence. His discourses were ordered and taken down in shorthand so deputies could see how professors acquitted themselves.

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• 6. Stars And Three Body Problems

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  Lagrange studied the three-body problem for the Earth Sun and Moon starting in 1764. He examined the movement of Jupiter's satellites in 1766 before finding special-case solutions to this problem in 1772. These solutions yielded what are now known as Lagrangian points where gravitational forces balance perfectly. Other important papers covered the secular equation of the Moon published in 1773 and the earliest introduction of potential theory. He determined the secular and periodic variations of planetary elements between 1781 and 1784. The upper limits assigned for these agreed closely with those obtained later by Le Verrier. Two papers from 1778 and 1783 completely worked out the method of determining comet orbits from three observations. Though not practically available, his system of calculating perturbations formed the basis of most subsequent research on the subject. Poisson reopened the subject of planetary motions in 1806 showing that Lagrange's formulae led to certain limits for orbital stability. Lagrange discussed the whole subject afresh and explained in a letter to the academy in 1808 how periodical inequalities could be determined.

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