The Mind of the Mathematician

Chapter 4. Lagrange, Gauss, Cauchy, and Dirichlet

67 Chapter 4 } Lagrange, Gauss, Cauchy, and Dirichlet Joseph-Louis Lagrange On 25 January 1736, Joseph-Louis Lagrange was born in a small town near the city of Turin, at that time capital of the Piedmont and the seat of the Savoyard kings of Sardinia. He was one of eleven children, only two of whom reached maturity. Their father held the o≈ce of treasurer of constructions and fortifications in Turin but had lost most of his money through speculation. Their mother was the daughter of a physician and a member of the wealthy Conti family. Lagrange’s father intended his son to become a lawyer. Lagrange raised no particular objections to this plan, but eventually decided he would prefer to study the exact sciences instead. He did so with such success that by the age of 19 he had been appointed professor of mathematics at the Royal School of Artillery in Turin. In his youth, his temperament was called mild and melancholic, and it was said that he knew no other pleasure than study. In 1763 Lagrange made his first visit to Paris; until then he had traveled little. He was received with honor but became seriously ill during his stay and returned home instead of continuing to London as he had planned. Thanks to Jean le Rond d’Alembert, then permanent secretary of the Paris Academy, Lagrange received an attractive o√er from Frederick the Great of Prussia, expressing the wish of the ‘‘greatest king in Europe’’ to have the ‘‘greatest mathematician in Europe’’ resident at his court; in 1766 Lagrange became director of mathematical physics at the Berlin Academy. Before leaving Turin for the Prussian capital he made another visit to Paris but again fell ill after a banquet in his honor and departed without regret. 68 Twenty Mathematical Personalities The next year Lagrange married a cousin, Vittoria Conti. In reply to an inquiry from d’Alembert, he wrote: I don’t know whether I calculated ill or well, or rather, I don’t believe I calculated at all; for I might have done as Leibniz did, who, compelled to reflect, could never make up his mind. I confess to you that I never had a taste for marriage . . . but circumstances decided me to engage one of my young kinswomen to take care of me and all my a√airs. If I neglected to inform you it was because the whole thing seemed to me so inconsequential in itself that it was not worth the trouble of informing you of it. However, the marital relationship deepened over the years, and when Vittoria died sixteen years later after a lingering illness, Lagrange was heartbroken . During his twenty years at the Berlin Academy, Lagrange worked on what he called mécanique analytique (analytical mechanics), the application of calculus to the motion of rigid bodies. His conclusions were organized into a volume under that title published in 1788. This was his masterpiece— a scientific poem, according to Hamilton. He was exceedingly fastidious with regard to the mathematical form of his writings: ‘‘I have a bad habit,’’ he wrote to d’Alembert, ‘‘which I am unable to shake o√. I often rewrite my articles, often many times, until I am passably satisfied with them.’’ He was a consummate artist, and his standard of mathematical elegance was exceptionally high. Lagrange was already somewhat nervous in disposition and inclined to melancholy, but around 1780 he developed a major depression and lost interest in mathematics for some years. ‘‘I begin to feel the pull of my inertia increasing little by little, and I cannot say I shall still be doing mathematics ten years from now,’’ he wrote to d’Alembert. ‘‘It also seems to me that the mine is already too deep, and that unless new veins are discovered it will have to be abandoned.’’ D’Alembert wrote back: ‘‘In God’s name do not renounce work, for you the strongest of all distractions. Good-bye, perhaps for the last time. Keep some memory of the man who of all in the world cherishes and honours you the most.’’ Following the death of Frederick the Great in 1786, an indi√erence towards science and a resentment of foreigners arose in Berlin. The following year Lagrange left the city, after twenty very successful years, to become pensionnaire vétéran of the Paris Academy, of which he had been a foreign [3.142.98.108] Project MUSE (2024-04-23 23...