Joseph Louis LaGrange
JOSEPH Louis Lagrange (1736-1813) was born in Turin, Italy, into an originally French family. In 1766 he succeeded Euler at the Berlin academy, to remain there for twenty years. Later in spite of the chaotic political situation in France, he moved to Paris and assisted at the newly established Ecole Normale and Ecole Polytechnique. Lagrange's work had a deep influence on later mathematical research, for he was the earliest mathematician of the first rank to attempt a rigorization of the calculus. He made notable contributions in the fields of mechanics, differential equations, and the calculus of variations. He also had a penchant for number theory and wrote important papers in this field. Some of his early work in the theory of equations later led Galois to the theory of groups.
Who was the most eminent mathematician of the eighteenth century ? The two most outstanding mathematicians of the eighteenth century were Euler and Lagrange, and which ofthe two is to be accorded first place is a matter of debate that often reflects the varying mathematical sensitivities of the debaters. Euler certainly published far more than Lagrange, and worked in many more diverse fields of mathematics than Lagrange, but he was largely a formalist or manipulator of formulas. Lagrange, on the other hand, may be considered the first true analyst and, though his collection of publications is a molehill compared with the Vesuvius of Euler's output, his work has a rare perfection, elegance, and exactness about it. Whereas Euler wrote with a profusion of detail and a free employment of intuition, Lagrange wrote concisely and with attempted rigor.
A spirited and exciting argument can be created at a sizable mathematics meeting or among the mathematics staff of a university by raising the question whether Euler or Lagrange is to be regarded as the superior mathematician. The result of the argument will, in all likelihood, exhibit an almost fifty-fifty split in the debaters, about half being supporters of Euler and half supporters of Lagrange.
Some years ago, Walter Crosby Eells endeavored to determine the one hundred most eminent mathematicians living prior to 1905, and to list these men in order of eminence. (See his paper, "One hundred eminent mathematicians," The Mathematics Teacher, Nov. 1962, PP. 582-588.) In this list Newton appears in first place, Leibuiz in second place, Lagrange in third place, and Euler in fourth place.
Concerning Eell's list, it is only fair to quote from him about the method he employed.
Various methods, none of them entirely free from objection, have been used by different investigators to select a group of men eminent in some field, and to arrange them in order of their eminence. On the whole there is little doubt that the so-called "space method" yields the most reliable results, particularly for the selection of men no longer living and whose places therefore have become relatively fixed in history. It consists essentially in measuring the amount of space occupied by the account of the man's career in biographical dictionaries, standard encyclopedias, and other suitable reference works, and designating as " eminent " all who occupy more than a minimum space....
Is the assumption that a man's eminence as a mathematician may be determined by the amount of space devoted to his life and accomplishments a satisfactory method to use ? " Eminence " in itself is a difficult term to define satisfactorily and a more difficult quality to measure quantitatively. Yet there is value in making the effort, if its limitations are frankly recognized.
Other methods than the space method have been used for measuring degrees of eminence. Among these are number of pages of work produced or published, relative frequency in portrait catalogues, frequency of mention in selected indexes, number of works catalogued in leading libraries, comparison of favorable and unfavorable adjectives used concerning them, and a combination of qualitative judgments of a group of selected judges.
A study of the various methods which have been used by different investigators leads to the conclusion that the space method is open to the least objections. It is true that many chance or controversial factors may lead to a man receiving an amount of space out of proportion to his prominence as a mathematician. If a man has had a long and varied career, much more space may be spent in discussing it than that given to another whose work may be of more real significance in the development of mathematics. His career may be more noteworthy for variety and length than for intrinsic mathematical worth. The unfortunate controversy over the discovery of the calculus between Newton and Leibniz and their protagonists occupies more space in the literature than its real importance justifies, but in this case (perhaps the most striking one of this type) the additional space redounds about equally to the advantage of both men. If it were eliminated entirely, Newton's position would still be preeminent, but Leibniz would probably be placed below Lagrange and Euler, rather than above them. As a matter of fact, however, all that we are justified in concluding, considering the probable errors of their positions, is that all three of these men are of practically equal rank....
A very short paper. Lagrange once thought that he had "proved" Euclid's parallel postulate. He wrote up his "proof," took it to the Institute, and began to read it. In the first paragraph he noted an oversight. He muttered, " I must think more on this," put the paper in his pocket, and sat down.