Présentation de l'éditeur
In considering the history of modern mathematics two questions at once arise: (1) What limitations shall be placed upon the term Mathematics? (2) What force shall be assigned to the word Modern? In other words, how shall Modern Mathematics be defined? In these pages the term Mathematics will be limited to the domain of pure science. Questions of the applications of the various branches will be considered only incidentally. Such great contributions as those of Newton in the realm of mathematical physics, of Laplace in celestial mechanics, of Lagrange and Cauchy in the wave theory, and of Poisson, Fourier, and Bessel in the theory of heat, belong rather to the field of applications. In particular, in the domain of numbers reference will be made to certain of the contributions to the general theory, to the men who have placed the study of irrational and transcendent numbers upon a scientific foundation, and to those who have developed the modern theory of complex numbers and its elaboration in the field of quaternions and Ausdehnungslehre. In the theory of equations the names of some of the leading investigators will be mentioned, together with a brief statement of the results which they secured. The impossibility of solving the quintic will lead to a consideration of the names of the founders of the group theory and of the doctrine of determinants. This phase of higher algebra will be followed by the theory of forms, or quantics. The later development of the calculus, leading to differential equations and the theory of functions, will complete the algebraic side, save for a brief reference to the theory of probabilities. In the domain of geometry some of the contributors to the later development of the analytic and synthetic fields will be mentioned, together with the most noteworthy results of their labors. Had the author’s space not been so strictly limited he would have given lists of those who have worked in other important lines, but the topics considered have been thought to have the best right to prominent place under any reasonable definition of Mathematics. Modern Mathematics is a term by no means well defined. Algebra cannot be called modern, and yet the theory of equations has received some of its most important additions during the nineteenth century, while the theory of forms is a recent creation. Similarly with elementary geometry; the labors of Lobachevsky and Bolyai during the second quarter of the century threw a new light upon the whole subject, and more recently the study of the triangle has added another chapter to the theory. Thus the history of modern mathematics must also be the modern history of ancient branches, while subjects which seem the product of late generations have root in other centuries than the present. To the influence of the schools and the journals must be added that of the various learned societies3 whose published proceedings are widely known, together with the increasing liberality of such societies in the preparation of complete works of a monumental character. CONTENTS: 1 - THEORY OF NUMBERS 2 - IRRATIONAL AND TRANSCENDENT NUMBERS 3 - COMPLEX NUMBERS 4 - QUATERNIONS AND AUSDEHNUNGSLEHRE 5 - THEORY OF EQUATIONS 6 - SUBSTITUTIONS AND GROUPS 7 - DETERMINANTS 8 - QUANTICS 9 - CALCULUS 10 - DIFFERENTIAL EQUATIONS 11 - INFINITE SERIES. 12 - THEORY OF FUNCTIONS 13 - PROBABILITIES AND LEAST SQUARES 14 - ANALYTIC GEOMETRY 15 - MODERN GEOMETRY 16 - ELEMENTARY GEOMETRY 17 - NON-EUCLIDEAN GEOMETRY
Biographie de l'auteur
David Eugene Smith (1860 – 1944) was an American mathematician, educator, and editor. David Eugene Smith is considered one of the founders of the field of mathematics education. Smith was born in Cortland, New York, to Abram P. Smith, attorney and surrogate judge, and Mary Elizabeth Bronson, who taught her young son Latin and Greek. He attended Syracuse University, graduating in 1881 (Ph. D., 1887; LL.D., 1905). He studied to be a lawyer concentrating in arts and humanities, but accepted an instructorship in mathematics at the Cortland Normal School in 1884 where he attended as a young man. While at the Cortland Normal School Smith became a member of the Young Men's Debating Club (today the Delphic Fraternity.) He became a professor at the Michigan State Normal College in 1891 (later Eastern Michigan University), the principal at the State Normal School in Brockport, New York (1898), and a professor of mathematics at Teachers College, Columbia University (1901) where he remained until his retirement in 1926. Smith became president of the Mathematical Association of America in 1920 and served as the president of the History of Science Society in 1927. He also wrote a large number of publications of various types. He was editor of the Bulletin of the American Mathematical Society; contributed to other mathematical journals; published a series of textbooks; translated Felix Klein's Famous Problems of Geometry, Fink's History of Mathematics, and the Treviso Arithmetic. He edited Augustus De Morgan's A Budget of Paradoxes (1915) and wrote many books on Mathematics.
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