 link for more information. and that of the calculus by Isaac NewtonNewton, Sir Isaac,
1642–1727, English mathematician and natural philosopher (physicist), who is considered by many the greatest scientist that ever lived. Early Life and Work
..... Click the link for more information. and, independently, by G. W. LeibnizLeibniz or Leibnitz, Gottfried Wilhelm, Baron von
, 1646–1716, German philosopher and mathematician, b. Leipzig.
..... Click the link for more information. . Descartes's invention (anticipated by Fermat, whose work was not published until later) made possible the expression of geometric problems in algebraic form and vice versa. It was indispensable in creating the calculus, which built upon and superseded earlier special methods for finding areas, volumes, and tangents to curves, developed by F. B. CavalieriCavalieri, Francesco Bonaventura
, 1598–1647, Italian mathematician, a Jesuit priest. Professor at Bologna from 1629, he invented the method of indivisibles (1635) that foreshadowed integral calculus.
..... Click the link for more information. , Fermat, and others. The calculus is probably the greatest tool ever invented for the mathematical formulation and solution of physical problems.
The history of mathematics in the 18th cent. is dominated by the development of the methods of the calculus and their application to such problems, both terrestrial and celestial, with leading roles being played by the BernoulliBernoulli
, name of a family distinguished in scientific and mathematical history. The family, after leaving Antwerp, finally settled in Basel, Switzerland, where it grew in fame.
..... Click the link for more information. family (especially Jakob, Johann, and Daniel), Leonhard EulerEuler, Leonhard
, 1707–83, Swiss mathematician. Born and educated at Basel, where he knew the Bernoullis, he went to St. Petersburg (1727) at the invitation of Catherine I, becoming professor of mathematics there on the departure of Daniel Bernoulli (1733).
..... Click the link for more information. , Guillaume de L'Hôpital, and J. L. LagrangeLagrange, Joseph Louis, Comte
, 1736–1813, French mathematician and astronomer, b. Turin, of French and Italian descent. Before the age of 20 he was professor of geometry at the royal artillery school at Turin.
..... Click the link for more information. . Important advances in geometry began toward the end of the century with the work of Gaspard MongeMonge, Gaspard, comte de Péluse
, 1746–1818, French mathematician, physicist, and public official. He was distinguished for his geometrical research, which laid the foundations of modern descriptive geometry, a field essential to mechanical drawing and architectural
..... Click the link for more information. in descriptive geometry and in differential geometry and continued through his influence on others, e.g., his pupil J. V. PonceletPoncelet, Jean Victor
, 1788–1867, French mathematician and army engineer. He taught at the school of mechanics at Metz and at the Faculté des Sciences and the École Polytechnique, both in Paris.
..... Click the link for more information. , who founded projective geometry (1822).
In the Nineteenth Century
The modern period of mathematics dates from the beginning of the 19th cent., and its dominant figure is C. F. GaussGauss, Carl Friedrich
, born Johann Friederich Carl Gauss, 1777–1855, German mathematician, physicist, and astronomer. Gauss was educated at the Caroline College, Brunswick, and the Univ.
..... Click the link for more information. . In the area of geometry Gauss made fundamental contributions to differential geometry, did much to found what was first called analysis situs but is now called topology, and anticipated (although he did not publish his results) the great breakthrough of non-Euclidean geometry. This breakthrough was made by N. I. LobachevskyLobachevsky, Nikolai Ivanovich
, 1793–1856, Russian mathematician. A pioneer in non-Euclidean geometry, he challenged Euclid's fifth postulate that one and only one line parallel to a given line can be drawn through a fixed point external 