Jean-Gaston Darboux (1842 – 1917) was a French mathematician. He is known owing to the results in the mathematical analysis (the theory of integration, the differential equations in private derivatives) and
differential geometry. Darboux made several important contributions to geometry and mathematical analysis. He was a biographer of Henri Poincare and he edited the selected works of Joseph Fourier and Joseph-Louis Lagrange.
Darboux received his Ph.D. from the Normal School in 1866. His thesis, written under the direction of Michel Chasles, was titled Sur les surfaces orthogonales. In 1873 has received a rank of the professor in Sorbonne,
assisted Liouville. Among his students were Emile Borel, Elie Cartan, Gheorghe Titeica and Stanislaw Zaremba. In 1876 Darboux has received Grand prix of the French Academy of sciences and was elected to the Academy of
Sciences in 1884. In 1895 he became a foreign member-correspondent of the Petersburg academy of sciences. In 1900, Darboux was appointed the Academy's permanent secretary of its Mathematics section. In 1902, he was
elected to the Royal Society; in 1916, he received the Sylvester’s Medal from the Society. Darboux's contribution to the differential geometry of surfaces appears in the four volume collection of studies he published
between 1887 and 1896.
His works on geometry (about sections of ring surfaces, about lines of curvature, about imposing surfaces, about asymptotic lines, about cycloids, about a surface of a wave, about geodetic curves, about surfaces of
constant full curvature), under the analysis (about Laplace’s number, about the equations with private derivatives, about the Storm’s theorem, of Pfaff ’s problem), on the mechanic and the mathematical physics (about
impact of bodies, about joints, about astatic systems, about the central forces, about the theory of rotation of bodies on Poinsot) are known. From many scientific results received by him we’ll specify the following.
He has defined lines of curvature on Lames tetrahedral surfaces, asymptotic lines on Steiner’s surface, on a surface of the centers of the main curvature of ellipsoid; has given the new proof of theorems about the
polygons inscribed in and circumscribed around conic sections; has shown, that from orthogonal system with n variables the same system with (n -1) variables is maybe received; Has applied elliptic functions
to research of deformations of the kinematic four-supporter; has given a new method of preparation of the differential equations of the surfaces imposed on given; has given new geometrical concept of rotation of a firm
body around of a motionless point by inertia, etc.