LIPKA, JOSEPH (1883-1924), American mathematician, was born at Briessin, Poland, in 1883. He emigrated to America as a child and was educated at Columbia university (A.B., 1905; A.M., 1906; Ph.D., 1912). He was instructor in mathematics at the University of California 1907-08, and afterwards instructor 1908-17, assistant professor 1917-23 and associate professor 1923-24 of mathematics at the Massachusetts Institute of Tech nology. His earlier work, done under the influence of Prof. Kasner of Columbia, was chiefly in the field of applying differen tial geometry to dynamics and developing in Euclidean spaces of two or three dimensions the geometric properties of dynamical trajectories and related systems of curves. One of his notable earlier achievements was the establishing of the validity in all cases of the Thomson-Tait criterion for a natural family. This was already proved to hold for a Euclidean space of three dimen sions, but Lipka established it first for four and then for n dimensions and finally for a general curved space. In 1921 he
went abroad for study under various European mathematicians, especially Levi-Civita of Italy. He subsequently published a group of papers revolving about Levi-Civita's notion of parallel ism. He generalized Levi-Civita's conception by replacing the geodesics at the basis of it by the trajectories of a natural family, which suggested a new type of parallelism called "conformal parallelism," an idea of great value in the study of problems in dynamics. By introducing conformed parallelism he developed a new set of invariants which yield corresponding results bearing on trajectories. His papers are models of clear thinking and clear expression, and his early death at Boston on Jan. 24, 1924, cut short a career of great promise.
See W. Graustein, "Scientific Work of Joseph Lipka," Amer. Math. Soc. Bull., vol. xxx. (5924) and N. Wiener, "In Memory of Joseph Lipka," Jour. of Math. and Physics, vol. iii. (1924), both of which articles contain bibliographies of his writings.