Italian mathematician who made important contributions to intrinsic geometry. He first defined Cesaro’s curves 1896.
Cesaro was born in Naples and studied at the Ecole des Mines in Ličge, Belgium, and at the University of Rome. He was professor of higher algebra at the University of Palermo 1886–91, and then professor of mathematical analysis at Naples.
In Lezione di geometrica intrinsica/Lessons in Intrinsic Geometry 1896, Cesaro simplified the analytical expression and made it independent of extrinsic coordinate systems. He stressed the intrinsic qualities of the objects. He also described the curves which now bear his name. The monograph also deals with the theory of surfaces and multidimensional spaces in general. Much later on, Cesaro was able to emphasize the independence of his geometry from the axioms of parallels, and also established other foundations on which to base non-Euclidean geometry.
Cesaro's other work covered topics ranging from elementary geometrical principles to the application of mathematical analysis; from the theory of numbers to symbolic algebra; and from the theory of probability to differential geometry. He also made notable interpretations of James Clerk Maxwell's work in theoretical physics.