Abstract: By means of matrix geometry and projective geometry,Hua Luo-geng studied and simplified the principles of Einstein＇s special relativity,found the symmetry of inertial motion and promoted the research on de Sitter invariant special relativity.His very deep considerations on these issues have guided us till now how to face the challenges from precise cosmology for Einstein＇s theory of relativity as foundation of cosmic physics characterized by the cosmological constant Λ0. The principle of relativity should further be generalized to the principle of relativity of two universal constants c and l with symmetry of inertial motion of 24 generators.Then there are three kinds of special relativity of Poincaré,de Sitter and anti-de Sitter invariance,respectively.They form a special relativity triple associated with a dual Poincaré invariant degenerated kinematics.The de Sitter special relativity of l=R≈3/Λ presents a new kinematics at cosmic scale and gets ride of relativity＇s cosmic puzzle.Hua is not only a great mathematician,but also a great thinker, great educator and one of great representatives of modernization in China.

Key words: L.G.Hua（L.K.Hua）, Einstein, special relativity, inertial motion group, de Sitter special relativity