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The problem of determining maximum number of orthonormal vector fields on spheres was solved completely in a large period of time. First, certain number of orthonormal vector fields have been constructed explicitly with the contributions of several mathematicians like Radon, Hurwitz, Hopf, Eckman between 1923-1942, and twenty years later Adams showed that this was the best possible. Since then, the attempts to construct these maximal number of orthonormal vector fields on spheres by new methods have been continuing. In this talk, after a quick survey of past results, we will mention some of these new attempts and results obtained.