The solvability of differential equations
It was a great surprise when Hans Lewy in 1957 presented a non-vanishing complex vector field that is not locally solvable. Actually, the vector field is the tangential Cauchy-Riemann operator on the boundary of a strictly pseudoconvex domain. Hörmander proved in 1960 that almost all linear partial differential equations are not locally solvable. This also has connections with the spectral instabi
