Offering glimpses into the fascinating world of nineteenth century mathematics, Thomas Hawkins follows a historical thread of ideas, beginning with a principle Hesse developed in 1886 for the transfer of theorems on the complex projective geometry of the plane to the complex geometry of the line and vice versa. Hawkins chronicles Klein's generalization of Hesse's principle and how this work, combined with that of Lie, led to all irreducible representations of \(SL(2)\). He also discusses Cartan's solution of Stutting's characterization problem for semisimple Lie algebras, a solution that relies on an application of Hesse's principle. Hawkins unifies his talk by emphasizing the flow of ideas between these and other mathematicians of the era. (New Orleans, LA, 1986)