The self-energy of the electron: a quintessential problem in the development of QED

The development of Quantum Electrodynamics (QED) is sketched from its earliest beginnings until the formulations of 1949, using the example of the divergent self-energy of the electron as a quintessential problem of the 1930's-40's. The lack of progress towards solving this problem led researchers to believe that after the conceptual revolution of quantum mechanics a new conceptual change was needed. It took a war and a new generation of algorithmically inclined physicists to pursue the conventional route of regularization and renormalization that led to the solution in 1947-1949. Some remarks on contemporary high energy physics are made.