414 NOTICES OF THE AMS VOLUME 53, NUMBER 4 I n September 1930 in Königsberg, on the third day of a symposium devoted to the foundations of mathematics, the young Kurt Gödel launched his bombshell announcing his incompleteness theorem. At that time, there were three recognized “schools” on the foundations of mathematics: the logicism based on the work of Frege, Russell, and Whitehead that saw mathematics as simply part of logic, Brouwer’s radical intuitionism, and Hilbert’s proof theory (also… CONTINUE READING