The Breakthrough

The meetings of various scholars in the so-called Signific Circle continued on a fairly informal level. It was mostly a small group of followers of Van Eeden, that met every fortnight in the pharmacy of Brouwer’s wife, in the colony of Van Eeden, or in Brouwer’s cottage or garden. Brouwer’s time and attention were mostly devoted to getting his intuitionism going. This was a success indeed; Brouwer managed to establish the ‘shocking’ facts that surprised, and partly alienated, the mathematical community. On the basis of his continuity theorem and an suitable form of transfinite induction the continuity theorem; every real function is (locally uniformly) continuous. This established beyond any doubt that intuitionism was not a poor subsystem of classical mathematics, but a system with its own strong principles and results. Fraenkel was one the first to appreciate Brouwer’s enterprise, he gave intuitionism ample space in his books on set theory. Brouwer’s Ph.D. student Heyting had started to join Brouwer in his project. He started to give presentations of intuitionism that could be grasped by the general mathematician, which did change the position of intuitionism as a mathematical doctrine.