Luitzen Egbertus Jan Brouwer was one of the first to clearly distinguish between language and metalanguage, as well as to distinguish between mathematics and metamathematics. Published in his dissertation from 1907—written in Dutch—these ideas did not disseminate quickly, although they soon found fertile ground when Brouwer explained them to David Hilbert on the beach of Scheveningen, Holland, in 1909.

Brouwer also had conversations with Ludwig Wittgenstein (Vienna, 1928), Edmund Husserl (Amsterdam, 1928), and Kurt Gödel (Princeton, New Jersey, 1953). These conversations may equally have been of philosophical interest, but little seems to be known about their actual contents.

Throughout his life, Brouwer explored a deep interest in the history and practice of mysticism, yet this had no effect on the content of intuitionistic mathematics. In fact, in Brouwer's view, not to engage in even the simplest mathematics is a necessary condition for...