Brouwer showed during his study his potential in mathematics by proving a significant decomposition theorem for four-dimensional rotations. During his student years Brouwer suffered from nervous breakdowns and minor physical problems. The cause was his military service, which brought him in a company with little patience for a young clever boy. The two basic exams at the university were passed cum laude. After the last one (1904) Korteweg accepted him as a Ph.D. student. 1904 brought more changes: he married the daughter, Lize, of the widow of a family doctor, bought a cottage, called the hut, in the countryside not far from Amsterdam. The architect was another friend from his student years, Ru Mauve (son of the famous painter). The hut allowed him to work in peace on his ambitious dissertation. In 1905 Brouwer lectured in Delft on "Life, Art, and Mysticism", a provocative view of a true mystic on life, society, language, …, which contained some elements of his philosophical views that came to underlie his intuitionistic mathematics.