Brouwer was unusually intelligent, which he demonstrated by graduating from high school at the age of fourteen. After studying Greek and Latin for two years, he was admitted, in 1897, to the University of Amsterdam, where he studied mathematics. His abilities were quickly noticed. In 1904, the Dutch Royal Academy published an important paper by Brouwer on the subject of continuous motions in four-dimensional space. Two years after receiving his doctor of science degree in 1907, Brouwer was hired as a lecturer at the university.

Early in his career, Brouwer became interested in the logical foundations of mathematics. The study of this problem took on the form of a debate between mathematicians of opposing views. Bertrand Russell and David Hilbert believed that formal logic alone could provide the basis on which mathematics is built. On the other side, mathematicians such as Henri Poincaré, with whom Brouwer agreed for the most...