"Pure mathematics grows when old problems are worked out by means of new methods," Klein liked to tell his students. "As a better understanding is thus gained of the older questions, new problems naturally arise."There is perhaps no better illustration of this statement of Klein's than the project which Hilbert now undertook. In the summer of 1899, immediately after the publication of The Foundations of Geometry, he turned to an old and celebrated problem known as the Dirichlet Principle, which involved all the greatest names in the mathematical tradition of Göttingen.