The Pragmatism of Hilbert's Programme

On 17 June 1899 the Göttingen society took part in the festive unveiling of the Gauss-Weber monument in memory of the great mathematical and physical tradition of the University of Göttingen. On the occasion of this event a commemorative volume was published containing two contributions: Emil Wiechert’s paper on the foundation of electrodynamics (Wiechert 1899 ) and David Hilbert’s paper on the foundations of geometry (Hilbert 1899 ). Hilbert’s paper became a mathematical bestseller, Hilbert himself one of the leading figures in the world of mathematics. This is best illustrated by the fact that Hilbert was honored to speak at the Second Congress of Mathematicians that took place in Paris in August 1900 on the occasion of the centenary world’s fair at that place. Hilbert’s lecture “Mathematical Problems” (Hilbert 1900 ) was intended to set and at least partly succeeded in setting the mathematical agenda for the new century. Hilbert was able to capture “the imagination of the mathematical world with his list of problems for the twentieth century,” as Constance Reid wrote (1970 , 84). “His rapidly growing fame,” she continues, “promised that a mathematician could make his reputation for himself by solving one of the Paris problems” (ibid.). In his Foundations of Geometry , published one year earlier, Hilbert introduced paradigmatically what can be called a formalist foundation of a branch of mathematics. This position in the philosophy of mathematics is