Historical Background

The history of “Proof Theory” begins with the foundational crisis of Mathematics in the first decades of the twentieth century. At the turn of the century, in reaction to the explosion of mathematical knowledge, endeavors began, to provide the growing body of mathematics with a firm foundation. Some of the notions used then seemed to be problematic. This was especially true for those notions that embodied “infinities”. On the one hand, there was the notion of “infinitesimals” which dealt with “infinity in the small”. The elimination of infinitesimals by limit processes meant a big progress in giving existing mathematics a firm fundament.