ABSTRACT
1. Systematic investigations concerning the structural properties of mathematical expressions were initiated by Hilbert. He wrote:
“Mathematics like all other sciences cannot be established by means of logic alone: rather, something is already given us in the imagination as a condition preliminary to the use of logical inference and the application of logical operations; prior to all thought there are certain extra-logical concrete objects which are present intuitively as immediate experience. In order that a logical inference may be certain, these objects must be completely surveyed in all their parts and their mode of production, their differences, their succession or their juxtaposition with the objects is at the same time given directly and intuitively as something, which cannot be reduced to anything else, or as something, which requires no such reduction … “ 1
