Chapter 9: Information-Oriented Analysis of Discovery and Invention in Mathematics

There is a lot of controversy about discovery and invention in mathematics. Platonists believe that mathematical objects exist as Platonic Ideas and mathematicians only discover them. Pragmatists assume that when mathematicians introduce new objects, they invent and then build them. The reality is more sophisticated and more beautiful because both processes — discovery and invention — took place in mathematics. However, from the perspective of information science, this statement has to be explained in a detailed constructive way. In addition, it needs persuasive arguments in the form of empirical evidence, such that allows to be tested and either approved or invalidated. The goal of this work is to provide such an explanation and empirical evidence validating the claim about existence of both processes in mathematics. This evidence is similar to but does not coincide with empirical evidence in physical sciences.