Chapter 8 Formal Conceptual Blending in the (Co-)Invention of (Pure) Mathematics

Abstract

We claim that conceptual blending plays a key role in mathematical discovery and invention. We use a formalisation of blending in terms of colimits of many-sorted first-order logical specifications to illustrate the processes involved. In particular we present a development structured around notions from abstract areas of pure mathematics such as Commutative Algebra, Number Theory, Fields and Galois Theory. This development shows a new formal route which builds up the classical theory in the area, and also gives rise to new equivalences that characterise the notion of Dedekind Domain. We comment on the significance of this work for the computer support of abstract mathematical theory construction, as well as for (co-)inventing classic and new mathematical notions (i.e., inventing with the help of a computer program), and on the cognitive aspects involved.