Mathematics as information compression via the matching and unification of patterns
Abstract
This paper describes a novel perspective on the foundations of mathematics: how mathematics may be seen to be largely about 'information compression via the matching and unification of patterns' (ICMUP). ICMUP is itself a novel approach to information compression, couched in terms of nonmathematical primitives, as is necessary in any investigation of the foundations of mathematics. This new perspective on the foundations of mathematics has grown out of an extensive programme of research developing the "SP Theory of Intelligence" and its realisation in the "SP Computer Model", a system in which a generalised version of ICMUP  the powerful concept of SPmultiplealignment  plays a central role. These ideas may be seen to be part of a "Big Picture" comprising six areas of interest, with information compression as a unifying theme. The paper describes the close relation between mathematics and information compression, and describes examples showing how variants of ICMUP may be seen in widelyused structures and operations in mathematics. Examples are also given to show how the mathematicsrelated disciplines of logic and computing may be understood as ICMUP. There are many potential benefits and applications of these ideas.
 Publication:

arXiv eprints
 Pub Date:
 August 2018
 arXiv:
 arXiv:1808.07004
 Bibcode:
 2018arXiv180807004W
 Keywords:

 Computer Science  Artificial Intelligence