Mathematics as information compression via the matching and unification
  of patterns
  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 non-mathematical
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 SP-multiple-alignment
-- 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 widely-used structures and operations in mathematics. Examples
are also given to show how the mathematics-related disciplines of logic and
computing may be understood as ICMUP. There are many potential benefits and
applications of these ideas.
