  Combinatorics is a powerful tool for dealing with relations among objectives
mushroomed in the past century. However, an more important work for
mathematician is to apply combinatorics to other mathematics and other sciences
not merely to find combinatorial behavior for objectives. Recently, such
research works appeared on journals for mathematics and theoretical physics on
cosmos. The main purpose of this paper is to survey these thinking and ideas
for mathematics and cosmological physics, such as those of multi-spaces, map
geometries and combinatorial cosmoses, also the combinatorial conjecture for
mathematics proposed by myself in 2005. Some open problems are included for the
21th mathematics by a combinatorial speculation.
