Linfan Mao

As a powerful tool for dealing with relations among objects, combinatorics had mushroomed in the past century. However, an even more important work for mathematician is to apply combinatorics to other mathematics and other sciences beside to find combinatorial behavior for objects. In the past few years, works of this kind frequently appeared on journals for mathematics and theoretical physics for cosmos. The main purpose of this paper is to survey these thinking and ideas for mathematics and cosmological physics, such as those of multi-space, map geometries and combinatorial cosmoses, also the combinatorial conjecture for mathematics proposed by myself in 2005. Some open problems are included for the advance of 21th mathematics by a combinatorial speculation.