Combinatorial Speculations and ̧ the Combinatorial Conjecture for Mathematics ̧

¸ maolinfan@163. com¸Abstract : 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. 1. The role of classical combinatorics in mathematics Modern science has so advanced that to find a universal genus in the society of sciences is nearly impossible. Thereby a scientist can only give his or her contribution in one or several fields. The same thing also happens for researchers in combinatorics. Generally, combinatorics deals with twofold questions: Question 1.1. determine or find structures or properties of configurations, such as those structure results appeared in graph theory, combinatorial maps and design Consider the contribution of a question to science. We can separate mathematical 1