Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combinatorial Speculations and the Combinatorial Conjecture for
  Mathematics   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.

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The categories of this paper are: q-alg
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph