Actually, different views result in different models on things in the universe. We usually view a microcosmic object to be a geometrical point and get into the macrocosmic for finding the truth locally which results in a topological skeleton or a complex network. Thus, all the known is local by ourselves but we always apply a local knowledge on the global. Whether a local knowledge can applies to things without boundary? The answer is negative because we can not get the global conclusion only by a local knowledge in logic. Such a fact also implies that our knowledge on a thing maybe only true locally. Could we hold on the reality of all things in the universe globally? The answer is uncertain for the limitation or local understanding of humans on things in the universe, which naturally causes the science’s dilemma: it gives the knowledge on things in the universe but locally or partially. Then, how can we globally hold on the reality of things in the universe? And what is the right way for applying scientific conclusions, i.e., technology? Clearly, different answers on these questions lead to different sciences with applications, maybe improper to the universe. However, if we all conform to a criterion, i.e., the coexistence of human beings with that of the nature, we will consciously review science with that of applications and get a right orientation on science’s development.

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There are no theory on antimatter structure unless the mirror of its normal matter, with the same mass but opposite qualities such as electric charge, spin, , etc. to its matter counterparts holding with the Standard Model of Particle. In theory, a matter will be immediately annihilated if it meets with its antimatter, leaving nothing unless energy behind, and the amounts of matter with that of antimatter should be created equally in the Big Bang. So, none of us should exist in principle but we are indeed existing. A few physicists explain this puzzling thing by technical assuming there were extra matter particles for every billion matter-antimatter pairs, or asymmetry of matter and antimatter in the end. Certainly, this assumption comes into beings by a priori hypothesis that the matter and antimatter forming both complying with a same composition mechanism after the Big Bang, i.e., antimatter consists of antimolecules, antimolecule consists of antiatoms and antiatom consists of antielectrons, antiprotons and antineutrons without experimental evidences unless the antihydrogen, only one antimolecule. Why only these antimatters are detected by experiments? Are there all antimatters in the universe? In fact, if the behavior of gluon in antimatter, i.e., antigluon is not like the behavior but opposites to its matter counterparts or reverses gluon interaction Fgk to

In the view of modern science, a matter is nothing else but a complex network G, i.e., the reality of matter is characterized by complex network. However, there are no such a mathematical theory on complex network unless local and statistical results. Could we establish such a mathematics on complex network? The answer is affirmative, i.e., mathematical combinatorics or mathematics over topological graphs. Then, what is a graph? How does it appears in the universe? And what is its role for understanding of the reality of matters? The main purpose of this paper is to survey the progressing process and explains the notion from graphs to complex network and then, abstracts mathematical elements for understanding reality of matters. For example, L.Euler’s solving on the problem of Kongsberg seven bridges resulted in graph theory and embedding graphs in compact n-manifold, particularly, compact 2-manifold or surface with combinatorial maps and then, complex networks with reality of matters. We introduce 2 kinds of mathematical elements respectively on living body or non-living body for self-adaptive systems in the universe, i.e., continuity flow and harmonic flow G which are essentially elements in Banach space over graphs with operator actions on ends of edges in graph G. We explain how to establish mathematics on the 2 kinds of elements, i.e., vectors underling a combinatorial structure G by generalize a few well-known theorems on Banach or Hilbert space and contribute mathematics on complex networks. All of these imply that graphs expand the mathematical field, establish the foundation on holding on the nature and networks are closer more to the real but without a systematic theory. However, its generalization enables one to establish mathematics over graphs, i.e., mathematical combinatorics on reality of matters in the universe.