As the history of human civilization demonstrates, sometimes it happens that some bright ideas of outstanding thinkers at first become popular. Then the development of science goes into another direction, and these ideas are considered false. However, the next stage of the development of science gives new birth to these ideas. Such has been the history of the idea of Democritus +  and Leucippus +  of atoms as the least particles of matter. For a long time this idea was considered false due to the fact that scientists were not able to go sufficiently deep into the matter. However, the development of scientific instruments and experimental methods made possible to discover such micro-particles that were and are called atoms although they possess very few of those properties that were ascribed to them by ancient philosophers.

Another great idea of ancient Greece was the world of ideas existence of which was postulated by Plato ^  ^^ ^^^  . In spite of the attractive character of this idea, the majority of scientists and philosophers believe (having no positive evidence in support of it) that the world of ideas does not exist. They argue that the main methods of verification in modern science are observation and experiment. However, nobody has been able to find this world by means of observations and experiments. Nevertheless, some modern thinkers, including such outstanding sages as philosopher Karl Popper #, mathematician Kurt Gödel #, and physicist Roger Penrose, continued to believe in the world of ideas giving different interpretations of this world but suggesting no ways for their experimental validation.

However, science is developing, and this development provided recently for the discovery of the world of structures. On the level of ideas, this world may be associated with the Platonic world of ideas (or pure forms) in the same way as atoms of the modern physics may be related to the atoms of Democritus. Existence of the world of structures is proved by means of observations and experiments. This world of structures constitutes the structural level of the world as whole. Each system, phenomenon, or process (either in nature or in society) has some structure. These structures exist like such things as tables, chairs, or buildings do and form the structural level of the world. When it is necessary to investigate or to create some system or process, it’s possible to do this only by means of knowledge of the corresponding structure. Structures determine the essence of things. As a result, structures correspond not only to Platonic ideas but also to forms of Aristotle ^ ^^  ^^^ .

The discovery of the structural level of reality makes possible to reconsider the global structure of world demonstrating that it has the structure of the existential triad. In addition to this, it provides for the essential unification of mathematics and physics shedding a new light on the essence of mathematics. Moreover, this discovery solves, in an unexpected way, some crucial problems and controversies of philosophy.