In this paper, we take a look at Henri Poincaré’s view on the methodology of mathematics, taken from the book Science
 and Method, and look at the role of choosing facts in the discovery of mathematics. The author deals with the foundations
 of the methodology of science and beautifully explains the future of mathematics and the direction of the development of
 mathematics, which started from the past and is continuing, and impresses the reader with this deep thinking. The author’s
 belief in the framework of discovery of mathematical rules based on facts is well evident in this book. Poincaré’s profound
 thinking in studying the laws of chance and its hidden realities in relation to the facts of existence is undeniable. This short
 article presents a selection of the content of the first part of the book to get familiar with it.