The Value of Science  The Value of Science () is a book by the French mathematician, physicist, and philosopher Henri Poincaré. It was published in 1905. The book deals with questions in the philosophy of science and adds detail to the topics addressed by Poincaré's previous book, "Science and Hypothesis" (1902). The first part of the book deals exclusively with the mathematical sciences, and particularly, the relationship between intuition and logic in mathematics. It first examines which parts of science correspond to each of these two categories of scientific thought, and outlines a few principles:  This "historic" intuition is therefore mathematical intuition. For Poincaré, it is a result of the principle of least effort, that is, of a link to scientific convention based on experimentation. Convention, thus given a context, permits one to consider different theories of the same problem, and subsequently make a choice based on the degree of simplicity and usefulness of explanations advanced by each of these theories (see also Occam's razor). The example chosen by Poincaré is that of three-dimensional space. He shows how the representation of this space is only one possibility, chosen for its usefulness among many models that the mind could create. His demonstration rests on the theory of "The Mathematical Continuum" (1893), one of Poincaré's earlier publications. Finally, Poincaré advances the idea of a fundamental relationship between the sciences of "geometry" and "analysis". According to him, intuition has two major roles: to permit one to choose which route to follow in search of scientific truth, and to allow one to comprehend logical developments: Moreover, this relation seems to him inseparable from scientific advancement, which he presents as an enlargement of the framework of science – new theories incorporating previous ones, even while breaking old patterns of thought. In the second part of his book, Poincaré studies the links between physics and mathematics. His approach, at once historical and technical, illustrates the preceding general ideas. Even though he was rarely an experimenter, Poincaré recognizes and defends the importance of experimentation, which must remain a pillar of the scientific method. According to him, it is not necessary that mathematics incorporate physics into itself, but must develop as an asset unto itself. This asset would be above all a tool: in the words of Poincaré, mathematics is "the only language in which [physicists] could speak" to understand each other and to make themselves heard.