Poincaré was one of the greatest mathematicians, who made significant contributions in serval fields. This scientist was considered the last polymath, discovering the mathematical issues of the 20th century. Over the years of his career, Poincaré has written more than 500 scientific papers. These works were devoted to algebraic topology, the number theory, hyperbolic geometry, a special theory of relativity, and many other areas. Among his interests and contributions, there is also mathematical physics and applied mathematics.
For Poincaré, the initial problem was the awareness of the consequences for the scientific picture of the world. Namely, the scholar created another positivistic philosophy for natural scientists. He argued that science can comprehend not the essence of things in itself, as naive dogmatists think, but only the relations between things (Walter, 2017). The experience was noted as the only source of truth: only experience can teach something new and provide reliability. The scholar contributed to algebraic topology by focusing on manifolds, also known as mathematical spaces, which were not previously studied extensively. The Poincaré conjecture is the problem that is still not resolved.
A significant number of Poincaré’s work in mathematics is connected to the solution of the problems of celestial mechanics, in particular, the problems of three bodies. Pursuing its solution, the scientist developed the theory of integral invariants. The key achievement in mathematics was related to elaborating the theories of Hertz, Lorentz, and Helmholtz on electromagnetism (Safranek, 2018). In his works, Poincaré was close to the discovery of special relativity theory that was formulated later by Einstein. Poincaré used the methods of mathematical physics to solve problems of heat conduction, electromagnetism, hydrodynamics, and the theory of elasticity. He framed the principle of relativity and showed that it is impossible to detect absolute motion on the basis of ideas about the ether and Maxwell – Lorentz equations.
The topics discussed by Poincaré resulted in the creation of new fields of mathematics, which are actively researched by modern scholars. In today’s world that focuses on applicable mathematics, the findings of this scientist serve as the basis for deeper and detailed studies (Safranek, 2018). For example, his conventionalism and relativity theories received great attention at the end of the 20th century. The critics of logicism use the works on mathematical philosophy as a source of inspiration. It is especially valuable that the ideas of Poincaré are properly explained and linked to each other, which allows modern mathematicians to use them in practice (Walter, 2017). Even though the evidence shows no historical events that were impacted by his works, this scientist has numerous awards. Oscar II, King of Sweden’s mathematical competition (1887), Gold Medal of the Royal Astronomical Society of London (1900), Foreign mMemberof the Royal Netherlands Academy of Arts and Sciences (1897), and others can be mentioned.
Modernsociety endowed with the powerful potential of scientific and technical progress, in which science, knowledge, technology, and education play a great role. The study of mathematics advances logical thinking and accustoms a person to accuracy, providing the necessary information to understand the complex problems that arise in different fields of activity. Many major economists, social researchers, and healthcare providers consider that the further development of their professions is related to the wider application of mathematics. Problems, the solutions to which were earlier thought of as impossible, are successfully resolved through the use of mathematical methods, which expand the potential of scientific knowledge.
References
Safranek, J. (2018). Science and hypothesis by Henri Poincare. The Review of Metaphysics, 72(2), 398-399.
Walter, S. A. (2017). Henri Poincaré’s life, science, and life in science. Historia Mathematica, 44(4), 425-435.