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Prof. Semyon Serovaysky Al-Farabi Kazakh National University, Kazakhstan The Logical Structure of Mathematics: from Foundational Sets to Categorical Synthesis The mathematical world, like no other, is extremely fragmented. Specialists in one direction of mathematics are often not only unaware of the current problems of other sections, but do not even understand the language spoken by their colleagues. In reality, mathematics is a single organism. Its description is the subject of the author's book The Logical Structure of Mathematics: An Overview of Mathematical Concepts, published by Taylor & Francis Group. Based on the languages of mathematical logic, set theory is described as the foundation of mathematics. By means of set theory, various classes of numbers are defined. By extending the properties of numbers to sets of arbitrary nature, the main mathematical objects are defined. With their help, theories are constructed that cover almost all the most important areas of modern mathematics. Finally, by means of category theory, common properties of various theories are revealed, connections between them are established, and the possibilities of describing mathematics as a whole are discussed. |
