Quantum Mathematics - briefly
Fundamentals of Quantum Mathematics
Briefly: what is this book about?
1. This is about fundamental questions of mathematics. The assertion of existing mathematics that space is a collection of points,
lines and planes is not true and is only a convenient model for solving practical problems, which in itself is not bad, but does not
allow us to understand the real structure of space. The book presents a model that, in the author's opinion, reflects the real structure
of space. An attempt is also made to resolve the question of the origin of numbers, and thereby reveal the internal structure of numbers.
2. Quantum Mathematics is built on three axioms, two of which are the unity of two independent assertions, combined into one due to
semantic necessity, that is, in reality, Quantum Mathematics is based on five independent assertions.
3. The concept of a functional dependence between series of numbers is introduced, which is not formal in nature, but reflects the real
properties objects of space, with specific examples provided.
4. The concept of trigonometric functions defined on a set of integers, the range of which is also integers, is introduced.
5. Based on the introduced trigonometric functions, as well as other new mathematical tools, combinatorial problems have been solved,
the solution of which is essentially a solution to the Gauss's problem on the number of integer "points" in circular and spherical "layers"
in the sense of not an estimated, but an exact solution. In this case, not only a specific formula is given for determining the exact number
of solutions, but also formulas are given for listing the corresponding pairs and triplets of integers without using algorithmic methods.
The book will be useful to all who believe that the existing mathematical view of the world requires a radical revision. If our world is
objective, then there must be an objective theory built on the basis of a logically substantiated and causative physical model, using a
mathematical apparatus that may not be simple, but at least understandable, figuratively representable, and devoid of the abstractness
and excessive idealization that is characteristic of mathematics existing today.
This book is a call for discussion on the issue of creating not abstract, but objective mathematics,
capable of reflecting the properties of discrete space.