The Nature of Mathematics

The essence of mathematics depends on logic and creativity, but it can be used not only for basic profit but also for various practical purposes. The essence of mathematics lies in its beauty and intellectual challenges. This paper is divided into three parts: pattern and relationship, mathematics, science and technology, and mathematical exploration. First, mathematics is the science of patterns and relationships. As a theoretical order, mathematics explores relationships that may exist between abstracts, regardless of whether the abstraction has something corresponding to the real world.

Keith: In natural science, mathematics is an absolute ruler. If you break the law of mathematics, you no longer do physics, astronomy etc. But in the humanities, mathematics is just a tool. It's all right, and it's always been more convenient, but it's still just a tool. Good bye to my book, Descartes seeks to clarify the inherent limitations of the mathematical method ("Cartesian method") in human science that I saw.

Mathematics is indispensable in various fields such as natural science, engineering, medicine, finance, social science and so on. Applied mathematics has led to new mathematical fields such as statistics and game theory. Mathematicians are engaged in mathematics without thinking of any application for pure mathematics or my interests. Actual applications often start with pure mathematics. The history of mathematics can be seen as ever-increasing abstraction. The first abstraction shared by many animals may be abstraction of numbers. I recognize that there are similarities between the two apple collections and the two orange collections.

This deep-shaped tautology applies to mathematics. The essence of mathematics enables and creates wisdom. Suppose there is another axiom, a rule based on mathematics. Is there an interaction of "chaotic edge" that is important for intelligence as well? Depending on the combination of axioms, complex dynamics such as our brain (or discolored silver color) may be generated, but many axioms generate self contradiction or structurally interesting system dynamics. There are actually closely related axioms, but they share the fundamental characteristics that enable very complex behavior. Our math is mathematics that creates complicated systems, intelligence of biology in nature, and silicon shell.