数学进化中的知识发现方法

A knowledge discovery approach in the evolution of mathematics

从数学历史发展过程中去发现数学的进化规律,从创造数学符号和包容对立的概念中获得了最早的数学知识.将数学符号组合而成的表达式和方程,使问题变换成了形式化表示,当表达式和方程通过推演和求证,判断其正确性时,就形成了公式和定理,它们是数学中的基础理论.推演和求证过程是采用了等价变换.数学进化中更重要的知识发现方法是利用进化变换(对变量、函数、方程、方法等的变换)来拓展数学的新概念和解决不能求解的问题(可拓变换),从而建立了数学的理论体系.创造、包容、形式化变换、等价变换和进化变换都是数学进化中的知识发现方法.

In this paper the mathematic evolution law is studied from the historical development of mathematics. The earliest knowledge of mathematics was acquired by creating mathematic symbols and the concepts of containment and contradiction. By combining mathematic symbols into expressions and equations, the problems are transformed into formalization descriptions. Expressions and equations become formulas and theorems when they are proven correct by simulations and proofs. Formulas and theorems are basic theories in mathematics. Simulations and proofs are equivalent transformations, while a more important knowledge discovery method in mathematic development is evolution transformation, such as transformation of variables, functions, formulas, and methods. These transformations extend new concepts and solve previously unsolvable problems. The theoretical system of mathematics is thereby constructed. Creation, containment, formalization transformation, equivalent transformation, and evolutional transformation are all knowledge discovery methods in the evolution progress of mathematics.