第二次数学危机的实质是方法论的变革

数学的主要研究对象是“数”和“形”，与“数”的研究领域所对应的方法主要是运算方法，与“形”的研究领域所对应的方法主要是逻辑证明的方法，两种方法的结果都是确定无疑的。微积分的出现产生了一种新的方法，即分析方法，分析方法是“算”和“证”的结合，是通过无穷趋近而确定某一结果。古代数学中就发现了这一方法，牛顿和莱布尼兹创立微积分实际上是将这一方法程序化和运算化，这导致了对分析方法的误解，从运算方法的原则去指责分析方法的程序过程，这就是第二次数学危机的实质。戴德金使分析算术化，通过对实数的分划奠定分析方法的基础，指明了通过无穷趋近确定某一常数的确切性和惟一性，开始为分析注入严密性。

On the Main Substance in the Second Math Crisis Which is the Revolution of Methodology

The main analytic subjects in mathematics are number and graph, Operation method is used to solve for number, while logic deduction is for graph. No matter which way can be used, the conclusions which are drawn from number or graph are all doubtless. With the birth of calculus, it develops a new method, namely analyzing method. It is operation method together with logic deduction. The conclusion from analyzing method is different from general method, it is not exactly equal to some value, but it converges to some value. Actually, the classic mathematics had explored analyzing method. However, with the establishment of calculus, lsaac Newton and Gottfried Wilhelm Leibniz made the analyzing method to be programming and operationalization. All that lead a misunderstanding in mathematic analysis in that use operation method to work for analyzing method problems, this is also the main substance in the second math trials. R.Dedelcind developed arithetization of analysis through classifying real number and pointed that there is a definitely and only constant that can be converged to. Arithetization of analysis improves the level of strictness in analyzing method.