某个命题可以从某一组公理通过某一规则系统推导出来，这一事实本身并不使其为真。

做音乐不是为了取悦别人，而是为了表达自己。

The use of a program to prove the 4-color theorem will not change mathematics - it merely demonstrates that the theorem, a challenge for a century, is a finite problem.