Gauss’ quadratic reciprocity theorem and mathematical fruitfulness

This paper presents an account of the fruitfulness of new mathematical calculi in terms of their relationship to existing mathematical methods which is suggested by Carl Friedrich Gauss. This is done by considering some remarks that Gauss made explaining the fruitfulness of new calculi. These can be clarified in the context of his own (very fruitful) theory of congruences, which is considered as a case study for this alternative account. Such an account has the benefit of not being dependent on a particular metaphysical view in the philosophy of mathematics.     

对一个密码算法的注记

计算群元素的整数倍是一切密码算法的基础，通常是采用整数的二进制表示，孙琦等人最近提出了标准二进制，从而对著名的“平方－和－乘法”算法进行了改进，节约时间的1／4，作者证明了这种标准二进制方法已无法再改进。