You may recall how Descartes wished to use mathematical method for philosophical reflection.

你可能还记得笛卡尔是如何希望用数学方法进行哲学反思的。

Quantitative research is the study of observable relationships in the world, using mathematical or statistical methods.

定量研究是使用数学或统计方法研究世界上可观察到的关系。

When he realized he didn't have the mathematical methods he needed, he invented new ones that we still use today.

当他意识到自己没有所需的数学方法时，他发明了我们今天仍在使用的新方法。

As a contrast, we may consider a famous story: the discovery by Henri Poincare, the great French mathematician, of a new mathematical method called the Fuchsian functions.

作为对照，我们可以举一个有名的事例，即法国伟大的数学家亨利? 庞加莱发现被称为富克斯函数的数学新方法的故事。