数学史：从辉格史到思想史

摘要

以代数解释为代表的辉格编史学一度在数学史研究中占据主导地位,这种编史学导致了数学史的盲目和贫乏。上世纪七十年代以来,许多数学史家努力开辟不同于辉格史的研究进路,然而迄今为止仍未能清除数学史中的辉格倾向。为揭示这一困难的根源,我们回顾了克莱因对数学史本身的起源的追溯,从中看到,数学史中辉格倾向的根源恰恰在于近代数学本身。因此,数学史要想摆脱辉格倾向,必须首先成为一种能够揭示自身根源的研究,即一门思想史。包括柯瓦雷的科学思想史在内的许多思想资源都可帮助数学史实现这一转变。%Whig historiography, represented by the algebraic reading of Greek mathematics, had been dominating the history of mathematics for a long time. It led to the blindness and poverty of the history of mathematics. Since 1970s, various efforts have been made to create new approaches different from Whig history, yet the history of mathematics nowadays is still colored with Whiggish tendency. To find out the root of this failure, we appeal to Jacob Klein＇s revelation of the true beginning of the history of mathematics itself, which shows that it is in the early modem mathematics itself that the root of the Whiggish tendency in the history of mathematics consists. To avoid Whiggish tendency, the history of mathematics has to become a research with the ability to rediscover its own root, that is, an intellectual history. A number of intellectual resources, including Alexandre Koyre＇s intellectual history of science, can be ＇very helpful for this transformation.