数学证明编史学中的一个理论问题

A Theoretical Issue in the Historiography of Mathematical Proof

在过去的30年中,研究美索不达米亚、古代中国和印度的数学史家们已经揭示出,现存最早的阿卡德文、中文和梵文文献证明了这样一个事实,那就是这三个地区的古代数学家用这样或那样的方式讨论着数学证明。这些数学史家们发表的论著对当前的编史学产生的影响还只是微乎其微。本文对这种未能产生影响的情况进行了大致分析,并试图开启一片数学证明史讨论的新空间,其中每一种证据都会被考虑。本文尤其利用数学家们最近的一次争论,提出了一种构造数学证明新编史学的途径。

In the last 30 years, historians of mathematics working on Mesopotamia, ancient China and India have shown that some of the earliest extant documents written in Akkadian, Chinese and Sanskrit testified to the fact that practitioners of mathematics in these three areas of the world wrote in one way or another mathematical proofs. These historians＇ publications have had almost no impact on the present-day historiography. This article sketches an analysis of this failed reception and attempts to open a space for the discussion on the history of mathematical proof in which each piece of evidence can be accounted for. In particular, it makes use of a recent debate among mathematicians to suggest one way towards a new historiography of mathematical proof.