In 1933, Borsuk proposed the following problem: Can every bounded set in \({{\mathbb{E}}^n}\) be divided into n + 1 subsets of smaller diameter? This problem has been studied by many authors, and a lot of partial results have been discovered. In particular, Kahn and Kalai’s counterexamples surprised the mathematical community in 1993. Nevertheless, the problem is still far away from being completely resolved. This paper presents a broad review on related subjects and, based on a novel reformulation, introduces a computer proof program to deal with this challenging problem.

中文翻译：

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Borsuk 的划分猜想

1933年，Borsuk提出了如下问题：\({{\mathbb{E}}^n}\)中的每个有界集能否分为n + 1个直径更小的子集？这个问题已经有很多作者进行了研究，并发现了很多部分结果。尤其是1993年卡恩和卡莱的反例让数学界大吃一惊。尽管如此，这个问题还远远没有得到彻底解决。本文对相关主题进行了广泛的回顾，并基于一种新颖的重新表述，介绍了一种计算机证明程序来处理这一具有挑战性的问题。