把数学说成是美丽的看来是一种常识。数学家常对他们所做的表现出满足和快乐。他们常常宣称定理、证明、方法乃至理论可以是优雅的和漂亮的。同样,说数学家中间存在着天才也是一种常识。然而,康德对这两个问题都改变了观点。直到18世纪80年代,我们还发现他接受数学里有美和天才的作用。但他随后就好像改了主意。从他在18世纪80年代到90年代的作品中我们发现他或明或暗地说过,美和天才的概念不应该被用于数学,而应被限制在仅用于艺术。这不仅仅与我们今天大多数人的说法相矛盾,而 It seems a common sense to speak of mathematics as beautiful. Mathematicians often satisfied and happy with what they did. They often claim that theorems, proofs, methods, and even theories can be elegant and beautiful. Similarly, it is common sense to say that genius exists among mathematicians. However, Kant changed opinion on both issues. Until the 1880s, we also found that he accepted the role of beauty and genius in mathematics. But then he seemed to change his mind. From his works in the 1880s to the 1990s, we find that he has said either explicitly or implicitly that the concept of beauty and genius should not be used in mathematics but should be restricted to art. This is not only contradictory to what most of us say today, but