Mathematicians and Poets
Mathematicians and Poets
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数学家和诗人
DOI：
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发表时间：
2011
期刊：
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通讯作者：
CAI TIANXIN
中科院分区：
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作者：
CAI TIANXIN
数学家和诗人在我们的世界里是神秘的先知。他们之间的区别在于，诗人被认为是傲慢的，因为他们天生就倾向于骄傲和孤独，而数学家则被认为是不可接近的，因为他们存在于一个超越的平面上。因此，在艺术和文学界，诗人往往被认为在社会地位上不如小说家，就像在科学和技术协会中，数学家被认为在社会地位上不如物理学家一样。但这些都只是表面现象。“我是一个失败的诗人，”小说家威廉·福克纳在晚年谦虚地说。“也许每个小说家都想先写诗，发现他不能，然后尝试短篇小说，这是诗歌之后最苛刻的形式。如果他不这样做，他才开始写小说。”相比之下，物理学家就不那么谦虚了。然而，对于一个物理学家来说，物理学知识的每一次增长总是以两种方式为指导，即数学直觉和经验观察。物理学的艺术在于设计实验以推导自然规律。在这个过程中，数学直觉是必不可少的。事实上，数学家很容易转向研究物理学、计算机科学或经济学，就像诗人转向写小说、散文或戏剧一样。当然，也有例外。数学通常被视为诗歌的截然相反，尽管这里也有例外。虽然反对派并不总是正确的，但它站在那里基本上是不可否认的。数学家致力于发现，而诗人致力于创造。画家德加偶尔写十四行诗，有一次还向诗人马拉美抱怨。他说他有很多想法，事实上太多了;他发现很难写。马拉美回答说：“诗不是用思想而是用文字写成的。”另一方面，数学家主要研究概念，将同类概念结合起来。换句话说，数学家用抽象的方式思考，而诗人用具体的方式思考。但情况并非总是如此。数学和诗歌都是想象力的产物。对于一个纯粹的数学家来说，他或她的材料就像花边，树上的叶子，一片草地，或者一个人脸上的光影。换句话说，被柏拉图斥为“诗人的狂热”的“灵感”对数学家来说同样重要。例如，当歌德听到他的朋友耶路撒冷自杀的消息时，他幻想自己看到了一道闪光。他立刻想出了《少年维特的烦恼》的大纲。他回忆说，自己“似乎是无意识地写了这本书”。另一个例子：高斯，“数学王子”，写信告诉一个朋友，在解决了一个困扰他多年的问题（高斯求和的符号）后，“终于，两天前，我成功了，不是因为我的努力，而是上帝的恩典。就像突然的闪电一样，谜团被解开了。我说不出是什么线索把我以前知道的东西和使我成功的东西联系起来的。”数学似乎经常与天文学、物理学和其他自然科学分支联系在一起并相互作用，但它是一个完全自我参照的广阔知识领域，其现实性比其他科学更持久。它就像一种真正的语言，它不仅记录和表达思想和思维过程，蔡天欣是浙江大学数学系教授。他的电子邮件地址是txcai@ziu.edu.cn或caitianxin@hotmail.com。
Mathematicians and poets exist in our world as uncanny prophets. The difference between them is that poets are thought to be arrogant because they tend to be proud and lonely by nature, while mathematicians are thought to be unapproachable because they exist on a transcendent plane. Thus in art and literary circles poets are often considered to be socially inferior to novelists in the same way that mathematicians are considered socially inferior to physicists in scientific and technological associations. But these things are only superficial. “I’m a failed poet,” the novelist William Faulkner said humbly in his later years. “Maybe every novelist wants to write poetry first, finds he can’t and then tries the short story, which is the most demanding form after poetry. And failing at that, only then does he take up novel writing.” Physicists, by comparison, are not so modest. Nevertheless, for a physicist every increase in knowledge of physics is always guided in two ways, by mathematical intuition and empirical observation. The art of physics is to design experiments in order to derive the laws of nature. In this process mathematical intuition is indispensable. In fact, it is easy for mathematicians to switch to studying physics, computer science, or economics, just as it is for poets to turn to writing novels, essays, or plays. Of course, there are exceptions. Mathematics is usually seen as the diametric opposite of poetry, although there are exceptions here, too. Although the opposition is not always true, yet it stands there basically undeniable. Mathematicians work to discover, while poets work to create. The painter Degas occasionally wrote sonnets and once complained to the poet Mallarmé. He said that he had many ideas, in fact too many; he found it difficult to write. Mallarmé replied, “poems are made not with ideas but with words.” On the other hand, mathematicians work mainly on concepts, combining concepts of the same kind. In other words, mathematicians think in an abstract way, while poets think in a concrete way. But again this is not always the case. Both mathematics and poetry are products of imagination. For a pure mathematician, his or her materials are like lacework, leaves on a tree, a patch of grass, or the light and shade on a person’s face. In other words, “inspiration”, which Plato denounced as “a mania of poets”, is equally important to mathematicians. For example, Goethe fancied that he saw a flash of light when he heard of his friend Jerusalem’s suicide. He immediately came up with the outline of The Sorrows of Young Werther. He recalled that he “seemed to have written the book unconsciously”. Another example: Gauss, “the prince of mathematics”, wrote to tell a friend, after solving a problem (symbols of Gaussian summation) that had been bothering him for years, “Finally, two days ago, I succeeded—not on account of my hard efforts, but by the grace of the Lord. Like a sudden flash of lightning, the riddle was solved. I am unable to say what the conducting thread was that connected what I previously knew with what made my success possible.” Mathematics often appears to be connected to and interactive with astronomy, physics, and other branches of natural science, but it is a completely self-referential and vast field of knowledge with a reality more enduring than other sciences. It is like a true language, which not only records and expresses ideas and the process of thinking but Cai Tianxin is professor of mathematics at Zhejiang University. His email address is txcai@ziu.edu.cn or caitianxin@hotmail.com.