The book A Mathematician’s Apology is a collections of essays by G. H. Hardy, a British mathematician. In my realm of knowledge, my first impression would the Hardy-Weinberg Principle in biology class, although I have no idea the “Hardy” refers to him in my high school. In addition, he was also the mentor of Ramanujan, a mathematical genius, the discovery of whom has been regarded by himself as the greatest contribution in his life. It was a little ironic because, in his book, he seems values mathematical discovery more than introducing and commenting on some minds in mathematics. Maybe it’s because the discovery of Ramanujan propelled him in his scientific career.

《一个数学家的辩白》是英国数学家哈代的杂文选。在我的知识范畴里，我对于哈代的第一印象应该是生物课上的哈代温伯格定律，只不过当初我并不认识哈代是谁（并且，生物老师说的是哈迪温伯格定律，我记得很清楚）。哈代也是拉马努金的导师。拉马努金是个数学天才，哈代把发掘他视为他人生中做出的最大贡献。这听起来感觉有点讽刺，毕竟在书里，他好像更看重对于数学内容的贡献，而不是引进什么数学人才。可能是因为拉马努金的到来驱使了他在数学领域上更有成就了？

下面是这本书的第一章，附上翻译和我的读书笔记。 想要这么做有几个原因：

  1. 之前对这本书有所耳闻
  2. 这本书比较短小
  3. 3Blue1Brown曾经在一个关于数学的演讲里提到了这本书，其中的引用很有意思（哈代的些许“偏执”和“天真”体现的很明显
"We have concluded that the trivial mathematics is,
on the whole, useful, and that the real mathematics,
on the whole, is not."
⸺ G. H. Hardy
  1. 我正准备学数学
  2. 我多半会是个“second-rated mind”，哈哈哈哈哈

OK，开始。

It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done. Statesmen despise publicists, painters despise art-critics, and physiologists, physicists, or mathematicians have usually similar feelings: there is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds.

对于一个职业数学家来说，发现自己在写有关数学界的事让人心生伤感。一个数学家，理应去做些大事，证明新的定理，给数学添砖加瓦，而不是谈论数学界发生了什么。政坛老手鄙视时闻记者，画家反感艺术评论家，而生理学家，物理学家，和数学家，大多有一样的想法：对于一个人嘲讽（试图）解释自己做了什么的人这件事，没有什么东西是又更加合理又更加深入灵魂的。阐述，批判，欣赏是二流选手才干的事情。

Hardy is straightforward. As he puts forward his “despise” for critics, he made a point which could be criticized many times in the future - the distribution and remarks of (possibly valuable) viewpoints is far less important than the generation of the viewpoint itself. It would be ridiculous to apply this idea to the whole human society, but who can blame him for his stubbornness when he is a top-notch genius mathematician who only needs his own utopia?

开篇“嘲讽”，作为一个数学家绝不嘴软。哈代在这里说出了一个可能以后会被反复批判的观点：观点的转播和转发，是远不及观点的产生所重要的。放眼全世界全人类来说，这个观点可谓不可笑。但是作为一个生活在自我乌托邦中的顶级数学家，有谁又能够去责备他的一丝自恃清高呢？

I can remember arguing this point once in one of the few serious conversations that I ever had with Housman1. Housman, in his Leslie Stephen lecture2 The Name and Nature of Poetry, had denied very emphatically that he was a ‘critic’; but he had denied it in what seemed to me a singularly perverse way, and had expressed an admiration for literary criticism which startled and scandalized me.

He had begun with a quotation from his inaugural lecture, delivered twenty-two years before—

Whether the faculty of literary criticism is the best gift that Heaven has in its treasures, I cannot say; but Heaven seems to think so, for assuredly it is the gift most charily bestowed. Orators and poets…, if rare in comparison with blackberries, are commoner than returns of Halley’s comet: literary critics are less common…

And he had continued—

In these twenty-two years I have improved in some respects and deteriorated in others, but I have not so much improved as to become a literary critic, nor so much deteriorated as to fancy that I have become one.

我能记起曾经我在和豪斯曼1少有的几次严肃谈话中讨论起这个观点。在他名为“诗歌的名字与本性”的莱斯利·史蒂芬演讲2中，豪斯曼着重否认了他是一个“评论家”这一说法；但是他否认的方式是在我看来非常不合常理，并且表达了对于文学批判的欣赏，这让我感到迷惑和震惊。

他引用二十二年前的就职演讲中的话来开头：

我并不敢说文学批评的才能是天堂宝藏里最美好的礼物；但天堂却这么认为，因为可以肯定，这是他所赠与的最好的礼物了。演讲家和诗人们……，如果说他们比起黑莓稀有的话，那他们会比哈雷彗星的回归（每76年一次）常见；文学批评家就更不常见了……

然后他继续说到：

这二十二年间，我有的方面进步了，有的方面退步了，但是我还没进步到成为一个文学批评家，也没有退步到自认为是个文学批评家的地步。

It had seemed to me deplorable that a great scholar and a fine poet should write like this, and, finding myself next to him in Hall a few weeks later, I plunged in and said so. Did he really mean what he had said to be taken very seriously? Would the life of the best of critics really have seemed to him comparable with that of a scholar and a poet? We argued the questions all through dinner, and I think that finally he agreed with me. I must not seem to claim a dialectical triumph over a man who can no longer contradict me, but ‘Perhaps not entirely’ was, in the end, his reply to the first question, and ‘Probably no’ to the second.

这么一个伟大学者、诗人竟然写出这样的话，而几个礼拜之后当我在他旁边的时候，我开口激动的议论（看不起批评家的观点）。这对我来说几乎是一件该被谴责的事情。他的这个观点真的是认真的吗？在他看来，最好的批评家的和诗人学者的生涯，是在同一个等级上吗？我们在晚饭时争论了各样的问题。我觉得他最后终于同意了我的观点。虽然我绝不应该因为对着一个无法接着反驳我的人的说教而感到胜利，但是，“大概不全是”，是他最后对于我第一个问题的答复。“大概不是”，是对第二个问题的回答。

There may have been some doubt about Housman’s feelings, and I do not wish to claim him as on my side; but there is no doubt at all about the feelings of men of science, and I share them fully. If then I find myself writing, not mathematics, but ‘about’ mathematics, it is a confession of weakness, for which I may rightly be scorned or pitied by younger and more vigorous mathematicians. I write about mathematics because, like any other mathematician who has passed sixty, I have no longer the freshness of mind, the energy, or the patience to carry on effectively with my proper job.

大家可能会对于豪斯曼的感受表示怀疑，而我也不愿意宣称他一定站在我这一边。但是科学家的感受是毫无疑问的，而我也毫无保留地分享出来。如果我发现我不在写数学，而是在写“关于”数学的事情，那么这是我承认我已经变弱了。我心甘情愿接受年轻并且有活力的数学家的嘲讽与怜悯。我现在写关于数学界的事情，是因为像大部分年过花甲的数学家一样，我的心神已经不再那么清醒，我的精力和耐心在耗尽，以至于我不再能够有效的进行数学家的本职工作。

剩下的三段则是哈代接触到不同观点之后内心的自我疑惑。有一点他说的没错，作为一个科学家，他的感受是真实而且毫无保留的表述出来了。他很不留情面的指出科学一浪推一浪反复上升的客观规律，也坦诚了自己的精力和智力都是相当有限。豪斯曼的演讲发生在1933年，那时候的哈代也已经54岁了，离他最近发表的大成就也有5-10年之久了，内心的变化也可想而知。理性的数学家，分析起自己来也依然是直截了当不留情面。

总的说来，第一篇哈代并没有抒发大家期望的“Apology”，但是他在第一段立下了一个很重要的基调：在他的眼里，数学家总比介绍数学的人脑力灵活值得仰慕，花时间来解释，批评一个东西，实际上是没有自己去投入创造些什么来的有意义。直白而又真实的口吻似乎在想让那些和他意见不合的人直接退下，毕竟，作为一个数学家，作为一个天性内向木讷的学者，他没有啥好畏惧的，他只愿意和自己信奉的真理（无论数学还是人生）交谈。这其实也为后面他所有的观点情感做了一个铺垫。

  1. Alfred Edward Housman (26 March 1859 – 30 April 1936), English classcial scholar and poet.
    阿尔弗雷德·爱德华·豪斯曼（1859年3月26日 – 1936年4月30日），英国国学家和诗人。 ↩ ↩2

  2. At University of Cambridge, Leslie Stephen lecture is given every other year and honors the memory of Sir Leslie Stephen (1832-1904), the British philosopher and man of letters who helped draw out the ethical implications of Darwinism and became first editor of the Dictionary of National Biography.
    莱斯利·史蒂芬演讲在剑桥大学每两年举行一次，为的是纪念莱斯利·史蒂芬爵士（1832-1904）。这位英国哲学家兼作家帮助总结出了达尔文主义的伦理意义，并且是《国家人物传记大词典》的首位编辑。 ↩ ↩2