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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.

I can remember arguing this point once in one of the few serious conversations that I ever had with Housman. Housman, in his Leslie Stephen lecture 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.

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 these 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.

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.

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让职业数学家去写一本关于数学的书,他一定会很发愁。数学家的工作应该是去证明新定理、发现新数学,不该谈论自己或其他数学家做了什么。政治家看不起时事评论家,画家轻视艺术评论家,生理学家、物理学家、数学家们通常也有类似的感觉:这是实干家对评论家的藐视,没有比这种藐视更深刻,或总体来说更无可非议的了。解说、评论、品鉴,都是二等人才从事的工作。

我记得,在和豪斯曼 1 为数不多的几次认真谈话里,就有一次对这个话题展开过辩论。豪斯曼在他的莱斯利 • 斯蒂芬 2 讲座《诗歌的名与实》上,坚决不承认自己是一个“批评家”。在我看来,他表达的方式很荒谬,其对文学批评表示的赞赏,也让我非常震惊。

1Alfred Edward Housman(1859.03.26—1936.04.30),英国古典文化学者、诗人。

2Leslie Stephen(1832.11.28—1904.02.22),英国作家。

他以 22 年前就职演说中的一段话作为开头:

我不能说,文学批评能力是否是上天赐予我们的最好礼物。但上天似乎是这样认为的,毫无疑问,它是一份最谨慎的馈赠。演说家和诗人……虽然不像随处可见的黑莓,但他们可比哈雷彗星的回归来得常见,而文学批评家则更稀缺……

他继续说道:

在这 22 年里,我在某些方面有所进步,不过在另一些方面退步了。但我还没有进步到足以成为一名文学批评家;同样,我也没有退步到幻想自己已经是一名文学批评家。

一位伟大的学者和优秀的诗人竟然这样认为,在我看来是很可悲的。几个星期后,当我在大厅里发现旁边坐的是豪斯曼时,便单刀直入地和他聊起了以下话题:他的话当真吗?在他看来,最好的评论家真的能与学者和诗人相提并论吗?整个晚餐,我们都在辩论这些问题,我想他最终同意了我的观点。对一个再也无法反驳我的人 3,我似乎并不能宣布这次辩论取得了胜利。不过,最终他对第一个问题的回答是“也许不能完全当真”,对第二个问题的回答是“或许不能相提并论”。

3本文写于 1940 年,而豪斯曼在 1936 年就去世了。

人们对豪斯曼的感受可能还有些不解,我也不指望他和我的想法是一致的。但科学家的感受是毋庸置疑的,我和他们有完全相同的体会。当我发现自己的创作只不过与数学“有关”,而并不是数学本身时,那就是在承认自己不行了,我很可能会因此而遭受更年轻、更有活力的数学家的轻视或怜悯。就像其他任何一位年逾花甲的数学家一样,我围绕着数学写作,是因为头脑已经老化,不再有足够的精力和耐心去有效地从事数学本职工作了。

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