一位数学家的辩白 —— 第八章

If intellectual curiosity, professional pride, and ambition are the dominant incentives to research, then assuredly no one has a fairer chance of satisfying them than a mathematician. His subject is the most curious of all—there is none in which truth plays such odd pranks. It has the most elaborate and the most fascinating technique, and gives unrivalled openings for the display of sheer professional skill. Finally, as history proves abundantly, mathematical achievement, whatever its intrinsic worth, is the most enduring of all.
We can see this even in semi-historic civilizations. The Babylonian and Assyrian civilizations have perished; Hammurabi, Sargon, and Nebuchadnezzar are empty names; yet Babylonian mathematics is still interesting, and the Babylonian scale of 60 is still used in astronomy. But of course the crucial case is that of the Greeks.
The Greeks were the first mathematicians who are still ‘real’ to us to-day. Oriental mathematics may be an interesting curiosity, but Greek mathematics is the real thing. The Greeks first spoke a language which modern mathematicians can understand: as Littlewood said to me once, they are not clever schoolboys or ‘scholarship candidates’, but ‘Fellows of another college’. So Greek mathematics is ‘permanent’, more permanent even than Greek literature. Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. ‘Immortality’ may be a silly word, but probably a mathematician has the best chance of whatever it may mean.
Nor need he fear very seriously that the future will be unjust to him. Immortality is often ridiculous or cruel: few of us would have chosen to be Og or Ananias or Gallio. Even in mathematics, history sometimes plays strange tricks; Rolle figures in the textbooks of elementary calculus as if he had been a mathematician like Newton; Farey is immortal because he failed to understand a theorem which Haros had proved perfectly fourteen years before; the names of five worthy Norwegians still stand in Abel’s Life, just for one act of conscientious imbecility, dutifully performed at the expense of their country’s greatest man. But on the whole the history of science is fair, and this is particularly true in mathematics. No other subject has such clear-cut or unanimously accepted standards, and the men who are remembered are almost always the men who merit it. Mathematical fame, if you have the cash to pay for it, is one of the soundest and steadiest of investments.
如果对于知识的好奇心，对于事业的自豪感和野心是从事研究的主要驱动力，那么没有人比一位数学家更有机会来满足他上述的三个动力。数学家所研究的对象最为奇特，只要在这里真理才会开如此古怪的玩笑。数学中蕴涵着最为精巧和奇妙的技艺，可以展现无与伦比的职业技能。最后，历史一再证明了，数学成就，无论其内在价值如何，都最为持久。
我们可以在半历史的文明中见到这一点，巴比伦和亚述文明早已湮没，汉摩拉比、萨尔恭、尼布甲尼撒都已成为空名，但巴比伦人的数学依然趣味十足，巴比伦的六十进制依然使用于天文学。当然希腊人是个更重要的例子。
古希腊首先出现了一些在当今依然名符其实的数学家。东方的数学也许看起来很有趣，但古希腊的才算的上真正的数学。古希腊人首先用一种当今还可以理解的语言来描述数学；就如同利特尔伍德对我所说的，他们不是聪明的学生或者“奖学金的候选人”，而是“另一个学院的同事”。所以古希腊数学是“永恒的”，甚至比古希腊文学更为永恒。当埃斯库罗斯（古希腊三大悲剧家之一）已被忘却时，阿基米德依然被人们记忆，因为语言已经死去，而数学思想依然存在。“不朽”也许是个愚蠢的词汇，但是一位数学家最有机会接近不朽。
他不必真地去害怕未来会对他不公平。不朽常常是荒谬或残酷的：我们中鲜有能成为奥格（旧约中的亚摩利王）、亚拿尼亚或者加里奥。即使是在数学界，历史也有时会开奇怪的玩笑；罗尔（米歇尔·罗尔，法国数学家，以罗尔定律闻名）出现在基础微积分的教材里，如同与牛顿齐名的数学家；法里（约翰·法里，英国地质学家，发现了法里数列）之所以不朽是因为他没能理解Haros在十四年前就已经完美证明了的定理；五位尊敬的挪威人的名字还留在阿贝尔的传记《生活》里，只因为他们忠实地执行了一项一丝不苟的蠢行，断送了他们国家最伟大的人物。但总体来说科学的历史还是公平的，在数学方面尤其如此。没有其他任何一门学科有如此清晰而一致接受的标准，那些被记住的人大多名符其实。数学声望，如果你能够买得到的话，是一笔最为值得和稳定的投资。