筆記:《一位數學家的辯白》
最近讀哈代《一位數學家的辯白》，雖然談論的主題是數學，但對其他學科或者工作依然有所藉鑒。這本書與其説是一本書，還不如說為一本小冊子。每一章短而精。大抵數學家都喜歡言簡意賅，如同他們的公式定理。學者，也如同衣服的材質有優劣之分。我自不是好學者，但好在還有點好奇心。所錄句子或段落於我有啓發，但支離破碎，使原文脈絡全失，有心者應通讀原文。
- 做創造者而不是解釋家。 這條自不必多解釋。 ⌈貝多芬⌋只有一個，但⌈貝多芬⌋作品的演奏者卻成千上萬。
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.
【注】：做創作者雖然很難，但人還是應該去嘗試，因爲他的回報要遠比做簡單的事高。 最近在twitter上看到Paul Graham的討論：
The idea that you can get rich without doing a lot of work is so false that you can use its falsity as a heuristic. You can make more by deliberately chasing hard problems.
I'm not saying that problems are valuable in proportion to how hard they are. Far from it. But you'll generally do better if you're excited by difficulty rather than frightened of it. And not just financially: this works in math and science too.
- ⌈謙虛⌋的人做不出好的工作。 這一條稍微有點反常識，尤其於中國人而言。中國人常被教育保持謙虛；這種教育我覺得是出於一種社交性的自我保護。古語常説⌈木秀于林，風必摧之⌋，這是叢林法則的習得。但做學問不同於處世，不可同一視之。哈代强調人不能總是自我懷疑，時不時問自己⌈我做的事值得嗎？⌋以及⌈我是做件事的合適人選嗎？⌋這兩個問題既不解決你從事的工作，同時還讓你身邊的人感到沮喪。
Good work is not done by 'humble' men. It is one of the first duties of a professor, for example, in any subject, to exaggerate a little both the importance of his subject and his own importance in it. A man who is always asking 'Is what I do worth while?' and 'Am I the right person to do it?' will always be ineffective himself and a discouragement to others. He must shut his eyes a little and think a little more of his subject and himself than they deserve. This is not too difficult: it is harder not to make his subject and himself ridiculous by shutting his eyes too tightly.
- 如果你發現自己在某一方面有天賦，你就該做好任何犧牲來把自己的天賦培養完美。 這是⌈龜兔賽跑⌋最好的注脚。兔子的天賦被它的自傲浪費了，天賦是一種先發優勢，卻並不會保你一生無憂，就像沒有永動機一樣，這是這個世界有趣的地方。如果你有天賦，就要做好準備儘一切之能事去把自己的天賦培養完美，這是有天賦者的使命。如此而言，天賦者甚至比普通人要更努力、更辛苦，當然成就也更大。
If a men has any genuine talent, he should be ready to make almost any sacrifice in order to cultivate it to the full.
- 數學是年輕人的游戲。 好在我不是學數學的...也只能如此告慰自己。
No mathematician should ever allow himself to forget that mathematics, more than any art or science, is a young man's game.
If a man of mature age loses interest in and abandons mathematics, the loss is not likely to be very serious either for mathematics or for himself.
- 讓人從事研究的三個動機：求知欲，職業榮譽感和野心。
There are many highly respectable motives which may lead men to prosecute research, but three which are much more important than the rest. The first (without which the rest must come to nothing) is intellectual curiosity, desire to know the truth. Then, professional pride, anxiety to be satisfied with one's performance, the shame that overcomes any self-respecting craftsman when his work is unworthy of his talent. Finally, ambition, desire for reputation, and the position, even the power or the money, which it brings. It may be fine to feel, when you have done your work, that you have added to the happiness or alleviated the sufferings of others, but that will not be why you did it.