給年輕數學家的建議 - Alain Connes

接續 上次 的文章，上一篇只摘錄了第一位數學家 Michael Atiyah 的話， 這次則是摘錄了第三位數學家 Alain Connes 的話，Alain Connes 是法國數學家，研究領域是 operator algebra， 1982 年拿過 Fields Medal， 曾將其工作應用到理論物理， 他在文章的開頭還將數學家跟物理學家比喻成物理中兩種的基本粒子。 這次摘錄的話比較難翻釋，因為句子較長， 而且有些地方比較抽象，我沒有把握可以完全翻釋出作者的意思， 閱讀時請小心。

The scientific life of mathematicians... This process often begins with an act of rebellion against the dogmatic descriptions of that space that can be found in existing books. Young, prospective mathematicians begin to realize that their own perception of the mathematical world captures some features that do not quite fit in with the existing dogma. This initial rebellion is, in most cases, due to ignorance, but it can nevertheless be beneficial, as it frees people from reverence for authority and allows them to rely on their intuition, provided that intuition can be backed up by actual proofs.

數學家的科學生涯始於對抗書中的教條式描述， 年輕有前途的數學家開始領悟到， 他們對數學世界的認識跟現有的教條並不一致， 這種對抗通常是因為無知，但可能還是有益處的， 因為這使人們擺脫對權威的敬畏，進而可以依靠自己的直覺， 前提是要有實際的證明可以支持直覺。

[Lying down] Mathematicians usually have a hard time explaining to their partner that the times when they work with most intensity are when they are lying down in the dark on a sofa. Unfortunately, with e-mail and the invasion of computer screens in all mathematical institutions, the opportunity to isolate oneself and concentrate is becoming rarer, and all the more valuable.

數學家通常很難向他們的伴侶解釋在幽暗的沙發上躺下來時是數學家們工作強度最高的時刻。 不幸的是，隨著電子郵件還有所有數學機構的電腦螢幕的侵襲， 把自己孤立起來並且專心的時間是很少的，也因此更加珍貴。

[Being brave] There are several phases in the process that leads to the discovery of new mathematics. While the checking phase is scary, but involves just rationality and concentration, the first, more creative, phase is of a totally different nature. In some sense, it requires a kind of protection of one's ignorance, since this also protects one from the billions of reasons there will always be for not looking at a problem that has already been unsuccessfully attacked by many other mathematicians.

發現新數學的過程可以分成很多階段， 檢查階段是令人提心吊膽的，但只需要理性跟專心， 最初也是更有創造力的階段則是完全不同的， 在某種意義下，需要某種程度地保護我們的無知， 因為這也保護了我們不會因為種種理由， 而不去研究一個被許多數學家嘗試但卻失敗的問題。

[Setbacks] Throughout their working lives, including at the very early stages, mathematicians will receive preprints from competitors and feel disrupted. The only suggestion I have here is to try to convert this feeling of frustration into an injection of positive energy for working harder. However, this is not always easy.

在數學家的工作生涯包含了初期， 常會看到其他競爭者的文章而分心， 我所能給的建議是試著將這種挫折的情緒轉成一種正向能量使自己工作的更勤奮， 然而這不容易。

[Grudging approbation] A colleague of mine once said, "We [mathematicians] work for the grudging approbation of a few friends." It is true that, since research work is of a rather solitary nature, we badly need that approbation in one way or another, but quite frankly one should not expect much. In fact, the only real judge is oneself. Nobody else is in as good a position to know what work was involved, and caring too much about the opinion of others is a waste of time: so far no theorem has been proved as the result of a vote. As Feynman put it, "Why do you care what other people think?"

一個同事曾說「我們數學家是為了獲得一些朋友不情願的認同而工作」， 這句話是有道理的， 既然研究的本質是孤獨的， 在某種方面我們常需要認同感，但不能期望的太多。 事實上，只有自己才是真正的審判者， 沒有人比自己更清楚工作的關聯性， 所以太過擔心別人的意見是浪費時間， 到目前為止沒有一個定理是由投票來證明的， 就像 Feynman 所說的「為什麼要管別人怎麼想？」