译 & 评 (陶哲轩:要有耐心)


fishman

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If I have ever made any valuable discoveries, it has been owing more to patient attention, than to any other talent. (Isaac Newton)

Any given problem generally requires months of effort in order to make satisfactory progress. While it is possible for routine or unexpectedly easy problems to fall within weeks, this is the exception rather than the rule.Thus it is not uncommon for months to pass with no visible progress; however by patiently eliminating fruitless avenues of attack, you are setting things up so that when the breakthrough does come, one can conclude the problem in relatively short order. (But be sceptical of any breakthrough which was “too easy” and mysteriously failed to address the key difficulty.)

In some cases, you (or the mathematical field in general) are simply not ready to tackle the problem yet; in this case, setting it aside (but not forgetting it entirely), building up some skill on other related problems, and returning back to the original problem in a couple years is often the optimal strategy (particularly if your formal mathematical education is still not complete). This is particularly likely to be the case for any really famous problem.

Incidentally, most problems are solved primarily by this sort of patient, thoughtful attack; there are remarkably few “Eureka!” moments in this business, and don’t be discouraged if they don’t magically appear for you (they certainly don’t for me).

See also “work hard” and “be flexible“.

Here is a short poster by Ira Glass making some related points, in the context of creative work.

如果我有过任何有价值的发现,那也应更多地归功于耐心的注意力,然后才是其它才能。(牛顿

对于任何给定的问题,为了得到令人满意的进展,通常需要花费几个月的精力。虽然有可能因为日常或者没有想到的极其简单的问题而沦为只需几个星期,但是这仅仅是例外,不是规则。因此,几个月都没有取得进展是很正常的;然而,通过耐心地排除无果而终的途径的攻击,你正在把一些事情给设置出来,这样,当突破来的时候,人们可以在相对较短的时间内得出问题的结论。(但是要怀疑任何突破,这些突破“太容易”并且神奇地不能解决问题难点)

在某些情况下,你(或一般的数学领域)根本就还没有准备好解决问题;在这种情况下,暂时先将它们放置一旁(但往往最好的策略是不完全忘记它,然后在其它与之相关的问题上先建立一些技巧),在若干年后返回到原来的问题(特别是当你的形式化的数学教育还不完整的时候)。对于“任何正在著名的问题”来说,这些策略是特别可能的例子。

顺便提一句,大多数问题的解决主要是由这种耐心以及思维周密的攻击。在这个行业只有屈指可数的“尤里卡”时刻。如果灵感不奇迹般地出现(它们肯定不适合我),不要气馁。

同见“努力工作”以及“灵活”。

这是Ira Glass 制作的一个在创造性工作领域内一些与本文相关点的短海报

成功的人都是类似的,失败的人各有各的原因。发现无论是刘未鹏的“暗时间”,还是陶哲轩的“先搁置问题,但不要忘记它”,还是钢铁侠的回到原点的“第一性原则”,对于创造性工作,这些都是及其优秀的思维策略,也是是解决问题的极好的方法论,当然也意味着更多时间与精力的投入。这些牛逼的人都有极强的耐心,为了解决一个问题,可以想好几年,在这个浮躁的社会,实属不易。向牛人学习耐心,因为耐心是一种美德,更是一种稀缺的资源。最近在调试四轴飞行器,遇到好多坑,现在还在坑里,看了牛人的博文,看来我还需要更大的耐心才能完成它。^~^

刘未鹏博客

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