我如何安排时间

陶哲轩

受到一些评论的鼓励，我最终决定在这里写一些关于如何安排时间的建议。其实，我有这个打算已经一段时间了，可是就我自己的情况而言，这方面也还在做着探索（读者应该看看我等着写的论文排了多少！）而且很多想法未必成熟。（已经有一些经验写在advice on writing papers,比如page on rapid prototyping）而且，我的一些个人经验恐怕也不能对所有人通通适用，因为每个人都有不同的性格类型以及工作状态。欢迎大家把自己的想法啊，经验啊，或者建议在评论中写出来。（其实，即使我自己的经验，我有时候也不能严格的遵照，挺遗憾的。）

这些经验并不系统，我慢慢的叙述如下。首先，我足够的幸运，自己的很多优秀的合作者都在我们合作的工作中付出了大量的心血。比如最近我的博客大家看到的论文，很多都在很大的程度上是我的合作者们辛勤劳作的成果。一般来讲，我觉得几个人合作的时候，虽然常常要花费的时间要多一些，但是每个人实际花费的力气却令人吃惊的少，而文章的质量却更高。我发现自己可以同时与很多人在不同的工作中合作（因为常常他们为主，或者该工作实际上在等待进一步发展。）可是在我独自写论文的时候，我却只能同时只做一件工作。

由于一些学院时间的规定，在夏季很多的工作要做结，数量要比其他任何时候都多。这些工作都已经经历了相当长一段时间了（比如，很快就要有一篇文章完成了。在这篇文章上，我们已经花费了三到四年；从2000年开始，我在关于波映射的全局正则问题（the global regularity problem for wave maps problem）上已经时断时续的花费了8年之久了。）所以说，当一篇论文一个星期就出现，这可不是说，从怀有这个论文的想法，到真正写出来，仅仅花费了一个星期。其实往往整个漫长过程多是不被世人所知的。

另外，我解决严肃数学问题的能力常常上下变化，甚至每天都有区别。有时候我可以在一个问题上连续想一个小时之久；而有时我更适合去把我和合作者们的草稿式的想法给具体到细节的写出来；另外一些时候，我觉得自己只能收收邮件，改改错误，甚至打个盹，散散步。我觉得非常重要的一点就是，我应该根据自己的状态变化来调整自己的工作安排。如果我有一整个下午的时间，同时又有很好的状态，我可能就会关掉办公室的门，关掉网络，静下心来写这篇苦思已久的论文；而状态不行的时候呢，我就看看这一周的e-mail，投几篇篇论文，写写blog。总之我要做些跟精力的热情的高低很相配的工作。做数学够幸运的一点就是，你可以把大部分的工作在时间上做非常自由的调整（但是讲课是一个非常重要的例外，我们必须围绕讲课的固定时间来做安排）。能够准确的判断自己在某个时段的工作能力以及对接下来的时间（比如这一天剩下的时间）做估计是很有帮助的。无论是太过自信，还是太不自信，在选择具体的工作内容的时候都会带来低效的后果。（我在这两方面可以说都有反面的经验。）

类似的。我有时会有一大堆事情，在长度，复杂度，困难度都非常不同。这一堆问题写在我的“要做”清单之中，如果其中有某个需要很细致的思考的话，我会完全排除掉其他干扰，只将注意力放在这一个问题之上，其他的能拖后的拖后，能放弃的放弃掉；我只有在各项工作都不会耗费我很多时间的情况下，才会同时在各个方面工作。（而且，我还在这些工作中都没有什么灵感。）常常发生的情况是，这些任务要比我预想的难，需要更多的精力，时间或者是耐心才能够完成。这时侯，你就必须要找到一个合适的“休息点”（比如，证明一篇论文中的关键命题；写下讨论中的一个想法，写出来黑板上的某个灵感，或者把一个论文草稿具体完成到细节。）使得这件工作可以放下来不想一段时间，等到回来的时候依然能够很舒服从断开的地方直接继续原来的工作。应当避免在一件工作完成一半的时候就停下来，没有找到合适的“休息点”。结果要么这件工作半途而废，要么留在脑袋中不能彻底忘掉，以至于影响其他的工作，而当你把这个问题捡起来的时候，常常要从前面的什么地方重新开始思考，浪费了时间。但是也无必要拿到一个任务就一次完全的完成，只要找到合适的暂停的地方就好。举一个俗气一些的例子：我在写信的时候（一般都是我工作状态较差，不能去做严肃的数学问题的时候），我会写完并打印好，装到信封之中，然后就把它们放在固定的地方，而一般不会马上就邮寄出去（包括很多类似的东西都放在一起）。直到我“固定的地方”堆满了文件，而我有没有什么其他事情好做的时候，我会统一的把他们一起处理。（比如当我的电脑出点问题的时候，就是个不错的时机。）

一般的讲，有些不需要很集中精力处理的问题最好能够成批的处理，而那些需要集中精力分别应对的任务，就不要被杂事分散了力量。

跟所谓的“休息点”的寻找相关的一点就是要会把又大又长的任务给切碎，让他们变成若干的小问题，而且每个问题又能够有很好的独立性以及自洽性。最好不过的就是每个小问题都能有他自己的意义。举一个例子就是，我是完全不大可能一次性完整的写出关于庞加莱猜想的证明，而当我把它们分成了19个部分之后，这些部分都相对可以很好的处理，而且又能够有其独立存在的价值。（而且，我还发现，把自己逼到悬崖边上也常常很有效。我提前宣布要讲庞加莱猜想的证明，这给我带来很多动力，不至于半途而废。）

（译者注： lectures on the Poincaré conjecture 是陶教授今年的一门博士课程，课程参考著名的Perelman的三篇论文，田刚的500页的书，以及朱熹平，曹怀东的300页的论文为教材。由于课程非常艰深，因此上课的具体要求十分简单，只要坚持听课就好，没有任何的作业或者考试要求。这门课的主页以及所有讲义在陶教授的博客上可以看到，链接在这里。）

现代文字处理的优点就是，任何时候都可以间断下来，将草稿保存。又很容易找个时间继续。这个blog就是这样。我非常惊叹于在计算机时代之前的那些数学家们，他们居然能够写出如此高质量的论文甚至是厚厚的一本书。而我即使有秘书的帮助，也会觉得这件事相当的困难。

有时候应当花费大段的时间来学习某种技术，因为这些技术将会在未来不断的被使用。这其中一个好的例子就是数学中的latex编辑软件。如果你打算写很多的论文，那么就应该花费些时间仔细研究一下这个软件，给自己将来带来方便。好好的学习一下譬如怎么画图怎么做表等等。近来，我试图利用宏定义的方法将标准的latex码（如\begin{theorem} … \end{theorem} \begin{proof} … \end{proof}等等）简化，节约了击键次数。每次的时间节约当然很少，但是累计起来，效果就会不同。而且，在工作的时候如果有效率很高的感觉，人也会精神抖擞，士气高涨。（写长论文的时候就能有体会。）

而在另外的一些情况下，却反而可以对一些任务进行推迟，延误，甚至放下去做些其他的工作。并不是所有的事情都同样的重要。面对一个给定的任务，如果一个人等到自己的技能更强悍，或者是发生了某件事情使得这个任务变得不再那么重要，那么这个工作显然就变得简单了。比如，我目前关于波映射的论文（papers on wave maps）被延误了好些年，主要是因为我自己没能坚持。然而回想起来，我看到把论文放在那一段时间也有不错的方面。当初我计划中的方法在技术上简直是个噩梦。真的很有必要等待合适的工具出现，等待对这个领域的理解的加深，然后在对问题有更深刻更有效的处理。   [也许这篇文章本身就是一个很好的例子。在我的博客中，还有很多的文章草稿我觉得还不成熟，至少现在还不是露面的时候。它们还在等待进一步的修改。并不是所有的想法或者话题都能够顺利完成，变成一个有意义的结果，参考我的另一篇“利用垃圾箱”。（use the wastebasket）]

我的最后一个建议就是要制定一个计划之后要尽最大努力坚持下去，一个不能全心投入的计划还不如干脆没有计划。我的计划包括我自己的PDA和笔记本，我的e-mail同步。我的各种计划和办公室中其他的设计好的东西保持一致。我还有一个“保留的”黑板，上面写得东西也许只有我自己能完全明白。我并不想很详细的在这里把这些写的很详细。总之，我已经很习惯于我的这些计划，而且到目前为止一切都非常好(尽管我可不希望有人把我的黑板擦干净！).选择怎样的计划显然是一个非常隐私的事情，我当然也不大可能对每个人给出最好的建议，只能讲讲自己正在实施的方法.我认为这些方法给我赢得了很多的时间;我不用花费精力去考虑自己在周二下午3点钟该做些什么；为了目的A，B，C，在X，Y，Z方面都需要做些什么也不用再操心，这样我可以投入更多的精力于理解数学本身，抑或证明一个有难度的命题，或者什么其他的的工作.  [I我还发现，当划掉计划中的任务时所带来的心理上的舒适感也会带来动力，不然，有些工作可能会由于没有兴致而最终搁置。]

哦，最后还有一条：有时又需要及时放弃自己的规则而容许有效地调整。比如说，当我在午饭时（随便抓些东西吃吃）为下午的工作做计划时,有时会被同事或某个访问者所打断，结果要出去吃饭。结果常常发生的情况是，在这顿饭上我得到的比在办公室中更多更好（在数学上或者在其他方面），尽管不是按我事先所预料的方式。而且这个过程常常更令人愉快 (有时候，脱离会议讲座甚至脱离会议本身去做自己的论文也会有相同效果)

上面的译文引自刘小川的博客

http://liuxiaochuan.wordpress.com/2008/08/08/我如何安排时间（译自陶哲轩博客）/

下面是陶哲轩博文的英文原文，这篇文章发表于2008年，来源于：

http://terrytao.wordpress.com/2008/08/07/on-time-management/#comment-31909

On time management

 by Terry Tao

Prodded by several comments, I have finally decided to write up some my thoughts on time management here.  I actually have been drafting something about this subject for a while, but I soon realised that my own experience with time management is still very much a work in progress (you should see my backlog of papers that need writing up) and I don’t yet have a coherent or definitive philosophy on this topic (other than my advice on writing papers, for instance my page on rapid prototyping). Also, I can only talk about my own personal experiences, which probably do not generalise to all personality types or work situations, though perhaps readers may wish to contribute their own thoughts, experiences, or suggestions in the comments here. [I should also add that I don't always follow my own advice on these matters, often to my own regret.]

I can maybe make some unorganised comments, though. Firstly, I am very lucky to have some excellent collaborators who put a lot of effort into our joint papers; many of the papers appearing recently on this blog, for instance, were to a large extent handled by co-authors. Generally, I find that papers written in collaboration take longer than singly-authored papers, but the net effort expended per author is significantly less (and the quality of writing higher). Also, I find that I can work on many joint papers in parallel (since the ball is often in another co-author’s court, or is pending some other development), but only on one single-authored paper at a time.

[For reasons having to do with the academic calendar, many more of these papers get finished during the summer than any other time of year, but many of these projects have actually been gestating for quite some time. (There should be a joint paper appearing shortly which we have been working on for about three or four years, for instance; and I have been thinking about the global regularity problem for wave maps problem on and off (mostly off) since about 2000.) So a paper being released every week does not actually correspond to a week being the time needed to conceive and then write up a paper; there is in fact quite a long pipeline of development which mostly happens out of public view.]

Another thing is that my ability to do any serious mathematics fluctuates greatly from day to day; sometimes I can think hard on a problem for an hour, other times I feel ready to type up the full details of a sketch that I or my coauthors already wrote, and other times I only feel qualified to respond to email and do errands, or just to take a walk or even a nap. I find it very helpful to organise my time to match this fluctuation: for instance, if I have a free afternoon, and feel inspired to do so, I might close my office door, shut off the internet, and begin typing on a languishing paper; or if not, I go and work on a week’s worth of email, referee a paper, write a blog article, or whatever else seems suited to my current levels of energy and enthusiasm. It is fortunate in mathematics that a large fraction of one’s work (with the notable exception of teaching, which one then has to build one’s schedule around) can be flexibly moved from one time slot to another in this manner. [A corollary to this is that one should deal with tasks before they become so urgent that they have to be done immediately, thus disrupting one's time flexibility.]

It helps a lot here to be able to honestly and accurately evaluate your work potential (a function of your location, your current level of motivation and energy, your upcoming duties and commitments, availability of resources, and the expected level of distraction) for a given period of time into the future (e.g. the rest of the day): being either overconfident or underconfident about what you can achieve leads to taking on either more or less than you can properly handle, both of which lead to inefficiencies (I have learned both sides of this from direct experience).

While I have a large number of things on my “to do” list, at various levels of complexity, difficulty, and length, when it comes to any task requiring dedicated thought, I try to focus on it exclusively, postponing or shutting out everything else; I find that multitasking only works for me when none of the tasks requires more than a fraction of my attention (in particular, it seems to work best when I am not inspired to do any one particular task). Quite often, these tasks take longer to complete than I have the energy, time, or patience for, in which case one has to find a natural break point (e.g. proving a key lemma in a paper that one is writing up, or writing down a full sketch of some idea that just came up in conversation or on the blackboard or scratch paper) where one can safely set the task aside and forget about it for a while, and be able to resume later without losing one’s place. The thing to avoid is to drop a task when it is only partially finished, without any good “closure”; it then either gets lost, or weighs on one’s mind and prevents one from fully thinking about something else, or has to be redone from an earlier point when one picks it up again. But one doesn’t have to finish each task off completely as it comes, as long as it can be picked up later. A mundane example: when I get around to writing physical letters (usually a low priority, when I don’t feel ready to do serious mathematics), I type them, print them out, seal them in an envelope, and then deposit them in my “out” tray, but I generally don’t mail them (or process any other paperwork in my out tray) until it piles up and I have nothing better to do, at which point I go out and deal with all of it at once.  [I find that a particularly good time for doing this is when my computer needs to reboot or is somehow not easily usable.]

More generally, tasks that require little concentration seem to be best done in batches if possible, while tasks that require a lot of concentration seem to be best done individually, with as few distractions as one can manage.

Related to the point about “closure” is the desirability of being able to chop up an extremely long task into smaller, self-contained ones, ideally each with its own immediate “payoff”.  To give one example: I doubt I would ever attempt to write (let alone finish) the equivalent of my 19 or so lectures on the Poincaré conjecture if I had decided to write one enormous article or monograph rather than 19 reasonably manageable and self-supporting shorter pieces.  (It helped also to “paint myself into a corner” a little bit here by announcing the lectures in advance, and building up some momentum, to stop myself from abandoning the project half-way.)

[One very nice thing about modern text editors, including the one on this blog, is that it is very easy to save a draft at some intermediate stage and flesh it out or polish it later, which greatly assists the task of writing long papers by chopping up this task into a sequence of much smaller tasks, as discussed above.  I am quite impressed by mathematicians from before the computer era who were able to meticulously write out high-quality papers and even books; even with good secretarial support, I would find this extremely difficult to do myself.]

It also makes good sense to invest a serious amount of time and effort into learning any skill that you are likely to use repeatedly in the future. A good example in mathematics is LaTeX: if you plan to write a lot of papers, it makes sense to go beyond the bare minimum of skill needed to jerry-rig whatever you need to write your paper, and go out and seriously learn how to make tables, figures, arrays, etc. Recently I’ve been playing with using prerecorded macros to type out a standard block of LaTeX code (e.g. \begin{theorem} … \end{theorem} \begin{proof} … \end{proof}) in a few keystrokes; the actual time saved per instance is probably minimal, but it presumably adds up over time, and in any event feels like you’re being efficient, which is good for morale (which becomes important when writing a long paper).

There are also many situations in which it makes tactical sense to defer, delay, delegate, or procrastinate on any given task, and go work on something else instead in the meantime; not everything is equally important, and also a given task may in fact become much easier (and be completed in a much better way) if one waits for one’s own skills to get stronger, or for other events to happen that reduce the importance or need for the task in the first place.  My currentpapers on wave maps, for instance, have been delayed for years, much to my own personal frustration, but in retrospect I can see that it was actually a good idea to let those papers sit for a while, as the project as I had originally conceived it was a technical nightmare, and it really was necessary to wait for the technology and understanding in the field to improve before being able to tackle it in a relatively civilised manner.   [Perhaps this very article on time management is an example of this, also.  There are also a number of other draft articles hidden in this blog that I felt were not quite working at the time, and are awaiting some further inspiration to complete.  It seems that not every idea or topic for an article necessarily leads to a viable end product; cf. "use the wastebasket".]

My final suggestion is to pick some sort of organisational system and make a real effort to stick to it; a half-hearted system is probably worse than no system at all. [A corollary to this is not to try to make an overly ambitious system ab nihilo that one is unlikely to follow faithfully; it is probably better to let such systems evolve over time.] I have my own system involving a PDA synchronised to my laptop, my email account, some in trays, out trays, and other designated spots in my office, and a “reserved” blackboard, that probably only I can understand completely, and I don’t think I can even explain it properly here, but I’m used to it now and it seems to work well enough (though I sure hope nobody ever erases that blackboard!). The choice of system though is presumably a very personal matter and I wouldn’t be able to advise on what would work best for anyone other than myself. But I do find that such systems free up a lot of memory; if I don’t have to worry about what I’m supposed to be doing at 3pm on Tuesday, or what work needs to be done on X, Y, and Z for purposes A, B, and C, I can devote more of my attention to trying to understand a mathematical argument, or proving a tricky lemma, or whatever else I need to work on.  [I also find it psychologically satisfying to be able to physically cross off an item from my organisational system, which can be a useful motivation when one feels otherwise uninspired to deal with something.]

Oh, and one final disclaimer: sometimes one should abandon one’s own rules and allow for serendipity.  There have been many times, for instance, when I had planned to work on something during my lunch hour (grabbing something quick to eat), when I was interrupted by a colleague or visitor to go out to eat.  It has often happened that I got a lot more out of that lunch (mathematically or otherwise) than I would have back at the office, though not in the way I would have anticipated.  And it was more enjoyable, too.  (Similarly with skipping talks at conferences (or skipping conferences altogether) to go work on one’s own papers, etc.)

梦里江河其实是看到人人网上好友的分享后，转自数学以及数学的主页的。