论文的动机
论文的动机
一位严谨的作者，在写每一句话时，都会至少问自己四个问题：
- 我想说什么？
- 用什么词来表达它？
- 什么形象或习语能让它更清晰？
- 这个形象足够新颖以产生效果吗？
乔治·奥威尔，《政治与英语》，1946年
一篇论文不应仅仅是一系列公式或逻辑步骤。
它也应该以这样的方式组织和激励，使读者始终意识到论文任何部分的近期和长期目标是什么，当前的论证如何朝着这些目标推进，它们对这些目标有多关键，以及为什么每一步声称的结果至少是合理的（或者如果它们令人惊讶，要确切指出为什么以及如何令人惊讶）。
因此，非正式的、启发式的或动机性的推理非常受欢迎，但应明确标示出来，以区别于正式的、严格的推理（例如，这些部分可以放在评论或脚注中）。
在每个章节的开头，通常最好给出一个简短的段落描述该章节的目的。例如，如果一个章节专门用于证明论文中的一个关键里程碑，可以在章节开头附近陈述这个里程碑，并讨论为什么这个里程碑很重要，也许还可以简要概述如何在本章节中证明它。
在展示你最一般的结果之前，可以先讨论一个技术性较低的特殊情况或”玩具”结果，以给出主要结果的意义和证明策略的一些味道。即使这个玩具结果在文献中已经为人所知，这也可能是值得的。例如，经常发生的情况是，将玩具结果的证明推广到更一般结果的关键是以一种能够推广到后者的方式重新解释前者的现有证明，并且在论文开头附近讨论这种重新解释对读者来说可能是极其清晰的。
另请参阅”为你的读者着想”。
Motivate the paper
A scrupulous writer, in every sentence that he writes, will ask himself at least four questions, thus:
- What am I trying to say?
- What words will express it?
- What image or idiom will make it clearer?
- Is this image fresh enough to have an effect?
George Orwell, “Politics and the English Language”, 1946
A paper should not just be a sequence of formulae or logical steps.
It should also be organized and motivated in such a way that the reader is always aware what the near-term and long-term objectives of any portion of the paper are, how the current arguments are advancing towards these goals, how crucial they are to those goals, and why the claimed results at each step are at least plausible (or if they are surprising, to indicate exactly why and how they are surprising).
Informal, heuristic, or motivational reasoning is therefore very welcome, but should be clearly indicated as such to distinguish it from formal, rigorous reasoning (for instance, these portions of the paper can be placed in remarks or footnotes).
At the start of each section, it is often a good idea to give a brief paragraph describing the purpose of that section. For instance, if a section is devoted to proving a key milestone in the paper, the milestone can be stated near the start of the section, next to a discussion as to why this milestone is important and perhaps a brief sketch as to how one is going to prove it in this section.
Before presenting your most general result, it can help to first discuss a less technical special case or “toy” result first to give some flavour of the significance of the main result, and also on the strategy of proof. This can be worthwhile even if this toy result was already known in the literature. For instance, it often happens that the key to generalising the proof of the toy result to the more general result was to re-interpret an existing proof of the former in a way that generalised to the latter, and discussing this re-interpretation near the beginning of the paper can be enormously clarifying to readers.
See also “Be considerate to your audience”.