## Atiyah先生の教え

- 論文の構成を練ってから書き始めよ．
- 長くて複雑な証明は，補題や命題を使って，足場を作れ．
- 明快かつ理路整然とした英語を書け．
- 可能な限り簡潔であれ．しかし，容易に理解可能でなければならない．その微妙なバランスを見極めよ．
- 良き論文のスタイルを見本にせよ．
- 論文の本体が書き上がったら，序文を書く．論文の構造と主結果と背景を非専門家にもわかるように説明する．
- 草稿を見てもらう．
- 原稿をしばらく寝かせる．
- 原稿を書き直すことにためらってはならない．

- Think through the whole logical structure of the paper before you start to write.
- Break up long complex proofs into short intermediate steps (lemmas, propositions, etc.) that will help the reader.
- Write clear coherent English (or the language of your choice). Remember that mathematics is also a form of literature.
- Be as succinct as it is possible to be while remain- ing clear and easy to understand.This is a difficult balance to achieve.
- Identify papers that you have enjoyed reading and imitate their style.
- When you have finished writing the bulk of your paper go back and write an introduction that explains clearly the structure and main results as well as the general context.Avoid unnecessary jargon and aim at a general mathematical reader, not just a narrow expert.
- Try out your first draft on a colleague and take heed of any suggestions or criticisms. If even your close friend or collaborator has difficulty under- standing it, then you have failed and need to try harder.
- If you are not in a desperate hurry to publish, put your paper aside for a few weeks and work on something else. Then return to your paper and read it with a fresh mind. It will read differently and you may see how to improve it.
- Do not hesitate to rewrite the paper, perhaps from a totally new angle, if you become convinced that this will make it clearer and easier to read. Well-written papers become
*classics* and are widely read by future mathematicians. Badly writ- ten papers are ignored or, if they are sufficiently important, they get rewritten by others.