Why be clear?Now that we framed it as a tradeoff between your time andeffort, and that of the readers, this is no longer an obvious question and it deserves afull explanation. And the key observation is – being clear is not about you! You mustthink of the reader and how they will read your paper.Imagine a graduate student at a small university with poor English skills.He isreading your paper. If confused on page 3, he is likely to give up and never finish thereading. He might use an older paper with a weaker result for his research, just becauseit’s better written.Conclusion:you didn’t make him spend 1 extra min – you just losta significant fraction of your readership.

Or imagine a postdoc at a major research university. She has a clear project to finishand her supervisor gave her 20 possible papers to “check if they might be helpful”. Sheis quickly looking through your paper. Not noticing your “notation explanation” sheis becoming completely confused about the notation and consequently the main result.Rather than making an effort, she assures herself that your paper is irrelevant to theproject and moves on to read the other 19 potentially helpful papers. As a result, sometheorems do not get proved and the project never gets finished.Conclusion: you didn’tmake her spend 1 extra min – you lost both the citation and a chance to advance thearea.

Let me mention two more reasons which are variations on the same theme. For juniormathematicians:clear writing will make people take you seriously.It is pretty easy forlazy senior scientists to brush off a paper on the subject with ambiguous results anduncertain proofs. But when you are clear they have no excuse. Don’t give them one!Forget that they themselves have been publishing sloppy writing for decades. You arenot competing on the same level (yet). In fact, there is an actual checklist on what ittakes for senior people to read your paper [1]. Study the checklist and make sure youget an easy pass.

Finally, for all mathematicians:clear writing will give you a competitive advantage.It is often the case that the same or nearly the same result is obtained in several papers.If your paper is clear and your competitors’ are not, you will get the credit. I know,this is unfair. Think about it differently – you outworked your competition and createda better product.Sometimes it’s not about the substance but the presentation.2Aseveryone knows, recording of the same symphony by different orchestra can have verydifferent values. In the era of winner-take-all society it shouldn’t be surprising that thesame happens to math papers.