{"id":19,"date":"2013-03-05T19:49:25","date_gmt":"2013-03-06T00:49:25","guid":{"rendered":"http:\/\/homepages.uc.edu\/~yaozo\/wordpress\/?p=19"},"modified":"2013-03-05T19:49:25","modified_gmt":"2013-03-06T00:49:25","slug":"terry-taos-advice-on-writing","status":"publish","type":"post","link":"https:\/\/zhuoyao.net\/index.php\/2013\/03\/05\/terry-taos-advice-on-writing\/","title":{"rendered":"Terry Tao&#8217;s advice on Writing"},"content":{"rendered":"<h1 id=\"post-78\">On\u00a0writing<\/h1>\n<div>\n<blockquote><p><em>There are three rules for writing the novel. Unfortunately, no one knows what they are.<\/em>\u00a0(<a href=\"http:\/\/en.wikipedia.org\/wiki\/W._Somerset_Maugham\">W. Somerset Maugham<\/a>)<\/p><\/blockquote>\n<p>Everyone has to\u00a0<a href=\"http:\/\/terrytao.wordpress.com\/advice-on-writing-papers\/write-in-your-own-voice\/\">develop their own writing style<\/a>, based on their own strengths and weaknesses, on the subject matter, on the target audience, and sometimes on the target medium. \u00a0As such, it is virtually impossible to prescribe rigid rules for writing that encompass all conceivable situations and styles.<\/p>\n<p>Nevertheless, I do have some general advice on these topics:<\/p>\n<ul>\n<li>Writing a paper\n<ul>\n<li>Use the introduction to\u00a0<a href=\"http:\/\/terrytao.wordpress.com\/advice-on-writing-papers\/use-the-introduction-to-%E2%80%9Csell%E2%80%9D-the-key-points-of-your-paper\/\">\u201csell\u201d the key points of your paper<\/a>; the results should\u00a0<a href=\"http:\/\/terrytao.wordpress.com\/advice-on-writing-papers\/describe-the-results-accurately\/\">be described accurately<\/a>. One should also invest some effort in both\u00a0<a href=\"http:\/\/terrytao.wordpress.com\/advice-on-writing-papers\/organise-the-paper\/\">organising<\/a>\u00a0and\u00a0<a href=\"http:\/\/terrytao.wordpress.com\/advice-on-writing-papers\/motivate-the-paper\/\">motivating<\/a>\u00a0the paper, and in particular in\u00a0<a href=\"http:\/\/terrytao.wordpress.com\/advice-on-writing-papers\/use-good-notation\/\">selecting good notation<\/a>\u00a0and\u00a0<a href=\"http:\/\/terrytao.wordpress.com\/advice-on-writing-papers\/give-appropriate-amounts-of-detail\/\">giving appropriate amounts of detail<\/a>. But\u00a0<a href=\"http:\/\/terrytao.wordpress.com\/advice-on-writing-papers\/dont-overoptimise\/\">one should not over-optimise<\/a>\u00a0the paper.<\/li>\n<li>It is also assists readability if you factor the paper into smaller pieces, for instance by\u00a0<a href=\"http:\/\/terrytao.wordpress.com\/advice-on-writing-papers\/create-lemmas\/\">making plenty of lemmas<\/a>.<\/li>\n<li>To reduce the time needed to write and organise a paper, I recommend\u00a0<a href=\"http:\/\/terrytao.wordpress.com\/advice-on-writing-papers\/write-a-rapid-prototype-first\/\">writing a rapid prototype first<\/a>.<\/li>\n<li>For first time authors especially, it is important to try to\u00a0<a href=\"http:\/\/terrytao.wordpress.com\/advice-on-writing-papers\/write-professionally\/\">write professionally<\/a>, and in\u00a0<a href=\"http:\/\/terrytao.wordpress.com\/advice-on-writing-papers\/write-in-your-own-voice\/\">one\u2019s own voice<\/a>. One should\u00a0<a href=\"http:\/\/terrytao.wordpress.com\/advice-on-writing-papers\/take-advantage-of-the-english-language\/\">take advantage of the English language<\/a>, and not just rely purely on mathematical symbols.<\/li>\n<li>The\u00a0<a href=\"http:\/\/www.google.com\/buzz\/114134834346472219368\/LpL6GT7HKVL\">ratio between results and effort in one\u2019s paper should be at a local maximum<\/a>.<\/li>\n<\/ul>\n<\/li>\n<li>Submitting a paper\n<ul>\n<li><a href=\"http:\/\/terrytao.wordpress.com\/advice-on-writing-papers\/proofread-and-double-check-your-paper-before-submission\/\">Proofread and double-check your article before submission<\/a>; you should be\u00a0<a href=\"http:\/\/terrytao.wordpress.com\/advice-on-writing-papers\/submit-a-final-draft-not-a-first-draft\/\">submitting a final draft, not a first draft<\/a>.<\/li>\n<li><a href=\"http:\/\/terrytao.wordpress.com\/advice-on-writing-papers\/submit-to-an-appropriate-journal\/\">Submit to an appropriate journal<\/a>.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>I should point out, of course, that my own writing style is not perfect, and I myself don\u2019t always adhere to the above rules, often to my own detriment. If some of these suggestions seem too unsuitable for your particular paper, use common sense.<\/p>\n<p>Dual to the art of\u00a0<em>writing<\/em>\u00a0a paper well, is the art of\u00a0<em>reading<\/em>\u00a0a paper well. \u00a0Here is some commentary of mine on this topic:<\/p>\n<ul>\n<li><a href=\"http:\/\/www.google.com\/buzz\/114134834346472219368\/GPQDR3gHsYr\">On \u201ccompilation errors\u201d in mathematical reading, and how to resolve them.<\/a><\/li>\n<li><a href=\"http:\/\/www.google.com\/buzz\/114134834346472219368\/1N1eaNU1mW6\">On the use of implicit mathematical notational conventions to provide contextual clues when reading<\/a>.<\/li>\n<li><a href=\"http:\/\/www.google.com\/buzz\/114134834346472219368\/jTJUyaibC8v\">On key \u201cjumps in difficulty\u201d in a mathematical argument, and how finding and understanding them is often key to understanding the argument as a whole<\/a>.<\/li>\n<li><a href=\"http:\/\/www.google.com\/buzz\/114134834346472219368\/WJkEENg19Sz\">On \u201clocal\u201d and \u201cglobal\u201d errors in mathematical papers, and how to detect them<\/a>.<\/li>\n<\/ul>\n<p>Some further advice on mathematical exposition:<\/p>\n<ul>\n<li>Mich\u00e8le Audin\u2019s \u201c<a href=\"http:\/\/www-irma.u-strasbg.fr\/~maudin\/newhowto.ps\">Conseils aux auteurs de textes math\u00e9matiques<\/a>\u201c<\/li>\n<li>Henry Cohn\u2019s \u201c<a href=\"http:\/\/research.microsoft.com\/en-us\/um\/people\/cohn\/Thoughts\/advice.html\">Advice for amateur mathematicians on writing and publishing papers<\/a>\u201c.<\/li>\n<li>Oded Goldreich\u2019s \u201c<a href=\"http:\/\/www.wisdom.weizmann.ac.il\/~oded\/writing.html\">How to write a paper<\/a>\u201c.<\/li>\n<li>David Goss\u2019 \u201c<a href=\"http:\/\/www.math.ohio-state.edu\/~goss\/hint.pdf\">Some hints on mathematical style<\/a>\u201c<\/li>\n<li>Timothy Gowers on \u201c<a href=\"http:\/\/gowers.wordpress.com\/2007\/10\/19\/my-favourite-pedagogical-principle-examples-first\">writing examples first!<\/a>\u201d (see also this\u00a0<a href=\"http:\/\/gowers.wordpress.com\/2007\/10\/24\/examples-first-ii\/\">followup post<\/a>)<\/li>\n<li>Paul Halmos\u2019 \u201c<a href=\"http:\/\/www.amazon.com\/How-Write-Mathematics-Steenrod\/dp\/0821800558\">How to write mathematics<\/a>\u201d (the book also contains similar pieces by Dieudonn\u00e9, Schiffer, and Steenrod); the article can be\u00a0<a href=\"http:\/\/retro.seals.ch\/digbib\/view?rid=ensmat-001:1970:16::59\">found here<\/a>.<\/li>\n<li>\u201c<a href=\"http:\/\/tex.loria.fr\/typographie\/mathwriting.pdf\">Mathematical Writing<\/a>\u201d \u2013 notes from a lecture course by Don Knuth, Tracy Larrabee, and Paul Roberts.<\/li>\n<li>Dick Lipton on an\u00a0<a href=\"http:\/\/rjlipton.wordpress.com\/2011\/05\/06\/navigating-cities-and-understanding-proofs\">analogy between paper writing and city planning<\/a>.<\/li>\n<li>Ashley Reiter\u2019s \u201c<a href=\"http:\/\/web.mit.edu\/jrickert\/www\/mathadvice.html\">Writing a research paper in mathematics<\/a>\u201c<\/li>\n<li>Jean-Pierre Serre\u2019s \u201c<a href=\"http:\/\/www.dailymotion.com\/video\/xf88b5_jean-pierre-serre-writing-mathemati_tech\">How to write mathematics badly<\/a>\u201c<\/li>\n<\/ul>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>On\u00a0writing There are three rules for writing the novel. Unfortunately, no one knows what they are.\u00a0(W. Somerset Maugham) Everyone has to\u00a0develop their own writing style,&hellip; <\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[30],"tags":[],"class_list":["post-19","post","type-post","status-publish","format-standard","hentry","category-writing"],"_links":{"self":[{"href":"https:\/\/zhuoyao.net\/index.php\/wp-json\/wp\/v2\/posts\/19","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/zhuoyao.net\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/zhuoyao.net\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/zhuoyao.net\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/zhuoyao.net\/index.php\/wp-json\/wp\/v2\/comments?post=19"}],"version-history":[{"count":0,"href":"https:\/\/zhuoyao.net\/index.php\/wp-json\/wp\/v2\/posts\/19\/revisions"}],"wp:attachment":[{"href":"https:\/\/zhuoyao.net\/index.php\/wp-json\/wp\/v2\/media?parent=19"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/zhuoyao.net\/index.php\/wp-json\/wp\/v2\/categories?post=19"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/zhuoyao.net\/index.php\/wp-json\/wp\/v2\/tags?post=19"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}