{"id":1489,"date":"2017-01-26T11:43:49","date_gmt":"2017-01-26T16:43:49","guid":{"rendered":"http:\/\/blogs.ams.org\/beyondreviews\/?p=1489"},"modified":"2018-03-14T09:06:18","modified_gmt":"2018-03-14T14:06:18","slug":"citations","status":"publish","type":"post","link":"https:\/\/blogs.ams.org\/beyondreviews\/2017\/01\/26\/citations\/","title":{"rendered":"#Citations"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-1995\" src=\"http:\/\/blogs.ams.org\/beyondreviews\/files\/2018\/03\/250px-Chevrolet_Citation_II_rear.jpg\" alt=\"Picture of a Chevrolet Citation\" width=\"225\" height=\"124\" \/>Mathematicians are good at counting. \u00a0We can count the number of ways to roll \u00a0a 7 with two dice. \u00a0(<a href=\"https:\/\/www.random.org\/dice\/?num=2\">Answer<\/a> = 6.) We can count the number of ways to shuffle a deck of cards so that every card is not in its original position. \u00a0(<a href=\"https:\/\/en.wikipedia.org\/wiki\/Derangement\">Answer<\/a> = $!52$ = 29672484407795138298279444403649511427278111361911893663894333196201.) \u00a0We can count the number of lines on a cubic surface in $mathbf{CP}^3$. (<a href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=2180\">Answer<\/a> = 27.) \u00a0 Sometimes we can count, but we don&#8217;t really know what the actual\u00a0<em>number<\/em> is, such as when we count\u00a0the minimum number of guests that must be invited so that at least $m$ will know each other or at least $n$ will not know each other. \u00a0(<a href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=1576401\">Answer<\/a> = the Ramsey number $R(m, n)$.) \u00a0Many times, it is better to use an asymptotic estimate, such as <a href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=16588\">Stirling&#8217;s formula<\/a>. \u00a0When we can&#8217;t estimate, we can bound, such as <a href=\"http:\/\/www.ams.org\/mathscinet\/MRAuthorID\/51070\">Conrey<\/a>\u2019s result that more than <a href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=1004130\">two-fifths of the zeros of the Riemann zeta function are on the critical line<\/a>. \u00a0Lately, we (along with our colleagues in other disciplines) have started counting citations. \u00a0<!--more--><\/p>\n<h2>What could go wrong?<\/h2>\n<p>Plenty. \u00a0Citation counts depend on matching algorithms. \u00a0The algorithms try to pair an item in the reference list of an article with a known item in a database. \u00a0Usually, you want to have matches or near matches on multiple points: author name, title, year of publication, page range, source (name of the journal). \u00a0However, bibliographic styles are not consistent. \u00a0And some authors make mistakes or take shortcuts, providing too little information. \u00a0Some journals enforce telegraphic\u00a0reference\u00a0styles. \u00a0Here is an example I chose at random from\u00a0a respected physics journal:<\/p>\n<ul>\n<li>R. Yang and Z.\u2009Q. Wu, <em>Earth Planet. Sci. Lett.<\/em> <strong>404<\/strong>, 14 (2014).<\/li>\n<li>J.\u2009C. Crowhurst, J.\u2009M. Brown, A.\u2009F. Goncharov, and S.\u2009D. Jacobsen, <em>Science<\/em> <strong>319<\/strong>, 451 (2008).<\/li>\n<li>H. Marquardt, S. Speziale, H.\u2009J. Reichmann, D.\u2009J. Frost, and F.\u2009R. Schilling, <em>Earth Planet. Sci. Lett.<\/em> <strong>287<\/strong>, 345 (2009).<\/li>\n<\/ul>\n<p>Note that there are no titles. \u00a0Also, a page range isn&#8217;t given, just a starting page. \u00a0This style makes\u00a0it hard for\u00a0the matching algorithm, but it is a\u00a0standard style in the physics literature, not just this journal.<\/p>\n<p>Some old-school citations are almost impossible for an algorithm to find. \u00a0Here&#8217;s an old old-school example, from an <a href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=1503620\">old paper by Lefschetz<\/a>\u00a0in the <a href=\"http:\/\/www.jstor.org\/stable\/2007214\">Annals of Mathematics in 1920<\/a>\u00a0.<br \/>\n<a href=\"http:\/\/blogs.ams.org\/beyondreviews\/files\/2017\/01\/Screen-Shot-Lefschetz-footnote.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1523 size-full\" src=\"http:\/\/blogs.ams.org\/beyondreviews\/files\/2017\/01\/Screen-Shot-Lefschetz-footnote.png\" alt=\"Lefschetz using a footnote to cite works\" width=\"615\" height=\"190\" srcset=\"https:\/\/blogs.ams.org\/beyondreviews\/files\/2017\/01\/Screen-Shot-Lefschetz-footnote.png 615w, https:\/\/blogs.ams.org\/beyondreviews\/files\/2017\/01\/Screen-Shot-Lefschetz-footnote-300x93.png 300w\" sizes=\"auto, (max-width: 615px) 100vw, 615px\" \/><\/a><\/p>\n<p style=\"text-align: left;\">\u00a0 \u00a0\u2022\u00a0\u2022\u00a0\u2022\u00a0\u2022\u00a0\u2022<\/p>\n<p><a href=\"http:\/\/blogs.ams.org\/beyondreviews\/files\/2017\/01\/Screen-Shot-Lefschetz-citation.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1522 size-full\" src=\"http:\/\/blogs.ams.org\/beyondreviews\/files\/2017\/01\/Screen-Shot-Lefschetz-citation.png\" alt=\"The citations in the footnote are spotty with the details\" width=\"615\" height=\"102\" srcset=\"https:\/\/blogs.ams.org\/beyondreviews\/files\/2017\/01\/Screen-Shot-Lefschetz-citation.png 615w, https:\/\/blogs.ams.org\/beyondreviews\/files\/2017\/01\/Screen-Shot-Lefschetz-citation-300x50.png 300w\" sizes=\"auto, (max-width: 615px) 100vw, 615px\" \/><\/a><br \/>\nThe references are given almost as prose, but heavily abbreviated. \u00a0 \u00a0My copy of <a href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=178117\">Whittaker and Watson<\/a> is \u00a0full of citations as footnotes. \u00a0(And I can only imagine how many times that book is referenced the way I just did, by the authors&#8217; names, not by the title.\u00b9) \u00a0 \u00a0Such citations are rarer now, but they still occur.<\/p>\n<p>Errors in citations can propagate. \u00a0When I wrote my PhD thesis, an important result that I used was the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Borel%E2%80%93Weil%E2%80%93Bott_theorem\">Borel-Weil-Bott Theorem<\/a>. \u00a0Bott&#8217;s paper is<\/p>\n<p><a href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=89473\">MR0089473<\/a><br \/>\nBott, Raoul<br \/>\nHomogeneous vector bundles.<br \/>\n<em>Ann. of Math. (2)<\/em> <strong>66<\/strong> (1957), 203\u2013248.<\/p>\n<p>However, I found that many papers cited it incorrectly. \u00a0Moreover, I could see that some authors copied the citation to Bott&#8217;s paper from the references in another paper. \u00a0If one paper had it incorrect, then subsequent articles make the same mistake. \u00a0I don&#8217;t remember exactly which ones I encountered way back in grad school, but examples are\u00a0easy to find. \u00a0For instance,\u00a0<a href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=776387\">one paper<\/a> has the year and pages correct, but has the volume number as 56. \u00a0<a href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=1214703\">Another<\/a> puts the volume number at 60. \u00a0(Getting warmer!) \u00a0Kostant&#8217;s <a href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=109192\">paper<\/a> establishing his famous formula for the multiplicity of a weight gets everything right except the page range. \u00a0In his <a href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=142696\">paper on Lie algebra cohomology and the Borel-Weil-Bott Theorem<\/a>\u00a0(published two years later), Kostant\u00a0has a complete and correct citation.<\/p>\n<h3>Special Case: Books<\/h3>\n<p>Citations to books can be troublesome. \u00a0 Often, the citation is spare, giving the author, title, and year. \u00a0Here is a citation from a paper published in 2016 to a famous book by Dautray and Lions:<\/p>\n<p style=\"padding-left: 30px;\">21. Dautray R, Lions JL. <em>Mathematical Analysis and Numerical Methods for Sciences and Technology<\/em>. Springer: Berlin, 1990.<\/p>\n<p>We matched that to<\/p>\n<p><a href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=1036731\"><strong>MR1036731<\/strong><\/a><br \/>\n<a href=\"http:\/\/jarvis.mr.ams.org\/mathscinet\/search\/author.html?mrauthid=54865\">Dautray, Robert<\/a><span class=\"instInfo\">(F-POLY)<\/span>; <a href=\"http:\/\/jarvis.mr.ams.org\/mathscinet\/search\/author.html?mrauthid=114525\">Lions, Jacques-Louis<\/a><span class=\"instInfo\">(F-CDF)<\/span><br \/>\n<span class=\"title\">Mathematical analysis and numerical methods for science and technology. Vol. 1.<\/span><br \/>\nPhysical origins and classical methods. With the collaboration of Philippe B\u00e9nilan, Michel Cessenat, Andr\u00e9 Gervat, Alain Kavenoky and H\u00e9l\u00e8ne Lanchon. Translated from the French by Ian N. Sneddon. With a preface by Jean Teillac.\u00a0<em>Springer-Verlag, Berlin,<\/em> 1990. <span class=\"rm\">xviii<\/span>+695 pp. ISBN: 3-540-50207-6; 3-540-66097-6.<\/p>\n<p>But it could also have been Volume 3 or Volume 4, which were also published in 1990:<\/p>\n<p><a href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=1064315\"><strong>MR1064315<\/strong><\/a><br \/>\n<a href=\"http:\/\/www.ams.org\/mathscinet\/search\/author.html?mrauthid=54865\">Dautray, Robert<\/a><span class=\"instInfo\">(F-POLY)<\/span>; <a href=\"http:\/\/www.ams.org\/mathscinet\/MRAuthorID\/114525\">Lions, Jacques-Louis<\/a><span class=\"instInfo\">(F-CDF)<\/span><br \/>\n<span class=\"title\">Mathematical analysis and numerical methods for science and technology. Vol. 3.<\/span><br \/>\nSpectral theory and applications. With the collaboration of Michel Artola and Michel Cessenat. Translated from the French by John C. Amson. <em>Springer-Verlag, Berlin,<\/em> 1990. <span class=\"rm\">x<\/span>+515 pp. ISBN: 3-540-50208-4; 3-540-66099-2<\/p>\n<p><a href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=1081946\"><strong>MR1081946<\/strong><\/a><br \/>\n<a href=\"http:\/\/www.ams.org\/mathscinet\/MRAuthorID\/54865\">Dautray, Robert<\/a><span class=\"instInfo\">(F-POLY)<\/span>; <a href=\"http:\/\/www.ams.org\/mathscinet\/MRAuthorID\/114525\">Lions, Jacques-Louis<\/a><span class=\"instInfo\">(F-CDF)<\/span><br \/>\n<span class=\"title\">Mathematical analysis and numerical methods for science and technology. Vol. 4.<\/span><br \/>\nIntegral equations and numerical methods. With the collaboration of Michel Artola, Philippe B\u00e9nilan, Michel Bernadou, Michel Cessenat, Jean-Claude N\u00e9d\u00e9lec, Jacques Planchard and Bruno Scheurer. Translated from the French by John C. Amson. <em>Springer-Verlag, Berlin,<\/em> 1990. <span class=\"rm\">x<\/span>+465 pp. ISBN: 3-540-50209-2; 3-540-66100-X<\/p>\n<p>Volume 2 was published in 1988. \u00a0Volume 5 was 1992, and Volume 6 was 1993.<\/p>\n<p>Formats vary greatly, with some including the city of publication, some including series information (such as <em>Ergebnisse<\/em>\u00a0or maybe <em>Ergebnisse der Mathematik<\/em>\u00a0or <em>Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge<\/em>). \u00a0If the series information is given, a volume number might be included. \u00a0 In checking changes in citations after releasing <a href=\"http:\/\/blogs.ams.org\/beyondreviews\/2016\/12\/30\/things-have-changed\/\">the new \u00a0features for MathSciNet<\/a>, we realized that there were instances of a citation to a book in a series mixing up the volume number and the year of publication. \u00a0(We fixed them.)<\/p>\n<h2>What can go right?<\/h2>\n<p>The propagation of the errors with citations to Bott&#8217;s paper described above was partly due to authors taking a shortcut. \u00a0Few people wanted to figure out the appropriate abbreviation for the <em>Annals of Mathematics<\/em> or where to put the volume number versus the publication year. \u00a0So many of us looked at the references in another paper to sort that out. With some of the tools built into\u00a0MathSciNet, such shortcuts are no longer necessary. \u00a0At Mathematical Reviews, we work very hard to make sure we have complete and accurate bibliographic information for the entries in MathSciNet. \u00a0We also work hard to make it easy for you to use that information. \u00a0My earlier post\u00a0<a href=\"http:\/\/blogs.ams.org\/beyondreviews\/2015\/07\/11\/references-and-citations\/\">References and Citations<\/a> tells you ways to do that, including obtaining the information in BibTeX format.<\/p>\n<p>If you use the bibliographic data from MathSciNet in your references, then everybody&#8217;s matching algorithms will have a much easier time pairing those references with the paper in their databases. \u00a0This helps people count. \u00a0And you will have an easier time writing up the paper!<\/p>\n<hr \/>\n<p>\u00b9 This is related to the problem of\u00a0<em>Alice&#8217;s Restaurant<\/em>. \u00a0Sometimes what we call a thing is not the name of the thing. There is a song called\u00a0<em><a href=\"https:\/\/youtu.be\/m57gzA2JCcM?t=35s\">Alice&#8217;s Restaurant<\/a><\/em>, which is about Alice&#8217;s restaurant. \u00a0But &#8220;Alice&#8217;s Restaurant&#8221; is not the name of the restaurant &#8211; it&#8217;s just the name of the song\u00a0<em>about<\/em> the restaurant.<\/p>\n<div style=\"margin-top: 0px; margin-bottom: 0px;\" class=\"sharethis-inline-share-buttons\" ><\/div>","protected":false},"excerpt":{"rendered":"<p>Mathematicians are good at counting. \u00a0We can count the number of ways to roll \u00a0a 7 with two dice. \u00a0(Answer = 6.) We can count the number of ways to shuffle a deck of cards so that every card is &hellip; <a href=\"https:\/\/blogs.ams.org\/beyondreviews\/2017\/01\/26\/citations\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n<div style=\"margin-top: 0px; margin-bottom: 0px;\" class=\"sharethis-inline-share-buttons\" data-url=https:\/\/blogs.ams.org\/beyondreviews\/2017\/01\/26\/citations\/><\/div>\n","protected":false},"author":86,"featured_media":1514,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[6],"tags":[],"class_list":["post-1489","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-general-information"],"jetpack_featured_media_url":"https:\/\/blogs.ams.org\/beyondreviews\/files\/2017\/01\/Screen-Shot-Citation-as-footnote.png","jetpack_shortlink":"https:\/\/wp.me\/p6C2KK-o1","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/blogs.ams.org\/beyondreviews\/wp-json\/wp\/v2\/posts\/1489","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ams.org\/beyondreviews\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ams.org\/beyondreviews\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ams.org\/beyondreviews\/wp-json\/wp\/v2\/users\/86"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ams.org\/beyondreviews\/wp-json\/wp\/v2\/comments?post=1489"}],"version-history":[{"count":46,"href":"https:\/\/blogs.ams.org\/beyondreviews\/wp-json\/wp\/v2\/posts\/1489\/revisions"}],"predecessor-version":[{"id":2033,"href":"https:\/\/blogs.ams.org\/beyondreviews\/wp-json\/wp\/v2\/posts\/1489\/revisions\/2033"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/blogs.ams.org\/beyondreviews\/wp-json\/wp\/v2\/media\/1514"}],"wp:attachment":[{"href":"https:\/\/blogs.ams.org\/beyondreviews\/wp-json\/wp\/v2\/media?parent=1489"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ams.org\/beyondreviews\/wp-json\/wp\/v2\/categories?post=1489"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ams.org\/beyondreviews\/wp-json\/wp\/v2\/tags?post=1489"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}