{"id":3753,"date":"2018-08-20T18:35:08","date_gmt":"2018-08-20T22:35:08","guid":{"rendered":"http:\/\/blogs.ams.org\/blogonmathblogs\/?p=3753"},"modified":"2018-08-20T18:35:08","modified_gmt":"2018-08-20T22:35:08","slug":"musings-on-a-mathematicians-duties","status":"publish","type":"post","link":"https:\/\/blogs.ams.org\/blogonmathblogs\/2018\/08\/20\/musings-on-a-mathematicians-duties\/","title":{"rendered":"Musings on a Mathematician&#8217;s Duties"},"content":{"rendered":"\r\n<div id=\"attachment_3768\" style=\"width: 479px\" class=\"wp-caption alignnone\"><a href=\"https:\/\/i0.wp.com\/blogs.ams.org\/blogonmathblogs\/files\/2018\/08\/5266588757_d816dfabc9_o.jpg\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-3768\" class=\" wp-image-3768\" src=\"https:\/\/i0.wp.com\/blogs.ams.org\/blogonmathblogs\/files\/2018\/08\/5266588757_d816dfabc9_o.jpg?resize=469%2C312\" alt=\"Diver figurines on fruit\" width=\"469\" height=\"312\" srcset=\"https:\/\/i0.wp.com\/blogs.ams.org\/blogonmathblogs\/files\/2018\/08\/5266588757_d816dfabc9_o.jpg?resize=300%2C199&amp;ssl=1 300w, https:\/\/i0.wp.com\/blogs.ams.org\/blogonmathblogs\/files\/2018\/08\/5266588757_d816dfabc9_o.jpg?resize=768%2C510&amp;ssl=1 768w, https:\/\/i0.wp.com\/blogs.ams.org\/blogonmathblogs\/files\/2018\/08\/5266588757_d816dfabc9_o.jpg?w=1024&amp;ssl=1 1024w\" sizes=\"auto, (max-width: 469px) 100vw, 469px\" \/><\/a><p id=\"caption-attachment-3768\" class=\"wp-caption-text\">Come with me to take a dive into the abc conjecture and the ethical duties of mathematicians! Image courtesy of HaPe_Gera via Flickr CC.<\/p><\/div>\r\n<p>As I mentioned in my last post, I <a href=\"https:\/\/blogs.ams.org\/blogonmathblogs\/2018\/08\/06\/what-wish-would-you-ask-a-math-genie-to-grant\/#more-3726\">wish<\/a> a genie would grant me thorough understanding of the proof Shinichi Mochizuki proposed for the abc conjecture. Much of this wish is motivated by a desire for the divisive debate to be settled concerning the more than 500 page text. Last year, it was announced that Go Yamashita had <a href=\"http:\/\/www.ams.org\/news?news_id=3711\">written a summary<\/a> of Mochizuki\u2019s proposed proof, but that summary was still 294 pages and didn\u2019t settle debates about Mochizuki\u2019s potential proof.<\/p>\r\n\r\n\r\n\r\n<p>In July, Ivan Fesenko, who has organized conferences on the inter-universal Teichm\u00fcller(IUT) theory that underlies Mochizuki\u2019s proposed proof, released a document titled <a href=\"https:\/\/www.maths.nottingham.ac.uk\/plp\/pmzibf\/rapm.pdf\">\u201cRemarks on Aspects of Modern Pioneering Mathematical Research,\u201d<\/a> which heavily focuses on Mochizuki\u2019s IUT theory and the abc conjecture.<\/p>\r\n\r\n<p><!--more--><\/p>\r\n\r\n<p>Here are some highlights from that document.<\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u201cThere is a fundamental aspect of speaking in tongues in the IUT, this aspect reflects the nature of the theory and the work on it,\u201d Fesenko wrote.<\/li>\r\n<li>\u201cThere is no obligation for the author of a breakthrough theory to write at the level of a well polished textbook\u2026All younger experts in IUT have not found the study of the theory more difficult than their study of other theories,\u201d he added. (All?)<\/li>\r\n<li>\u201cThe ethical responsibility of mathematicians includes a certain duty, never precisely stated in any formal way, but of course felt by and known to serious researchers: to dedicate an appropriate amount of time to study each new groundbreaking theory or proof in one\u2019s general area,\u201d Fesenko wrote.<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p>After reading that text, it is unclear to me how Fesenko defines \u201cappropriate amount of time\u201d or what constitutes a \u201cgroundbreaking theory or proof in one\u2019s general area.\u201d It also left me with questions about where certain duties lie. For example, is it the responsibility of someone who seeks to understand a new theory to bridge gaps between their understanding and the available explanations? How much of that responsibility also lies with the researchers behind the theory?<\/p>\r\n\r\n\r\n\r\n<p>John Baez discussed Fesenko\u2019s text in his post <a href=\"https:\/\/golem.ph.utexas.edu\/category\/2018\/07\/the_duties_of_a_mathematician.html\">\u201cThe Duties of a Mathematician\u201d<\/a> on the n-Category Caf\u00e9 group blog. Peter Woit also wrote about <a href=\"http:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=10436\">\u201cabc News\u201d<\/a> (and Fesenko\u2019s remarks) on his \u201cNot Even Wrong\u201d blog.<\/p>\r\n\r\n\r\n\r\n<p>Woit begins by sharing a claim he had heard but was waiting to discuss:<\/p>\r\n\r\n\r\n\r\n<p>\u201cThe last couple months I\u2019ve heard reports from several people claiming that arithmetic geometers Peter Scholze and Jakob Stix had identified a serious problem with Mochizuki\u2019s claimed proof of the abc conjecture,\u201d he writes, adding that he was waiting to publicly discuss the matter until the three had time to meet and \u201csort out the mathematics\u201d and \u201chave something to say publicly.\u201d However, Fesenko\u2019s text mentions the matter between Mochizuki, Scholze and Stix in a footnote, which Woit discussed in his blog post. Two of the sentences which most resonate with me from Woit\u2019s post are \u201cFesenko\u2019s document has a lot of unpleasant things to say about those who have written anything at all skeptical concerning Mochizuki\u2019s claimed proof, mostly without naming names\u201d and, concerning Peter Scholze, who was recently awarded a Fields Medal \u201cThat his questions about Mochizuki\u2019s proof were \u2018shallow\u2019 seems highly unlikely, to me at least.\u201d<\/p>\r\n\r\n\r\n\r\n<p>I think Baez\u2019s first reaction to Fesenko\u2019s remarks on \u201cthe ethical responsibility of mathematicians\u201d is highly relatable:<\/p>\r\n\r\n\r\n\r\n<p>\u201cMy first reaction to this claimed duty was quite personal: namely that I couldn\u2019t possibly meet it. My research is too thinly spread over too many fields to \u2018study each new groundbreaking theory or proof\u2019 in my general area. While Fesenko says that \u2018truly groundbreaking theories are rare, and this duty is not too cumbersome,\u2019 I feel the opposite\u2026More importantly, while it is undeniably <em>good <\/em>to know what\u2019s going on, that doesn\u2019t make it a duty.\u201d I believe mathematicians should be free to study what they\u2019re interested in.\u201d<\/p>\r\n\r\n\r\n\r\n<p>Many of the comments written on those two blog posts were also illuminating. For example, Simon Willerton commented (on \u201cThe Duties of a Mathematician\u201d post) \u201cThe AMS has some ethical guidelines [<a href=\"http:\/\/www.ams.org\/about-us\/governance\/policy-statements\/sec-ethics\">http:\/\/www.ams.org\/about-us\/governance\/policy-statements\/sec-ethics<\/a>] which includes the following under the responsibilities of mathematicians with regard to mathematical research and its presentation.<\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>To endeavor to be knowledgeable in their field, especially about work related to their research;<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p>Do you feel that\u2019s different to what Fesenko is asking for? The ethical guidelines perhaps give the AMS\u2019s answer to your question about the duties of a mathematician.\u201d<\/p>\r\n\r\n\r\n\r\n<p>What do you think about the duties of a mathematician and related ethics, or steps that should be taken to settle the debate about Mochizuki\u2019s proof for the abc conjecture? Please share your ideas in the comments or reach out to me on Twitter <a href=\"https:\/\/twitter.com\/writesRCrowell\">@writesRCrowell<\/a>!<\/p>\r\n<div style=\"margin-top: 0px; margin-bottom: 0px;\" class=\"sharethis-inline-share-buttons\" ><\/div>","protected":false},"excerpt":{"rendered":"<p>As I mentioned in my last post, I wish a genie would grant me thorough understanding of the proof Shinichi Mochizuki proposed for the abc conjecture. Much of this wish is motivated by a desire for the divisive debate to &hellip; <a href=\"https:\/\/blogs.ams.org\/blogonmathblogs\/2018\/08\/20\/musings-on-a-mathematicians-duties\/\">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\/blogonmathblogs\/2018\/08\/20\/musings-on-a-mathematicians-duties\/><\/div>\n","protected":false},"author":143,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[372,38,18,1],"tags":[757,826,825,827,685],"class_list":["post-3753","post","type-post","status-publish","format-standard","hentry","category-math-communication","category-number-theory-2","category-publishing-in-math","category-uncategorized","tag-abc-conjecture","tag-duties","tag-ethics","tag-iut-theory","tag-mathematicians"],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p3tW3N-Yx","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/posts\/3753","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/users\/143"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/comments?post=3753"}],"version-history":[{"count":15,"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/posts\/3753\/revisions"}],"predecessor-version":[{"id":3774,"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/posts\/3753\/revisions\/3774"}],"wp:attachment":[{"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/media?parent=3753"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/categories?post=3753"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/tags?post=3753"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}