{"id":15277,"date":"2025-09-20T14:09:17","date_gmt":"2025-09-20T18:09:17","guid":{"rendered":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=15277"},"modified":"2026-02-05T18:34:37","modified_gmt":"2026-02-05T23:34:37","slug":"two-number-theory-items-and-woody-allen","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=15277","title":{"rendered":"Two Number Theory Items (and Woody Allen)"},"content":{"rendered":"<ul>\n<li>James Douglas Boyd has recently spent a lot of time interacting with Mochizuki and others at RIMS working in anabelian geometry.  Material from interviews he conducted are available <a href=\"https:\/\/www.sci-sci.org\/_files\/ugd\/e7f2c3_ae5655c77cac467d910ab0c75ef60370.pdf\">here<\/a> (Mochizuki on IUT) and <a href=\"https:\/\/www.sci-sci.org\/_files\/ugd\/e7f2c3_cee9d11d6fb54bc88e6859a23193befd.pdf\">here<\/a> (on anabelian geometry at RIMS).  He also has written a <a href=\"https:\/\/www.sci-sci.org\/_files\/ugd\/e7f2c3_babfab84a56e45fe9e78670028015817.pdf\">summary of IUT and of the basic problem with the abc proof<\/a>.  These include detailed comments on the issue pointed out by Scholze-Stix and why this is a significant problem for the proof.  I&#8217;d be curious to hear from anyone who has looked at this closely about whether they agree with Boyd&#8217;s characterization of the situation.\n<p>There&#8217;s also a lot of material the IUT ideas, independent of the problematic abc proof, and about what Mochizuki and others are now trying to do with these ideas.\n<\/li>\n<li>Videos from the talks at the <a href=\"https:\/\/www.mpim-bonn.mpg.de\/maninmemorial\">conference last month in honor of Manin<\/a> are now available <a href=\"https:\/\/archive.mpim-bonn.mpg.de\/id\/eprint\/5179\/\">here<\/a>.  I was especially interested in <a href=\"https:\/\/archive.mpim-bonn.mpg.de\/id\/eprint\/5179\/20\/ManinMemorialConf-Clausen.mp4\">Dustin Clausen&#8217;s talk on Weil groups<\/a> and ideas about how to go beyond the conventional definition to get something more satisfactory.  The twistor line makes an appearance.<\/li>\n<li>From <a href=\"https:\/\/www.wsj.com\/arts-culture\/books\/at-89-woody-allen-is-not-done-yet-f0878437\">a story in today&#8217;s Wall Street Journal<\/a> about Woody Allen and his new novel:<br \/>\n<blockquote><p>Though he\u2019s already at work on a second novel, he rarely reads fiction\u2014\u201cI feel like I\u2019m wasting time.\u201d  More often he reads philosophy and books by physicists. \u201cI keep thinking I\u2019m going to learn something of deep value that\u2019s going to make me feel better in life,\u201d he says. \u201cIt never does.\u201d <\/p><\/blockquote>\n<\/li>\n<\/ul>\n<p><strong>Update<\/strong>:  A commenter points to <a href=\"https:\/\/www.kurims.kyoto-u.ac.jp\/~motizuki\/IUT-report-2025-10.pdf\">this from Mochizuki<\/a>, which denounces Boyd and his report, as well as discussing prospects for formalizing IUT and the abc proof.<br \/>\n<strong><br \/>\nUpdate<\/strong>:  Kirti Joshi has a new <a href=\"https:\/\/hal.science\/hal-05363791v1\/document\">FAQ about the proof of the abc-conjecture<\/a>. He has also sent me <a href=\"https:\/\/www.math.columbia.edu\/~woit\/letterfromjoshi.pdf\">this letter<\/a>, which more about his view.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>James Douglas Boyd has recently spent a lot of time interacting with Mochizuki and others at RIMS working in anabelian geometry. Material from interviews he conducted are available here (Mochizuki on IUT) and here (on anabelian geometry at RIMS). He &hellip; <a href=\"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=15277\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_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":"","jetpack_post_was_ever_published":false},"categories":[33,1],"tags":[],"class_list":["post-15277","post","type-post","status-publish","format-standard","hentry","category-abc-conjecture","category-uncategorized"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/15277","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=15277"}],"version-history":[{"count":12,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/15277\/revisions"}],"predecessor-version":[{"id":15454,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/15277\/revisions\/15454"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=15277"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=15277"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=15277"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}