{"id":11397,"date":"2019-10-11T11:57:39","date_gmt":"2019-10-11T15:57:39","guid":{"rendered":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=11397"},"modified":"2019-10-11T11:57:39","modified_gmt":"2019-10-11T15:57:39","slug":"foundations","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=11397","title":{"rendered":"Foundations"},"content":{"rendered":"<p>Some links related to the foundations of math and physics:<\/p>\n<ul>\n<li>Kevin Hartnett at Quanta has a <a href=\"https:\/\/www.quantamagazine.org\/with-category-theory-mathematics-escapes-from-equality-20191010\">long article on Jacob Lurie and his work on infinity categories<\/a>. Unfortunately Lurie didn&#8217;t participate in the article himself, so comments are only from others.  The article does a good job of giving at least a vague sense of what these very abstract foundational ideas are about, as well as examining the math community&#8217;s struggle to absorb them.  Lurie&#8217;s work on this is spread out over more than 900 pages <a href=\"http:\/\/www.math.harvard.edu\/~lurie\/papers\/HTT.pdf\">here<\/a> and more than 1500 pages <a href=\"http:\/\/www.math.harvard.edu\/~lurie\/papers\/HA.pdf\">here<\/a>. Recently he has been putting together an online textbook\/reference version of this material as <a href=\"https:\/\/kerodon.net\/\">Kerodon<\/a>, which is modeled after and uses much of the same software as Johan de Jong&#8217;s <a href=\"https:\/\/stacks.math.columbia.edu\/\">Stacks project<\/a>.<\/li>\n<li>At <a href=\"https:\/\/mathematicswithoutapologies.wordpress.com\/2019\/10\/08\/roundtable-video-incorrect-proofs-true-theorems\/\">Mathematics without Apologies<\/a>, Michael Harris has some comments on a recent discussion of the <a href=\"https:\/\/www.helixcenter.org\/roundtables\/mechanization-of-math\/\">Mechanization of Math<\/a>, held here in New York at the Helix Center.  A video of the discussion is available <a href=\"https:\/\/www.helixcenter.org\/videos\/#\/KNWPmhc2sh8\">here<\/a>.<\/li>\n<li>In the new (November) issue of the AMS Notices John Baez has a <a href=\"https:\/\/www.ams.org\/journals\/notices\/201910\/rnoti-p1690.pdf\">review<\/a> of a recent collection of articles about the foundations of mathematics and physics.  The book, <a href=\"https:\/\/link.springer.com\/book\/10.1007%2F978-3-319-64813-2\">Foundations of Mathematics and Physics One Century After Hilbert<\/a>, contains contributions about both math and physics, although in his review Baez concentrates on issues related to physics.  He notes &#8220;The  elephant  in  the  room  is  string  theory.&#8221;<br \/>\nThe same issue of the Notices contains an informative l<a href=\"https:\/\/www.ams.org\/journals\/notices\/201910\/rnoti-p1660.pdf\">ong article about Michael Atiyah and his career<\/a>, written by Alain Connes and Joseph Kouneiher (Kouneiher is the editor of the book reviewed by Baez).\n<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Some links related to the foundations of math and physics: Kevin Hartnett at Quanta has a long article on Jacob Lurie and his work on infinity categories. Unfortunately Lurie didn&#8217;t participate in the article himself, so comments are only from &hellip; <a href=\"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=11397\">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_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":[1],"tags":[],"class_list":["post-11397","post","type-post","status-publish","format-standard","hentry","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\/11397","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=11397"}],"version-history":[{"count":4,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/11397\/revisions"}],"predecessor-version":[{"id":11401,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/11397\/revisions\/11401"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=11397"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=11397"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=11397"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}