{"id":62122,"date":"2018-06-30T21:27:34","date_gmt":"2018-07-01T02:27:34","guid":{"rendered":"http:\/\/www.kateva.org\/sh\/?p=62122"},"modified":"2018-06-30T21:31:13","modified_gmt":"2018-07-01T02:31:13","slug":"when-will-ai-explore-equivalent-representations-in-math-space","status":"publish","type":"post","link":"http:\/\/www.kateva.org\/sh\/?p=62122","title":{"rendered":"When will AI explore equivalent representations in math-space?"},"content":{"rendered":"<p>Wiles proof of Fermat&#8217;s Last Theorem borrowed from from <a href=\"https:\/\/en.m.wikipedia.org\/wiki\/Algebraic_geometry\">algebraic geometry<\/a> and <a href=\"https:\/\/en.m.wikipedia.org\/wiki\/Number_theory\">number theory<\/a> (Wikipedia). Presumably these are equivalent representations for some problems. I imagine this as the grown-up equivalent of switching from Cartesian to polar coordinates to solve a freshman physics problem.<\/p>\n<p>I wonder when AI will start exploring math-space, searching for more of these unexpected alignments and concordances.<\/p>\n<p>It feels like that might happen soon, but I have no idea how it would work.<\/p>\n<p>Update: from the Wikipedia article on Wiles proof, a much better example of what I&#8217;m trying to describe:<\/p>\n<blockquote><p>Japanese mathematician <a href=\"https:\/\/en.m.wikipedia.org\/wiki\/Goro_Shimura\">Goro Shimura<\/a>, drawing on ideas posed by <a href=\"https:\/\/en.m.wikipedia.org\/wiki\/Yutaka_Taniyama\">Yutaka Taniyama<\/a>, conjectured that a connection might exist between two different mathematical objects then being studied, known as <a href=\"https:\/\/en.m.wikipedia.org\/wiki\/Elliptic_curve\">elliptic curves<\/a> and <a href=\"https:\/\/en.m.wikipedia.org\/wiki\/Modular_form\">modular forms<\/a>.<\/p><\/blockquote>\n<blockquote><p>Taniyama and Shimura posed the question whether, unknown to mathematicians, the two kinds of object were actually identical mathematical objects, just seen in different ways.<\/p><\/blockquote>\n<p>What I&#8217;m describing is an automated search for &#8220;identical mathematical objects &#8230; seen in different ways&#8221;.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Wiles proof of Fermat&#8217;s Last Theorem borrowed from from algebraic geometry and number theory (Wikipedia). Presumably these are equivalent representations for some problems. I imagine this as the grown-up equivalent of switching from Cartesian to polar coordinates to solve a &hellip; <a href=\"http:\/\/www.kateva.org\/sh\/?p=62122\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[36],"tags":[],"class_list":["post-62122","post","type-post","status-publish","format-standard","hentry","category-t"],"_links":{"self":[{"href":"http:\/\/www.kateva.org\/sh\/index.php?rest_route=\/wp\/v2\/posts\/62122","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.kateva.org\/sh\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.kateva.org\/sh\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.kateva.org\/sh\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.kateva.org\/sh\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=62122"}],"version-history":[{"count":2,"href":"http:\/\/www.kateva.org\/sh\/index.php?rest_route=\/wp\/v2\/posts\/62122\/revisions"}],"predecessor-version":[{"id":62124,"href":"http:\/\/www.kateva.org\/sh\/index.php?rest_route=\/wp\/v2\/posts\/62122\/revisions\/62124"}],"wp:attachment":[{"href":"http:\/\/www.kateva.org\/sh\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=62122"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.kateva.org\/sh\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=62122"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.kateva.org\/sh\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=62122"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}