{"id":5913,"date":"2023-05-20T14:33:36","date_gmt":"2023-05-20T06:33:36","guid":{"rendered":"http:\/\/tsinghualogic.net\/JRC\/?page_id=5913"},"modified":"2023-05-20T14:34:13","modified_gmt":"2023-05-20T06:34:13","slug":"hugh-woodin","status":"publish","type":"page","link":"http:\/\/tsinghualogic.net\/JRC\/hugh-woodin\/","title":{"rendered":"Hugh Woodin"},"content":{"rendered":"<div class=\"wp-block-image\">\n<figure class=\"alignleft size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"http:\/\/tsinghualogic.net\/JRC\/wp-content\/uploads\/2023\/05\/Hugh_Woodin.jpeg\" alt=\"\" class=\"wp-image-5906\" width=\"378\" height=\"250\" srcset=\"http:\/\/tsinghualogic.net\/JRC\/wp-content\/uploads\/2023\/05\/Hugh_Woodin.jpeg 400w, http:\/\/tsinghualogic.net\/JRC\/wp-content\/uploads\/2023\/05\/Hugh_Woodin-200x133.jpeg 200w\" sizes=\"(max-width: 378px) 100vw, 378px\" \/><figcaption class=\"wp-element-caption\">Hugh Woodin<\/figcaption><\/figure><\/div>\n\n\n<p><\/p>\n\n\n\n<p>William Hugh Woodin is an American mathematician and&nbsp;set theorist&nbsp;at&nbsp;Harvard University. He has made many notable contributions to the theory of&nbsp;inner models&nbsp;and&nbsp;determinacy. A type of&nbsp;large cardinals, the&nbsp;Woodin cardinals, bear his name. In 2023, he was elected to the&nbsp;National Academy of Sciences.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p>Homepage: <a rel=\"noreferrer noopener\" href=\"https:\/\/www.math.harvard.edu\/people\/woodin-hugh\/\" target=\"_blank\">https:\/\/www.math.harvard.edu\/people\/woodin-hugh\/<\/a><\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><\/p>\n\n\n\n<div style=\"height:29px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p><\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><em><strong>Is there mathematical truth beyond the reach of mathematical proof?<\/strong><\/em><\/p>\n\n\n\n<p>Is all mathematical truth simply the product of formal calculations, more&nbsp;precisely the result of formal proofs from formal axioms? This is arguably the&nbsp;most basic question in the Philosophy of Mathematics.<\/p>\n\n\n\n<p>The incompleteness theorems of G\u00f6del argue that the answer is no. But&nbsp;the extent to which this is actually a compelling answer is debatable.<\/p>\n\n\n\n<p>However, there are new proofs of the incompleteness theorems which are based on&nbsp;computational complexity, and which definitively show that mathematical truth transcends&nbsp;mathematical proof.<\/p>\n\n\n\n<p>Nowhere is the issue of truth versus proof more central than in Set Theory,&nbsp;which is the mathematical study of Infinity. Here many of the most basic questions,&nbsp;such as that of Cantor\u2019s Continuum Hypothesis (CH), are known to be&nbsp;beyond the reach of proofs from the accepted ZFC axioms of Set Theory.&nbsp;So any resolution of the problem of CH must involve truth beyond proof.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>William Hugh Woodin is an American mathematician and&#038;nb [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"http:\/\/tsinghualogic.net\/JRC\/wp-json\/wp\/v2\/pages\/5913"}],"collection":[{"href":"http:\/\/tsinghualogic.net\/JRC\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/tsinghualogic.net\/JRC\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/tsinghualogic.net\/JRC\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/tsinghualogic.net\/JRC\/wp-json\/wp\/v2\/comments?post=5913"}],"version-history":[{"count":2,"href":"http:\/\/tsinghualogic.net\/JRC\/wp-json\/wp\/v2\/pages\/5913\/revisions"}],"predecessor-version":[{"id":5916,"href":"http:\/\/tsinghualogic.net\/JRC\/wp-json\/wp\/v2\/pages\/5913\/revisions\/5916"}],"wp:attachment":[{"href":"http:\/\/tsinghualogic.net\/JRC\/wp-json\/wp\/v2\/media?parent=5913"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}