{"id":135153,"date":"2022-02-03T09:44:49","date_gmt":"2022-02-03T17:44:49","guid":{"rendered":"https:\/\/lifeboat.com\/blog\/2022\/02\/mathematicians-prove-30-year-old-andre-oort-conjecture"},"modified":"2022-02-03T09:44:49","modified_gmt":"2022-02-03T17:44:49","slug":"mathematicians-prove-30-year-old-andre-oort-conjecture","status":"publish","type":"post","link":"https:\/\/lifeboat.com\/blog\/2022\/02\/mathematicians-prove-30-year-old-andre-oort-conjecture","title":{"rendered":"Mathematicians Prove 30-Year-Old Andre\u0301-Oort Conjecture"},"content":{"rendered":"<p><a class=\"aligncenter blog-photo\" href=\"https:\/\/lifeboat.com\/blog.images\/mathematicians-prove-30-year-old-andre-oort-conjecture2.jpg\"><\/a><\/p>\n<p>\u201cThe methods used to approach it cover, I would say, the whole of mathematics,\u201d said <a href=\"https:\/\/www.ucl.ac.uk\/~ucahaya\/\">Andrei Yafaev<\/a> of University College London.<\/p>\n<p>The new paper begins with one of the most basic but provocative questions in mathematics: When do polynomial equations like <em>x<\/em><sup>3<\/sup> + <em>y<\/em><sup>3<\/sup> = <em>z<\/em><sup>3<\/sup> have integer solutions (solutions in the positive and negative counting numbers)? In 1994, <a href=\"https:\/\/www.maths.ox.ac.uk\/people\/andrew.wiles\">Andrew Wiles<\/a> solved a version of this question, known as Fermat\u2019s Last Theorem, in one of the great mathematical triumphs of the 20th century.<\/p>\n<p>In the quest to solve Fermat\u2019s Last Theorem and problems like it, mathematicians have developed increasingly abstract theories that spark new questions and conjectures. Two such problems, <a href=\"https:\/\/www.cambridge.org\/core\/books\/abs\/lfunctions-and-galois-representations\/andreoort-conjecture-a-survey\/522E310ACFFFD3AAAAF5B0281FBB8212\">stated in 1989 and 1995<\/a> by Yves Andre\u0301 and Frans Oort, respectively, led to what\u2019s now known as the Andre\u0301-Oort conjecture. Instead of asking about integer solutions to polynomial equations, the Andre\u0301-Oort conjecture is about solutions involving far more complicated geometric objects called Shimura varieties.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u201cThe methods used to approach it cover, I would say, the whole of mathematics,\u201d said Andrei Yafaev of University College London. The new paper begins with one of the most basic but provocative questions in mathematics: When do polynomial equations like x3 + y3 = z3 have integer solutions (solutions in the positive and negative [\u2026]<\/p>\n","protected":false},"author":662,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[41,2229],"tags":[],"class_list":["post-135153","post","type-post","status-publish","format-standard","hentry","category-information-science","category-mathematics"],"_links":{"self":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/135153","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/users\/662"}],"replies":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/comments?post=135153"}],"version-history":[{"count":0,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/135153\/revisions"}],"wp:attachment":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/media?parent=135153"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/categories?post=135153"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/tags?post=135153"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}