{"589875":{"#nid":"589875","#data":{"type":"news","title":"Set Game Proof Stuns Mathematicians","body":[{"value":"\u003Cp\u003EThrough a series of research papers posted online in recent weeks, mathematicians have solved a problem about the pattern-matching card game, \u003Ca href=\u0022https:\/\/en.wikipedia.org\/wiki\/Set_%28game%29\u0022 target=\u0022_blank\u0022 title=\u0022Set\u0022\u003ESet\u003C\/a\u003E, that predates the game itself. The proof, whose simplicity has stunned mathematicians, is leading to advances in other combinatorics problems.\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003EThree mathematicians in particular, \u003Ca href=\u0022https:\/\/www.math.gatech.edu\/users\/ecroot\u0022 target=\u0022_blank\u0022 title=\u0022Ernie Croot\u0022\u003EErnie Croot\u003C\/a\u003E of the Georgia Institute of Technology (pictured to the right), \u003Ca href=\u0022http:\/\/math.haifa.ac.il\/seva\/\u0022 target=\u0022_blank\u0022 title=\u0022Vsevolod Lev\u0022\u003EVsevolod Lev\u003C\/a\u003E of the University of Haifa, Oranim, in Israel, and \u003Ca href=\u0022https:\/\/www.cs.bme.hu\/%7Eppp\/indexen.html\u0022 target=\u0022_blank\u0022 title=\u0022P\u00e9ter P\u00e1l Pach\u0022\u003EP\u0026eacute;ter P\u0026aacute;l Pach\u003C\/a\u003E of the Budapest University of Technology and Economics in Hungary, \u003Ca href=\u0022https:\/\/arxiv.org\/abs\/1605.01506\u0022 target=\u0022_blank\u0022 title=\u0022posted a paper online\u0022\u003Eposted a paper online\u003C\/a\u003E, on May 5, showing how to use a polynomial method to solve a closely related problem. In their work, the three researchers used Set attributes with four different options instead of three. For technical reasons, this problem is more tractable than the original Set problem. Not long after this, two mathematicians, \u003Ca href=\u0022http:\/\/www.math.wisc.edu\/%7Eellenber\/\u0022 target=\u0022_blank\u0022 title=\u0022Jordan Ellenberg\u0022\u003EJordan Ellenberg\u003C\/a\u003E, and \u003Ca href=\u0022http:\/\/homepage.tudelft.nl\/64a8q\/\u0022 target=\u0022_blank\u0022 title=\u0022Dion Gijswijt\u0022\u003EDion Gijswijt\u003C\/a\u003E, each independently posted papers showing how to modify the argument to polish off the original cap set problem, and\u0026nbsp;\u003Ca href=\u0022https:\/\/arxiv.org\/pdf\/1605.09223v1.pdf\u0022 target=\u0022_blank\u0022 title=\u0022a joint paper combining their results\u0022\u003Ea joint paper combining their results\u003C\/a\u003E.\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003EThe work of Ernie Croot and his collaborators is continuing to make huge waves, with many interesting consequences now unfolding. Their work has already been \u003Ca href=\u0022http:\/\/arxiv.org\/abs\/1605.06702\u0022 target=\u0022_blank\u0022 title=\u0022applied to matrix multiplication\u0022\u003Eapplied to matrix multiplication\u003C\/a\u003E, \u003Ca href=\u0022http:\/\/arxiv.org\/abs\/1605.08416\u0022 target=\u0022_blank\u0022 title=\u0022tri-colored sum-free sets\u0022\u003Etri-colored sum-free sets\u003C\/a\u003E, and \u003Ca href=\u0022https:\/\/gilkalai.wordpress.com\/2016\/05\/17\/polymath-10-emergency-post-5-the-erdos-szemeredi-sunflower-conjecture-is-now-proven\/\u0022 target=\u0022_blank\u0022 title=\u0022the Erd\u00f6s-Szemer\u00e9di sunflower conjecture\u0022\u003Ethe Erd\u0026ouml;s-Szemer\u0026eacute;di sunflower conjecture\u003C\/a\u003E, which concerns sets that overlap in a sunflower pattern. Their work was also \u003Ca href=\u0022https:\/\/www.quantamagazine.org\/20160531-set-proof-stuns-mathematicians\/\u0022 target=\u0022_blank\u0022 title=\u0022featured on Quanta Magazine\u0022\u003Efeatured in an article in Quanta Magazine\u003C\/a\u003E, which gives a more detailed history of this recent breakthrough.\u003C\/p\u003E\r\n","summary":null,"format":"limited_html"}],"field_subtitle":"","field_summary":"","field_summary_sentence":[{"value":"Mathematicians have solved a problem about the pattern-matching card game, Set, that predates the game itself."}],"uid":"34469","created_gmt":"2017-04-06 13:47:16","changed_gmt":"2017-04-06 13:47:16","author":"nmcleish3","boilerplate_text":"","field_publication":"","field_article_url":"","dateline":{"date":"2016-06-05T00:00:00-04:00","iso_date":"2016-06-05T00:00:00-04:00","tz":"America\/New_York"},"extras":[],"hg_media":{"589874":{"id":"589874","type":"image","title":"Ernie Croot","body":null,"created":"1491486311","gmt_created":"2017-04-06 13:45:11","changed":"1491486311","gmt_changed":"2017-04-06 13:45:11","alt":"","file":{"fid":"224723","name":"ErnieCroot.jpg","image_path":"\/sites\/default\/files\/images\/ErnieCroot.jpg","image_full_path":"http:\/\/www.tlwarc.hg.gatech.edu\/\/sites\/default\/files\/images\/ErnieCroot.jpg","mime":"image\/jpeg","size":31169,"path_740":"http:\/\/www.tlwarc.hg.gatech.edu\/sites\/default\/files\/styles\/740xx_scale\/public\/images\/ErnieCroot.jpg?itok=pW5ZBbPp"}}},"media_ids":["589874"],"groups":[{"id":"1279","name":"School of Mathematics"}],"categories":[],"keywords":[{"id":"173647","name":"_for_math_site_"}],"core_research_areas":[],"news_room_topics":[],"event_categories":[],"invited_audience":[],"affiliations":[],"classification":[],"areas_of_expertise":[],"news_and_recent_appearances":[],"phone":[],"contact":[],"email":[],"slides":[],"orientation":[],"userdata":""}}}