{"id":192834,"date":"2015-10-23T00:00:00","date_gmt":"2015-10-23T21:47:10","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/what-are-the-prospects-for-automatic-theorem-proving\/"},"modified":"2016-07-15T15:26:50","modified_gmt":"2016-07-15T22:26:50","slug":"what-are-the-prospects-for-automatic-theorem-proving","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/what-are-the-prospects-for-automatic-theorem-proving\/","title":{"rendered":"What are the prospects for automatic theorem proving?"},"content":{"rendered":"<div class=\"asset-content\">\n<p>For several decades people have tried to write computer programs that can find proofs of mathematical statements. There have been some notable successes, such as a computer-discovered proof of the Robbins conjecture, which had previously been an open problem. But in general, progress has been disappointing: many problems that are well within the reach of an averagely good undergraduate are way beyond what the best programs can manage, and for a certain class of problems we seem to have reached an impasse.<\/p>\n<p>There are two main approaches to automatic theorem proving: the human-oriented approach, which tries to get a computer to mimic as closely as possible the way that a human would find a proof, and the machine-oriented approach, which aims to surpass what humans can do by exploiting the vastly superior speed and memory of computers. Currently, the machine-oriented approach is more fashionable, but I shall argue that to get beyond the impasse it will be essential to return to the human-oriented approach. I shall describe some preliminary work that I have done with Mohan Ganesalingam, and speculate about how one might go about programming a computer to solve problems that for the moment cannot be solved without human ingenuity.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>For several decades people have tried to write computer programs that can find proofs of mathematical statements. There have been some notable successes, such as a computer-discovered proof of the Robbins conjecture, which had previously been an open problem. But in general, progress has been disappointing: many problems that are well within the reach of [&hellip;]<\/p>\n","protected":false},"featured_media":199305,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr_hide_image_in_river":0,"footnotes":""},"research-area":[],"msr-video-type":[],"msr-locale":[268875],"msr-post-option":[],"msr-session-type":[],"msr-impact-theme":[],"msr-pillar":[],"msr-episode":[],"msr-research-theme":[],"class_list":["post-192834","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/VamEGCJozgU","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/192834","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-video"}],"version-history":[{"count":0,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/192834\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/199305"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=192834"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=192834"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=192834"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=192834"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=192834"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=192834"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=192834"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=192834"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=192834"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=192834"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}