{"id":649,"date":"2009-03-20T17:54:58","date_gmt":"2009-03-20T17:54:58","guid":{"rendered":"http:\/\/spinor.info\/weblog\/?p=649"},"modified":"2009-03-20T17:54:58","modified_gmt":"2009-03-20T17:54:58","slug":"mathematical-mysteries","status":"publish","type":"post","link":"https:\/\/spinor.info\/weblog\/?p=649","title":{"rendered":"Mathematical mysteries"},"content":{"rendered":"<p>In the Futurama movie, The Beast with a Billion Backs, one scene features a blackboard with two different proofs of the <a href=\"http:\/\/en.wikipedia.org\/wiki\/Goldbach%27s_conjecture\">Goldbach conjecture<\/a>. The Goldback conjecture is one of the oldest unsolved problems in mathematics. One of those problems, like Fermat&#8217;s last theorem or the 4-color problem of maps that is deceivingly easy to state and fiendishly hard to prove: that every even number greater than 4 can be expressed as the sum of two primes.<\/p>\n<p>Just how intriguing this problem is, it&#8217;s well illustrated by the following plot that shows the number of ways an even number between 4 and 1 million can be split into a sum of two primes:<\/p>\n<div id=\"attachment_650\" style=\"width: 441px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/en.wikipedia.org\/wiki\/Goldbach%27s_conjecture\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-650\" class=\"size-full wp-image-650\" title=\"Golbach to 1000000\" src=\"http:\/\/spinor.info\/weblog\/wp-content\/uploads\/2009\/03\/goldbach-1000000.gif\" alt=\"Golbach to 1000000\" width=\"431\" height=\"302\" srcset=\"https:\/\/spinor.info\/weblog\/wp-content\/uploads\/2009\/03\/goldbach-1000000.gif 431w, https:\/\/spinor.info\/weblog\/wp-content\/uploads\/2009\/03\/goldbach-1000000-300x210.gif 300w\" sizes=\"(max-width: 431px) 100vw, 431px\" \/><\/a><p id=\"caption-attachment-650\" class=\"wp-caption-text\">Golbach partitioning to 1000000<\/p><\/div>\n<p>This plot, taken from Wikipedia, clearly shows that the results cluster along curves (asymptotes? attractors?) that follow some kind of a power law with an exponent between ~0.68 and ~0.77, and there may also be some fractal splitting involved, too. This plot is known as <a href=\"http:\/\/en.wikipedia.org\/wiki\/Goldbach%27s_comet\">Goldbach&#8217;s comet<\/a>. All I have to do is look at it to understand why many people find number theory endlessly fascinating.<\/p>\n<fb:like href='https:\/\/spinor.info\/weblog\/?p=649' send='false' layout='button_count' show_faces='true' width='450' height='65' action='like' colorscheme='light' font='lucida grande'><\/fb:like>","protected":false},"excerpt":{"rendered":"<p>In the Futurama movie, The Beast with a Billion Backs, one scene features a blackboard with two different proofs of the Goldbach conjecture. The Goldback conjecture is one of the oldest unsolved problems in mathematics. One of those problems, like Fermat&#8217;s last theorem or the 4-color problem of maps that is deceivingly easy to state <a href='https:\/\/spinor.info\/weblog\/?p=649' class='excerpt-more'>[&#8230;]<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[30],"tags":[],"class_list":["post-649","post","type-post","status-publish","format-standard","hentry","category-mathematics","category-30-id","post-seq-1","post-parity-odd","meta-position-corners","fix"],"_links":{"self":[{"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=\/wp\/v2\/posts\/649","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=649"}],"version-history":[{"count":1,"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=\/wp\/v2\/posts\/649\/revisions"}],"predecessor-version":[{"id":651,"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=\/wp\/v2\/posts\/649\/revisions\/651"}],"wp:attachment":[{"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=649"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=649"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=649"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}