{"id":3860,"date":"2018-10-01T21:11:44","date_gmt":"2018-10-02T01:11:44","guid":{"rendered":"http:\/\/blogs.ams.org\/blogonmathblogs\/?p=3860"},"modified":"2019-01-10T19:33:53","modified_gmt":"2019-01-11T00:33:53","slug":"on-michael-atiyah-and-the-riemann-hypothesis","status":"publish","type":"post","link":"https:\/\/blogs.ams.org\/blogonmathblogs\/2018\/10\/01\/on-michael-atiyah-and-the-riemann-hypothesis\/","title":{"rendered":"On Michael Atiyah and the Riemann Hypothesis"},"content":{"rendered":"
\"Riemann\"<\/a>

Riemann has been back in the news lately, thanks to an announcement that his nearly 160 year old hypothesis might be solved.
Public domain image courtesy of Wikimedia CC.<\/p><\/div>\n

At the 2018 Heidelberg Laureate Forum (HLF)<\/a>, Sir Michael Atiyah gave a\u00a0lecture<\/a>\u00a0in which he claimed to have found a proof for the Riemann hypothesis. If Atiyah’s proof holds up, then the nearly 160 year problem concerning the distribution of primes will finally have a solution.\u00a0 It’s on the\u00a0Clay Mathematics Institute’s list of seven Millennium Prize Problems<\/a> and just one of those — the\u00a0Poincar\u00e9 Conjecture<\/a> — is listed as solved on the institute’s website. However, the $1 million prize for a proof of the Riemann hypothesis is yet to be awarded, and some folks doubt that the long-open problem is finally solved.<\/p>\n

It’s unsurprising that the world is watching Atiyah — and waiting to hear the verdict about the proof he proposed. Atiyah received a\u00a0Fields Medal in 1966. In 2004, he and\u00a0Isadore Singer\u00a0were jointly awarded the Abel Prize for their discovery and proof<\/a> of the Atiyah-Singer index theorem. Yet many other supposed proofs for the Riemann hypothesis have been proposed, only to fall apart under further scrutiny.<\/p>\n

The Clay Mathematics Institute’s “Official Problem Description”<\/a> for the Riemann hypothesis is 11 pages long (with nearly two full pages of references), while Atiyah’s current write-up<\/a> of the proof is five pages long. “Atiyah attributes much of the theoretical work that underpins the proof to a paper of his own that has been submitted to the\u00a0Proceedings of the Royal Society A,”\u00a0<\/cite>Frankie Schembri wrote<\/a> for Science. “That paper has yet to be published,” she added. In fact, Atiyah’s list of references includes just three works: the aforementioned unpublished paper, his 2018 Abel lecture at the ICM in Rio de Janeiro and\u00a0Friedrich\u00a0Hirzebruch’s 1966\u00a0Topological Methods in Geometry<\/em>.<\/p>\n

News of Atiyah’s claim has reached far and wide since his announcement. Articles about the development appeared in Science News<\/a>, Gizmodo<\/a>, Popular Science<\/a>,\u00a0NBCNews.com<\/a>,\u00a0the Irish Times<\/a> and more. Bloggers also covered the announcement, including Katie Steckles and\u00a0Christian Lawson-Perfect for the Aperiodical<\/a>, John D. Cook for his consulting blog<\/a>, as well as Dick Lipton and Ken Regan for\u00a0G\u00f6del\u2019s Lost Letter and P=NP<\/a>. <\/span><\/p>\n

John Baez also wrote a lengthy thread<\/a> about Atiyah’s claimed proof on Twitter, starting on September 23 (the day before Atiyah’s lecture at the HLF). He wrote “I bet that Atiyah’s claimed proof…will not convince experts.\u00a0In 2017 he claimed to have a 12-page proof of the Feit-Thompson theorem, which usually takes 255 pages:\u00a0https:\/\/www.maths.ed.ac.uk\/~v1ranick\/atiyahtimes2017.pdf.\u00a0<\/span>He showed it to experts, and… silence.” What’s more, “In 2016 Atiyah put a paper on the arXiv claiming to have solved a famous problem in differential geometry. The argument was full of big holes: https:\/\/<\/span>mathoverflow.net\/questions\/2633<\/span>01\/what-is-the-current-understanding-regarding-complex-structures-on-the-6-sphere<\/span>\u00a0<\/span>\u2026<\/span><\/a> So, I’m not holding my breath this time. But of course I’d be happy to be wrong,” Baez added.<\/span><\/p>\n

Steven Strogatz<\/a> tweeted<\/a> “Uh oh. I have a bad feeling about this. Famed mathematician Michael Atiyah claims proof of Riemann hypothesis,” along with a link to the September 21 New Scientist article<\/a> about Atiyah’s claimed proof. When asked by Twitter user Jonathan Horrocks<\/a> “Why bad? I take anything Atiyah says very seriously,” Strogatz responded “I take him seriously too. It\u2019s the same bad feeling I have when a diver attempts an extremely difficult dive: afraid, yet hoping for success.”<\/p>\n

The skepticism surrounding the claimed proof doesn’t appear to faze Atiyah. “Nobody believes any proof of the Riemann hypothesis, let alone a proof by someone who\u2019s 90,” he said to Gilead Amit\u200b, author of the New Scientist article. “People say \u2018we know mathematicians do all their best work before they\u2019re 40,'” Atiyah said, adding “I\u2019m trying to show them that they\u2019re wrong. That I can do something when I\u2019m 90.\u201d<\/p>\n

Regardless of whether Atiyah’s proof holds, he has already done something phenomenal: reignited a worldwide conversation\u00a0about the Riemann hypothesis. That alone is something to celebrate.<\/p>\n

What do you think? Share your thoughts in the comments below or reach out to me on Twitter @writesRCrowell! As always, I’m also happy to hear ideas for future blog posts.<\/p>\n

<\/div>","protected":false},"excerpt":{"rendered":"

At the 2018 Heidelberg Laureate Forum (HLF), Sir Michael Atiyah gave a\u00a0lecture\u00a0in which he claimed to have found a proof for the Riemann hypothesis. If Atiyah’s proof holds up, then the nearly 160 year problem concerning the distribution of primes … Continue reading →<\/span><\/a><\/p>\n

<\/div>\n","protected":false},"author":143,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[688,86,1],"tags":[159,846,96,57,201,351,575,663],"class_list":["post-3860","post","type-post","status-publish","format-standard","hentry","category-current-events","category-people-in-math","category-uncategorized","tag-aperiodical","tag-godels-lost-letter-and-pnp","tag-heidelberg-laureate-forum","tag-john-baez","tag-john-d-cook","tag-michael-atiyah","tag-riemann-hypothesis","tag-steven-strogatz"],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p3tW3N-10g","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/posts\/3860","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/users\/143"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/comments?post=3860"}],"version-history":[{"count":19,"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/posts\/3860\/revisions"}],"predecessor-version":[{"id":4182,"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/posts\/3860\/revisions\/4182"}],"wp:attachment":[{"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/media?parent=3860"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/categories?post=3860"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/tags?post=3860"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}