{"id":196,"date":"2015-05-24T18:17:24","date_gmt":"2015-05-24T23:17:24","guid":{"rendered":"http:\/\/blogs.ams.org\/beyondreviews\/?p=196"},"modified":"2015-05-26T21:15:21","modified_gmt":"2015-05-27T02:15:21","slug":"john-nash","status":"publish","type":"post","link":"https:\/\/blogs.ams.org\/beyondreviews\/2015\/05\/24\/john-nash\/","title":{"rendered":"John Nash"},"content":{"rendered":"<p>As many of you may have heard by now, John Nash died in a car crash while traveling home from Norway where he had just received the Abel Prize. \u00a0Here is the <a href=\"http:\/\/www.nytimes.com\/2015\/05\/25\/science\/john-nash-a-beautiful-mind-subject-and-nobel-winner-dies-at-86.html\">obituary in the\u00a0<em>New York Times<\/em><\/a>. \u00a0 Most people are aware of Nash&#8217;s work on non-cooperative games, for which he won the Nobel Prize:<\/p>\n<ul>\n<li><a href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=43432\"><strong>MR0043432<\/strong> <strong>(13,261g)<\/strong><\/a>\u00a0<a href=\"http:\/\/www.ams.org\/mathscinet\/search\/author.html?mrauthid=366251\">Nash, John<\/a> <span class=\"title\">Non-cooperative games.<\/span> <a href=\"http:\/\/www.ams.org\/mathscinet\/search\/journaldoc.html?cn=Ann_of_Math_2\"><em>Ann. of Math. (2)<\/em><\/a> <strong>54, <\/strong>(1951). 286\u2013295<\/li>\n<li><a href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=35977\"><strong>MR0035977<\/strong> <strong>(12,40a)<\/strong><\/a>\u00a0<a href=\"http:\/\/www.ams.org\/mathscinet\/search\/author.html?mrauthid=366251\">Nash, John F., Jr.<\/a> <span class=\"title\">The bargaining problem.<\/span> <a href=\"http:\/\/www.ams.org\/mathscinet\/search\/journaldoc.html?cn=Econometrica\"><em>Econometrica<\/em><\/a> <strong>18, <\/strong>(1950). 155\u2013162.<\/li>\n<\/ul>\n<p>Within mathematics, he is equally\u00a0known for <!--more-->\u00a0his work on differential equations, such as<\/p>\n<ul>\n<li><a href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=100158\"><strong>MR0100158<\/strong> <strong>(20 #6592)<\/strong><\/a>\u00a0<a href=\"http:\/\/www.ams.org\/mathscinet\/search\/author.html?mrauthid=366251\">Nash, J.<\/a> <span class=\"title\">Continuity of solutions of parabolic and elliptic equations.<\/span> <a href=\"http:\/\/www.ams.org\/mathscinet\/search\/journaldoc.html?cn=Amer_J_Math\"><em>Amer. J. Math.<\/em><\/a> <strong>80 <\/strong>1958 931\u2013954,<\/li>\n<\/ul>\n<p>his work on the embedding problem<\/p>\n<ul>\n<li><a href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=75639\"><strong>MR0075639<\/strong> <strong>(17,782b)<\/strong><\/a>\u00a0<a href=\"http:\/\/www.ams.org\/mathscinet\/search\/author.html?mrauthid=366251\">Nash, John<\/a> <span class=\"title\">The imbedding problem for Riemannian manifolds.<\/span> <a href=\"http:\/\/www.ams.org\/mathscinet\/search\/journaldoc.html?cn=Ann_of_Math_2\"><em>Ann. of Math. (2)<\/em><\/a> <strong>63 <\/strong>(1956), 20\u201363<\/li>\n<li><a href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=65993\"><strong>MR0065993<\/strong> <strong>(16,515e)<\/strong><\/a>\u00a0<a href=\"http:\/\/www.ams.org\/mathscinet\/search\/author.html?mrauthid=366251\">Nash, John<\/a> <span class=\"title\"><span id=\"MathJax-Element-2-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-4\" class=\"math\"><span id=\"MathJax-Span-5\" class=\"mrow\"><span id=\"MathJax-Span-6\" class=\"msubsup\"><span id=\"MathJax-Span-7\" class=\"mi\">C<\/span><span id=\"MathJax-Span-8\" class=\"mn\">1<\/span><\/span><\/span><\/span><\/span> isometric imbeddings.<\/span> <a href=\"http:\/\/www.ams.org\/mathscinet\/search\/journaldoc.html?cn=Ann_of_Math_2\"><em>Ann. of Math. (2)<\/em><\/a> <strong>60, <\/strong>(1954). 383\u2013396,<\/li>\n<\/ul>\n<p>and his work on real algebraic manifolds<\/p>\n<ul>\n<li><a href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=50928\"><strong>MR0050928<\/strong> <strong>(14,403b)<\/strong><\/a>\u00a0<a href=\"http:\/\/www.ams.org\/mathscinet\/search\/author.html?mrauthid=366251\">Nash, John<\/a> <span class=\"title\">Real algebraic manifolds.<\/span> <a href=\"http:\/\/www.ams.org\/mathscinet\/search\/journaldoc.html?cn=Ann_of_Math_2\"><em>Ann. of Math. (2)<\/em><\/a> <strong>56, <\/strong>(1952). 405\u2013421.<\/li>\n<\/ul>\n<p>The embedding theorem depended heavily on what is now known as the Nash-Moser Inverse Function Theorem. \u00a0Richard Hamilton gave <a href=\"http:\/\/www.ams.org\/journals\/bull\/1982-07-01\/S0273-0979-1982-15004-2\/\">an excellent presentation of that work<\/a> in the\u00a0<em>Bulletin of the American Mathematical Society.<\/em><\/p>\n<p><strong>Note: \u00a0<\/strong>In order to access the reviews, you need to have a subscription to MathSciNet. \u00a0If your institution ha a subscription and you want to access MathSciNet from home or on the road, you can pair your laptop, tablet or smartphone with that subscription. \u00a0Instructions for how to do that can be found <a href=\"http:\/\/www.ams.org\/pairing\/pair_my_device.html\">here<\/a>.<\/p>\n<div style=\"margin-top: 0px; margin-bottom: 0px;\" class=\"sharethis-inline-share-buttons\" ><\/div>","protected":false},"excerpt":{"rendered":"<p>As many of you may have heard by now, John Nash died in a car crash while traveling home from Norway where he had just received the Abel Prize. \u00a0Here is the obituary in the\u00a0New York Times. \u00a0 Most people &hellip; <a href=\"https:\/\/blogs.ams.org\/beyondreviews\/2015\/05\/24\/john-nash\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n<div style=\"margin-top: 0px; margin-bottom: 0px;\" class=\"sharethis-inline-share-buttons\" data-url=https:\/\/blogs.ams.org\/beyondreviews\/2015\/05\/24\/john-nash\/><\/div>\n","protected":false},"author":86,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[8],"tags":[],"class_list":["post-196","post","type-post","status-publish","format-standard","hentry","category-mathematicians"],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p6C2KK-3a","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/blogs.ams.org\/beyondreviews\/wp-json\/wp\/v2\/posts\/196","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ams.org\/beyondreviews\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ams.org\/beyondreviews\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ams.org\/beyondreviews\/wp-json\/wp\/v2\/users\/86"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ams.org\/beyondreviews\/wp-json\/wp\/v2\/comments?post=196"}],"version-history":[{"count":7,"href":"https:\/\/blogs.ams.org\/beyondreviews\/wp-json\/wp\/v2\/posts\/196\/revisions"}],"predecessor-version":[{"id":203,"href":"https:\/\/blogs.ams.org\/beyondreviews\/wp-json\/wp\/v2\/posts\/196\/revisions\/203"}],"wp:attachment":[{"href":"https:\/\/blogs.ams.org\/beyondreviews\/wp-json\/wp\/v2\/media?parent=196"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ams.org\/beyondreviews\/wp-json\/wp\/v2\/categories?post=196"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ams.org\/beyondreviews\/wp-json\/wp\/v2\/tags?post=196"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}