{"id":230717,"date":"2026-02-06T17:05:29","date_gmt":"2026-02-06T23:05:29","guid":{"rendered":"https:\/\/lifeboat.com\/blog\/2026\/02\/long-sought-proof-tames-some-of-maths-unruliest-equations"},"modified":"2026-02-06T17:05:29","modified_gmt":"2026-02-06T23:05:29","slug":"long-sought-proof-tames-some-of-maths-unruliest-equations","status":"publish","type":"post","link":"https:\/\/lifeboat.com\/blog\/2026\/02\/long-sought-proof-tames-some-of-maths-unruliest-equations","title":{"rendered":"Long-Sought Proof Tames Some of Math\u2019s Unruliest Equations"},"content":{"rendered":"<p><a class=\"aligncenter blog-photo\" href=\"https:\/\/lifeboat.com\/blog.images\/long-sought-proof-tames-some-of-maths-unruliest-equations.jpg\"><\/a><\/p>\n<p>The trajectory of a storm, the evolution of stock prices, the spread of disease \u2014 mathematicians can describe any phenomenon that changes in time or space using what are known as partial differential equations. But there\u2019s a problem: These \u201cPDEs\u201d are often so complicated that it\u2019s impossible to solve them directly.<\/p>\n<p>Mathematicians instead rely on a clever workaround. They might not know how to compute the exact solution to a given equation, but they can try to show that this solution must be \u201cregular,\u201d or well-behaved in a certain sense \u2014 that its values won\u2019t suddenly jump in a physically impossible way, for instance. If a solution is regular, mathematicians can use a variety of tools to approximate it, gaining a better understanding of the phenomenon they want to study.<\/p>\n<p>But many of the PDEs that describe realistic situations have remained out of reach. Mathematicians haven\u2019t been able to show that their solutions are regular. In particular, some of these out-of-reach equations belong to a special class of PDEs that researchers spent a century developing a theory of \u2014 a theory that no one could get to work for this one subclass. They\u2019d hit a wall.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The trajectory of a storm, the evolution of stock prices, the spread of disease \u2014 mathematicians can describe any phenomenon that changes in time or space using what are known as partial differential equations. But there\u2019s a problem: These \u201cPDEs\u201d are often so complicated that it\u2019s impossible to solve them directly. Mathematicians instead rely on [\u2026]<\/p>\n","protected":false},"author":511,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11,385,41,2229],"tags":[],"class_list":["post-230717","post","type-post","status-publish","format-standard","hentry","category-biotech-medical","category-evolution","category-information-science","category-mathematics"],"_links":{"self":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/230717","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/users\/511"}],"replies":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/comments?post=230717"}],"version-history":[{"count":0,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/230717\/revisions"}],"wp:attachment":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/media?parent=230717"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/categories?post=230717"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/tags?post=230717"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}