{"id":246147,"date":"2026-10-29T11:13:18","date_gmt":"2026-10-29T16:13:18","guid":{"rendered":"https:\/\/lifeboat.com\/blog\/2026\/10\/mathematical-puzzle-from-1904-takes-physical-form-in-gold-studded-helium-droplets"},"modified":"2026-10-29T11:13:18","modified_gmt":"2026-10-29T16:13:18","slug":"mathematical-puzzle-from-1904-takes-physical-form-in-gold-studded-helium-droplets","status":"publish","type":"post","link":"https:\/\/lifeboat.com\/blog\/2026\/10\/mathematical-puzzle-from-1904-takes-physical-form-in-gold-studded-helium-droplets","title":{"rendered":"Mathematical puzzle from 1904 takes physical form in gold-studded helium droplets"},"content":{"rendered":"\n<p>When identical charges repel each other but are confined to the surface of a sphere, they seek the arrangement with the lowest possible energy. The idea is simple, but the problem gets harder to solve with every charge added. The so-called Thomson problem dates back to the \u201cplum-pudding\u201d model of the atom, which Nobel laureate Joseph J. Thomson proposed in 1904. The atomic model has long been superseded, but the mathematical problem has endured.<\/p>\n<p>In 1998, mathematician Stephen Smale listed it as Problem No. 7 among his 18 major mathematical challenges for the 21st century. Exact solutions still exist only for a few small systems. The question also matters well beyond mathematics\u2014for example, for the structure of viruses, fullerenes and colloidal shells.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>When identical charges repel each other but are confined to the surface of a sphere, they seek the arrangement with the lowest possible energy. The idea is simple, but the problem gets harder to solve with every charge added. The so-called Thomson problem dates back to the \u201cplum-pudding\u201d model of the atom, which Nobel laureate [\u2026]<\/p>\n","protected":false},"author":396,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2229,48],"tags":[],"class_list":["post-246147","post","type-post","status-publish","format-standard","hentry","category-mathematics","category-particle-physics"],"_links":{"self":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/246147","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\/396"}],"replies":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/comments?post=246147"}],"version-history":[{"count":0,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/246147\/revisions"}],"wp:attachment":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/media?parent=246147"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/categories?post=246147"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/tags?post=246147"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}