5 \u6708 20 \u65e5\uff0cOpenAI \u5ba3\u5e03\u5176\u5185\u90e8\u63a8\u7406\u6a21\u578b\u72ec\u7acb\u8bc1\u4f2a\u4e86 Paul Erd\u0151s\uff08\u4fdd\u7f57\u00b7\u57c3\u5c14\u5fb7\u4ec0\uff091946 \u5e74\u63d0\u51fa\u7684\u5355\u4f4d\u8ddd\u79bb\u731c\u60f3\uff08Unit Distance Conjecture\uff09\u3002\u8fd9\u4e2a\u56f0\u6270\u6570\u5b66\u5bb6 80 \u5e74\u7684\u79bb\u6563\u51e0\u4f55\u95ee\u9898\uff0c\u88ab\u4e00\u4e2a\u901a\u7528 AI \u6a21\u578b\u7528\u4ee3\u6570\u6570\u8bba\u7684\u65b9\u6cd5\u89e3\u51b3\u4e86\u3002<\/p>\n
\u83f2\u5c14\u5179\u5956\u5f97\u4e3b Tim Gowers \u5728\u914d\u5957\u8bba\u6587\u4e2d\u79f0\u4e4b\u4e3a”AI \u6570\u5b66\u7684\u91cc\u7a0b\u7891”\u3002\u666e\u6797\u65af\u987f\u6570\u8bba\u5b66\u5bb6 Arul Shankar \u7684\u8bc4\u4ef7\u66f4\u76f4\u63a5\uff1a”AI has gone beyond being mere assistants to human mathematicians and generating and executing original ideas”\uff08AI \u5df2\u7ecf\u8d85\u8d8a\u4e86\u4eba\u7c7b\u6570\u5b66\u5bb6\u7684\u52a9\u624b\u89d2\u8272\uff0c\u80fd\u591f\u81ea\u4e3b\u751f\u6210\u5e76\u6267\u884c\u539f\u521b\u60f3\u6cd5\uff09\u3002<\/p>\n
\u8fd9\u4e0d\u662f AI \u5e2e\u4eba\u7c7b\u505a\u8ba1\u7b97\u3002\u8fd9\u662f AI \u81ea\u5df1\u60f3\u51fa\u4e86\u4e00\u4e2a\u4eba\u7c7b\u6ca1\u60f3\u5230\u7684\u65b9\u6cd5\u3002<\/p>\n
\u8fd9\u4e2a\u731c\u60f3\u5230\u5e95\u8bf4\u4e86\u4ec0\u4e48<\/p>\n
\u95ee\u9898\u672c\u8eab\u5f88\u7b80\u5355\uff1a\u5728\u5e73\u9762\u4e0a\u653e n \u4e2a\u70b9\uff0c\u6700\u591a\u80fd\u6709\u591a\u5c11\u5bf9\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u6070\u597d\u7b49\u4e8e 1\uff1f<\/p>\n
Erd\u0151s \u5728 1946 \u5e74\u7ed9\u51fa\u4e86\u4e00\u4e2a\u57fa\u4e8e\u65b9\u683c\u7f51\u683c\u7684\u6784\u9020\uff0c\u5f97\u5230\u7684\u5355\u4f4d\u8ddd\u79bb\u5bf9\u6570\u91cf\u5927\u7ea6\u662f n \u7684 1+C\/loglog(n) \u6b21\u65b9\u3002\u7531\u4e8e loglog(n) \u589e\u957f\u6781\u6162\uff0c\u6570\u5b66\u5bb6\u4eec\u666e\u904d\u731c\u6d4b\uff1a\u5355\u4f4d\u8ddd\u79bb\u5bf9\u7684\u6570\u91cf\u4e0d\u4f1a\u4ee5\u56fa\u5b9a\u901f\u7387\u8d85\u8fc7 n\u2014\u2014\u4e5f\u5c31\u662f\u8bf4\uff0c\u6307\u6570\u90e8\u5206\u6700\u7ec8\u4f1a\u8d8b\u8fd1\u4e8e 0\u3002<\/p>\n
80 \u5e74\u6765\u6ca1\u4eba\u80fd\u6253\u7834\u8fd9\u4e2a\u4e0a\u754c\u3002\u76f4\u5230\u4e0a\u5468\u3002<\/p>\n
AI \u505a\u4e86\u4ec0\u4e48<\/p>\n
OpenAI \u7684\u6a21\u578b\u6784\u9020\u4e86\u4e00\u7c7b\u65b0\u7684\u70b9\u914d\u7f6e\uff0c\u8bc1\u660e\u5bf9\u65e0\u7a77\u591a\u4e2a n\uff0c\u5355\u4f4d\u8ddd\u79bb\u5bf9\u7684\u6570\u91cf\u81f3\u5c11\u662f n \u7684 1+\u03b4 \u6b21\u65b9\uff08\u03b4 \u662f\u4e00\u4e2a\u56fa\u5b9a\u7684\u6b63\u6570\uff09\u3002\u8fd9\u76f4\u63a5\u63a8\u7ffb\u4e86”\u6307\u6570\u8d8b\u8fd1\u4e8e 0″\u7684\u731c\u60f3\u3002<\/p>\n
\u5173\u952e\u5728\u4e8e\u65b9\u6cd5\uff1a\u4f20\u7edf\u6784\u9020\u7528\u7684\u662f\u9ad8\u65af\u6574\u6570\uff08Gaussian integers\uff0c\u5f62\u5982 a+bi \u7684\u590d\u6570\uff09\uff0cAI \u6a21\u578b\u7528\u4e86\u66f4\u590d\u6742\u7684\u4ee3\u6570\u6570\u57df\uff08algebraic number fields\uff09\uff0c\u6316\u6398\u51fa\u66f4\u4e30\u5bcc\u7684\u5bf9\u79f0\u6027\u3002\u5b83\u8fd8\u7528\u5230\u4e86 Golod-Shafarevich \u7406\u8bba\u6765\u8bc1\u660e\u6240\u9700\u7684\u65e0\u7a77\u7c7b\u57df\u5854\uff08infinite class field towers\uff09\u786e\u5b9e\u5b58\u5728\u3002<\/p>\n
\u8fd9\u4e9b\u5de5\u5177\u6765\u81ea\u4ee3\u6570\u6570\u8bba\uff0c\u4e0d\u662f\u51e0\u4f55\u5b66\u5bb6\u7684\u5e38\u89c4\u6b66\u5668\u5e93\u3002AI \u505a\u4e86\u4e00\u4ef6\u4eba\u7c7b\u4e13\u5bb6\u6ca1\u6709\u4f18\u5148\u8003\u8651\u7684\u4e8b\uff1a\u628a\u4e24\u4e2a\u770b\u4f3c\u65e0\u5173\u7684\u6570\u5b66\u9886\u57df\u8fde\u63a5\u8d77\u6765\u3002<\/p>\n
\u666e\u6797\u65af\u987f\u6570\u5b66\u5bb6 Will Sawin \u540e\u6765\u6539\u8fdb\u4e86\u8fd9\u4e2a\u8bc1\u660e\uff0c\u628a \u03b4 \u7684\u5177\u4f53\u503c\u786e\u5b9a\u4e3a 0.014\u3002<\/p>\n
\u4e3a\u4ec0\u4e48\u8fd9\u4ef6\u4e8b\u91cd\u8981<\/p>\n
\u4e0d\u662f\u56e0\u4e3a\u8fd9\u4e2a\u731c\u60f3\u672c\u8eab\u6709\u591a\u5927\u7684\u5e94\u7528\u4ef7\u503c\u3002\u800c\u662f\u56e0\u4e3a\u5b83\u8bc1\u660e\u4e86\u4e00\u4ef6\u4e8b\uff1aAI \u80fd\u591f\u72ec\u7acb\u4ea7\u751f\u539f\u521b\u7684\u6570\u5b66\u601d\u60f3\u3002<\/p>\n
\u4e4b\u524d AI \u5728\u6570\u5b66\u9886\u57df\u7684\u89d2\u8272\u4e00\u76f4\u662f”\u52a9\u624b”\u2014\u2014\u5e2e\u4eba\u7c7b\u9a8c\u8bc1\u8bc1\u660e\u3001\u641c\u7d22\u53cd\u4f8b\u3001\u505a\u7b26\u53f7\u8ba1\u7b97\u3002\u8fd9\u6b21\u4e0d\u4e00\u6837\u3002\u6a21\u578b\u662f\u5728\u6ca1\u6709\u4eba\u7c7b\u6307\u5bfc\u7684\u60c5\u51b5\u4e0b\uff0c\u81ea\u4e3b\u9009\u62e9\u4e86\u4ee3\u6570\u6570\u8bba\u4f5c\u4e3a\u653b\u51fb\u8def\u5f84\uff0c\u81ea\u4e3b\u6784\u9020\u4e86\u53cd\u4f8b\uff0c\u81ea\u4e3b\u5b8c\u6210\u4e86\u8bc1\u660e\u3002<\/p>\n
\u666e\u6797\u65af\u987f\u7ec4\u5408\u6570\u5b66\u5bb6 Noga Alon \u8bf4\uff0c\u5355\u4f4d\u8ddd\u79bb\u95ee\u9898\u662f Erd\u0151s \u6700\u559c\u7231\u7684\u95ee\u9898\u4e4b\u4e00\uff0c\u8fd9\u4e2a\u7ed3\u679c\u662f”\u89e3\u51b3\u957f\u671f\u672a\u89e3\u95ee\u9898\u7684\u6770\u51fa\u6210\u5c31”\u3002<\/p>\n
\u5bf9\u666e\u901a\u4eba\u610f\u5473\u7740\u4ec0\u4e48<\/p>\n
\u5982\u679c AI \u80fd\u5728\u7eaf\u6570\u5b66\u9886\u57df\u505a\u51fa\u539f\u521b\u53d1\u73b0\uff0c\u90a3\u5b83\u5728\u5de5\u7a0b\u3001\u533b\u5b66\u3001\u6750\u6599\u79d1\u5b66\u7b49\u5e94\u7528\u9886\u57df\u7684\u6f5c\u529b\u5c31\u66f4\u4e0d\u7528\u8bf4\u4e86\u3002\u8fd9\u4e9b\u9886\u57df\u7684\u95ee\u9898\u901a\u5e38\u6bd4\u7eaf\u6570\u5b66\u66f4”\u810f”\u2014\u2014\u7ea6\u675f\u66f4\u591a\u3001\u6570\u636e\u66f4\u6742\u3001\u8fb9\u754c\u66f4\u6a21\u7cca\u2014\u2014\u4f46\u4e5f\u610f\u5473\u7740 AI \u7684\u8de8\u9886\u57df\u8fde\u63a5\u80fd\u529b\u6709\u66f4\u5927\u7684\u53d1\u6325\u7a7a\u95f4\u3002<\/p>\n
\u5bf9\u4e8e\u5f00\u53d1\u8005\u6765\u8bf4\uff0cOpenAI \u7684\u63a8\u7406\u6a21\u578b\uff08reasoning models\uff09\u6b63\u5728\u53d8\u5f97\u8d8a\u6765\u8d8a\u5f3a\u3002\u5982\u679c\u4f60\u5728\u505a\u4efb\u4f55\u9700\u8981\u590d\u6742\u63a8\u7406\u7684\u5e94\u7528\u2014\u2014\u4ee3\u7801\u5ba1\u67e5\u3001\u67b6\u6784\u8bbe\u8ba1\u3001\u6570\u636e\u5206\u6790\u2014\u2014\u8fd9\u4e9b\u6a21\u578b\u7684\u80fd\u529b\u63d0\u5347\u76f4\u63a5\u5f71\u54cd\u4f60\u7684\u5de5\u4f5c\u8d28\u91cf\u3002<\/p>\n
\u6211\u81ea\u5df1\u6d4b\u8bd5\u63a8\u7406\u7c7b\u4efb\u52a1\u65f6\u7528\u7684\u662f aifuel.cc\uff0c\u4e0a\u9762 GPT-5 \u7cfb\u5217\u548c GPT-4o \u90fd\u80fd\u8c03\uff0c\u8fd8\u6709 DeepSeek \u7684\u63a8\u7406\u6a21\u578b\u53ef\u4ee5\u5bf9\u6bd4\u3002\u5982\u679c\u60f3\u767d\u5ad6\u90a3\u4e9b\u6ee1\u8840\u6a21\u578b\uff0c\u5c31\u53bb\u67d0\u9c7c\u627e\u4e00\u4e2a\u7a33\u5b9a\u7684\u4e2d\u8f6c\u7ad9\uff0c\u50cf\u6211\u5728\u7528\u7684\u8fd9\u4e2a aifuel.cc\uff0c\u521a\u6ce8\u518c\u65f6\u9001\u4e86 100 \u5200\u7684\u989d\u5ea6\uff0c\u529e\u5b8c\u65b0\u624b\u4efb\u52a1\u518d\u9001 50\uff0c\u52a0\u4e0a\u6bcf\u65e5\u7b7e\u5230\u9886\u7684\u989d\u5ea6\uff0c\u6ee1\u6253\u6ee1\u7b97\u65e5\u5e38\u4f7f\u7528\u5b8c\u5168\u591f\u4e86\u3002<\/p>\n
\u51b7\u601d\u8003<\/p>\n
\u4e0d\u8fc7\u4e5f\u522b\u592a\u5174\u594b\u3002\u8fd9\u4e2a\u8bc1\u660e\u662f OpenAI \u5185\u90e8\u6a21\u578b\u505a\u7684\uff0c\u4e0d\u662f\u516c\u5f00\u53ef\u7528\u7684 GPT-4o \u6216 o3\u3002OpenAI \u6ca1\u6709\u516c\u5e03\u5177\u4f53\u662f\u54ea\u4e2a\u6a21\u578b\uff0c\u53ea\u8bf4\u662f”\u901a\u7528\u63a8\u7406\u6a21\u578b”\u3002\u8fd9\u610f\u5473\u7740\u666e\u901a\u7528\u6237\u6682\u65f6\u8fd8\u7528\u4e0d\u5230\u8fd9\u4e2a\u7ea7\u522b\u7684\u63a8\u7406\u80fd\u529b\u3002<\/p>\n
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\u4f46\u65b9\u5411\u662f\u6e05\u6670\u7684\uff1aAI \u6b63\u5728\u4ece”\u5de5\u5177”\u53d8\u6210”\u7814\u7a76\u8005”\u3002\u8fd9\u4e2a\u8f6c\u53d8\u7684\u901f\u5ea6\uff0c\u53ef\u80fd\u6bd4\u5927\u591a\u6570\u4eba\u9884\u671f\u7684\u8981\u5feb\u3002<\/p>\n
\u4e0b\u4e00\u7bc7\u804a\u804a AI \u7f16\u7a0b\u5de5\u5177\u56db\u5f3a\uff08Claude Code \/ Cursor \/ Copilot \/ Codex\uff09\u7684\u5b9e\u9645\u4f7f\u7528\u4f53\u9a8c\u548c\u7ec4\u5408\u7b56\u7565\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"
OpenAI \u7684\u63a8\u7406\u6a21\u578b\u72ec\u7acb\u8bc1\u4f2a\u4e86 Paul Erd\u0151s 1946 \u5e74\u63d0\u51fa\u7684\u5355\u4f4d\u8ddd\u79bb\u731c\u60f3\u3002\u83f2\u5c14\u5179\u5956\u5f97\u4e3b\u79f0\u4e4b\u4e3a”AI \u6570\u5b66\u7684\u91cc\u7a0b\u7891”\u3002<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-24","post","type-post","status-publish","format-standard","hentry","category-ai-tools"],"_links":{"self":[{"href":"https:\/\/aifuel.cc\/blog\/wp-json\/wp\/v2\/posts\/24","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/aifuel.cc\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/aifuel.cc\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/aifuel.cc\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/aifuel.cc\/blog\/wp-json\/wp\/v2\/comments?post=24"}],"version-history":[{"count":0,"href":"https:\/\/aifuel.cc\/blog\/wp-json\/wp\/v2\/posts\/24\/revisions"}],"wp:attachment":[{"href":"https:\/\/aifuel.cc\/blog\/wp-json\/wp\/v2\/media?parent=24"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/aifuel.cc\/blog\/wp-json\/wp\/v2\/categories?post=24"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/aifuel.cc\/blog\/wp-json\/wp\/v2\/tags?post=24"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}