{"id":23816,"date":"2024-12-30T11:07:22","date_gmt":"2024-12-30T03:07:22","guid":{"rendered":"https:\/\/aif.amtbbs.org\/?p=23816"},"modified":"2024-12-30T11:07:22","modified_gmt":"2024-12-30T03:07:22","slug":"%e8%ae%a9ai%e7%90%86%e8%a7%a3%e8%b4%b9%e9%a9%ac%e5%a4%a7%e5%ae%9a%e7%90%86%e7%9a%84%e8%af%81%e6%98%8e%ef%bc%8c%e4%b8%a4%e4%b8%aa%e6%9c%88%e8%bf%87%e5%8e%bb%e4%ba%86%ef%bc%8c%e8%bf%9b%e5%b1%95%e5%a6%82","status":"publish","type":"post","link":"https:\/\/aif.amtbbs.org\/index.php\/2024\/12\/30\/23816\/","title":{"rendered":"\u8ba9AI\u7406\u89e3\u8d39\u9a6c\u5927\u5b9a\u7406\u7684\u8bc1\u660e\uff0c\u4e24\u4e2a\u6708\u8fc7\u53bb\u4e86\uff0c\u8fdb\u5c55\u5982\u4f55\uff1f"},"content":{"rendered":"<div><img data-dominant-color=\"2876a4\" data-has-transparency=\"false\" style=\"--dominant-color: #2876a4;\" loading=\"lazy\" decoding=\"async\" class=\"not-transparent alignnone size-full wp-image-23818\" src=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2024\/12\/666b45aa-61a5-469f-95c5-f2ea9c13f5f3-300x167-1.png\" width=\"300\" height=\"167\" alt=\"\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2024\/12\/666b45aa-61a5-469f-95c5-f2ea9c13f5f3-300x167-1.png 300w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2024\/12\/666b45aa-61a5-469f-95c5-f2ea9c13f5f3-300x167-1-150x84.png 150w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/div>\n<div><\/div>\n<div class=\"article-desc\">\u8fd1\u65e5\uff0c\u4f26\u6566\u5e1d\u56fd\u5b66\u9662\u6570\u5b66\u6559\u6388 Kevin Buzzard \u5728\u81ea\u5df1\u7684\u535a\u5ba2\u4e0a\u5206\u4eab\u4e86\u4e00\u4e2a\u975e\u5e38\u6709\u8da3\u7684\u9879\u76ee\uff1a\u6559\u8ba1\u7b97\u673a\u7406\u89e3\u8d39\u9a6c\u5927\u5b9a\u7406\u7684\u8bc1\u660e\u3002\u8fd9\u9879\u5de5\u4f5c\u53ef\u4ee5\u5e2e\u52a9\u9a8c\u8bc1\u5bf9\u8d39\u9a6c\u5927\u5b9a\u7406\u7684\u8bc1\u660e\uff0c\u4fee\u6b63\u5176\u4e2d\u53ef\u80fd\u5b58\u5728\u758f\u6f0f\u7684\u90e8\u5206\u3002\u867d\u7136\u8ba1\u7b97\u673a\u8fd8\u6ca1\u6709\u5b8c\u5168\u7406\u89e3\uff0c\u4f46\u4e5f\u786e\u5b9e\u53d6\u5f97\u4e86\u4e00\u4e9b\u8fdb\u5c55\u3002<\/div>\n<div id=\"postspictures\" class=\"article-content\">\n<div id=\"container\" class=\"container am-engine\" data-v-1d7a5742=\"\" data-element=\"root\">\n<p>1637 \u5e74\uff0c\u8d39\u9a6c\u5728\u9605\u8bfb\u4e22\u756a\u56fe\u300a\u7b97\u672f\u300b\u62c9\u4e01\u6587\u8bd1\u672c\u65f6\uff0c\u66fe\u5728\u7b2c 11 \u5377\u7b2c 8 \u547d\u9898\u65c1\u5199\u9053\uff1a\u300c\u5c06\u4e00\u4e2a\u7acb\u65b9\u6570\u5206\u6210\u4e24\u4e2a\u7acb\u65b9\u6570\u4e4b\u548c\uff0c\u6216\u4e00\u4e2a\u56db\u6b21\u5e42\u5206\u6210\u4e24\u4e2a\u56db\u6b21\u5e42\u4e4b\u548c\uff0c\u6216\u8005\u4e00\u822c\u5730\u5c06\u4e00\u4e2a\u9ad8\u4e8e\u4e8c\u6b21\u7684\u5e42\u5206\u6210\u4e24\u4e2a\u540c\u6b21\u5e42\u4e4b\u548c\uff0c\u8fd9\u662f\u4e0d\u53ef\u80fd\u7684\u3002\u5173\u4e8e\u6b64\uff0c\u6211\u786e\u4fe1\u6211\u53d1\u73b0\u4e00\u79cd\u7f8e\u5999\u7684\u8bc1\u6cd5\uff0c\u53ef\u60dc\u8fd9\u91cc\u7684\u7a7a\u767d\u5904\u592a\u5c0f\uff0c\u5199\u4e0d\u4e0b\u3002\u300d<\/p>\n<p>\u8fd9\u5c31\u662f\u8457\u540d\u7684\u8d39\u9a6c\u5927\u5b9a\u7406\uff08FLT\uff0c\u4e5f\u53eb\u8d39\u9a6c\u6700\u540e\u5b9a\u7406\uff09\uff1a<\/p>\n<p><strong>\u5f53\u6574\u6570 n &gt; 2 \u65f6\uff0c\u5173\u4e8e x, y, z \u7684\u4e0d\u5b9a\u65b9\u7a0b x\u207f + y\u207f = z\u207f \u65e0\u6b63\u6574\u6570\u89e3\u3002<\/strong><\/p>\n<p>\u6b64\u540e\uff0c\u65e0\u6570\u6570\u5b66\u5bb6\u548c\u6570\u5b66\u7231\u597d\u8005\u90fd\u5c1d\u8bd5\u8fc7\u8bc1\u660e\u8fd9\u4e2a\u5b9a\u7406\uff1b\u751a\u81f3\u5bf9\u8be5\u5b9a\u7406\u7684\u8bc1\u660e\u4e00\u5ea6\u6210\u4e3a\u300c\u6c11\u95f4\u6570\u5b66\u5bb6\u300d\u6700\u7231\u6311\u6218\u7684\u96be\u9898\u4e4b\u4e00\uff0c\u8fd9\u4e2a\u73b0\u8c61\u8ba9\u6570\u5b66\u5386\u53f2\u5b66\u5bb6\u970d\u534e\u5fb7\u30fb\u4f0a\u592b\u65af\uff08Howard Eves\uff09\u5fcd\u4e0d\u4f4f\u611f\u6168\uff1a\u300c\u8d39\u9a6c\u5927\u5b9a\u7406\u7684\u72ec\u7279\u4e4b\u5904\u5728\u4e8e\u5b83\u662f\u8fc4\u4eca\u4e3a\u6b62\u53d1\u8868\u9519\u8bef\u8bc1\u660e\u6700\u591a\u7684\u6570\u5b66\u95ee\u9898\u3002\u300d<\/p>\n<p>\u5bf9\u8d39\u9a6c\u5927\u5b9a\u7406\u7684\u9996\u4e2a\u5b8c\u6574\u8bc1\u660e\u76f4\u5230 358 \u5e74\u4e4b\u540e\u7684 1995 \u5e74\u624d\u771f\u6b63\u53d1\u8868\u3002\u4e3a\u6b64\uff0c\u82f1\u56fd\u6570\u5b66\u5bb6\u5b89\u5fb7\u9c81\u30fb\u6000\u5c14\u65af\uff08Andrew Wiles\uff09\u4f7f\u7528\u4e86\u4e00\u7cfb\u5217\u590d\u6742\u7684\u6570\u5b66\u5de5\u5177\u548c\u7406\u8bba\u3002\u6574\u4f53\u800c\u8a00\uff0c\u6000\u5c14\u65af\u7684\u8bc1\u660e\u5efa\u7acb\u5728\u6a21\u5f62\u5f0f\u548c\u692d\u5706\u66f2\u7ebf\u4e4b\u95f4\u7684\u6df1\u523b\u8054\u7cfb\uff08\u5373\u8c37\u5c71 &#8211; \u5fd7\u6751\u731c\u60f3\u7684\u4e00\u90e8\u5206\uff09\u4e4b\u4e0a\uff0c\u6574\u4e2a\u8bc1\u660e\u975e\u5e38\u590d\u6742\uff0c\u8bba\u6587\u300aModular elliptic curves and Fermat\u2019s Last Theorem\u300b\u5c31\u6709 109 \u9875\u3002<\/p>\n<p><img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s6.51cto.com\/oss\/202412\/28\/53ef4723387a4f7978a772ac5ee34a35f98b16.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/><\/p>\n<p>\u8fd1\u65e5\uff0c\u4f26\u6566\u5e1d\u56fd\u5b66\u9662\u6570\u5b66\u6559\u6388 Kevin Buzzard \u5728\u81ea\u5df1\u7684\u535a\u5ba2\u4e0a\u5206\u4eab\u4e86\u4e00\u4e2a\u975e\u5e38\u6709\u8da3\u7684\u9879\u76ee\uff1a\u6559\u8ba1\u7b97\u673a\u7406\u89e3\u8d39\u9a6c\u5927\u5b9a\u7406\u7684\u8bc1\u660e\u3002\u8fd9\u9879\u5de5\u4f5c\u53ef\u4ee5\u5e2e\u52a9\u9a8c\u8bc1\u5bf9\u8d39\u9a6c\u5927\u5b9a\u7406\u7684\u8bc1\u660e\uff0c\u4fee\u6b63\u5176\u4e2d\u53ef\u80fd\u5b58\u5728\u758f\u6f0f\u7684\u90e8\u5206\u3002\u867d\u7136\u8ba1\u7b97\u673a\u8fd8\u6ca1\u6709\u5b8c\u5168\u7406\u89e3\uff0c\u4f46\u4e5f\u786e\u5b9e\u53d6\u5f97\u4e86\u4e00\u4e9b\u8fdb\u5c55\u3002<\/p>\n<p>\u8fd9\u7bc7\u535a\u5ba2\u5728 Hacker News \u4e0a\u5438\u5f15\u4e86\u5927\u91cf\u8ba8\u8bba\uff0c\u5f88\u591a\u4eba\u90fd\u5206\u4eab\u4e86\u81ea\u5df1\u7684\u89c1\u89e3\u6216\u7ecf\u5386\uff0c\u5c24\u5176\u662f\u5173\u4e8e\u6570\u5b66\u5f62\u5f0f\u5316\u7684\u91cd\u8981\u6027\u3002<\/p>\n<p><img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s6.51cto.com\/oss\/202412\/28\/d64307b4196d9681838967cd39c1c05b20194f.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/><\/p>\n<p><img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s8.51cto.com\/oss\/202412\/28\/c68da2169b6b4e8d7cd6141f11ab512c6f8dd5.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/><\/p>\n<p><img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s5.51cto.com\/oss\/202412\/28\/161693174574c21a165773ee5d2674c4f90374.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/><\/p>\n<p>\u4ee5\u4e0a\u622a\u56fe\u5747\u6765\u81ea Hacker News \u548c\u8c37\u6b4c\u7ffb\u8bd1\uff0c\u66f4\u591a\u8ba8\u8bba\u8bf7\u8bbf\u95ee\uff1a<br \/>\nhttps:\/\/news.ycombinator.com\/item?id=42399397<\/p>\n<p>\u4ee5\u4e0b\u662f Buzzard \u6559\u6388\u7684\u535a\u5ba2\u5168\u6587\uff08\u539f\u6587\u6bb5\u843d\u8f83\u957f\uff0c\u8fd9\u91cc\u8fdb\u884c\u4e86\u9002\u5f53\u62c6\u5206\u548c\u8c03\u6574\uff09\u3002<\/p>\n<h3>\u8d39\u9a6c\u5927\u5b9a\u7406 \u2014\u2014 \u8fdb\u5c55\u5982\u4f55\uff1f<\/h3>\n<p>\u6211\u5df2\u7ecf\u82b1\u4e86\u4e24\u4e2a\u6708\u65f6\u95f4\u6765\u6559\u8ba1\u7b97\u673a\u7406\u89e3\u9a6c\u5927\u5b9a\u7406\uff08FLT\uff09\u7684\u4e00\u4e2a\u8bc1\u660e\u3002<\/p>\n<p>\u5927\u90e8\u5206\u7684\u300c\u8fdb\u5c55\u5982\u4f55\u300d\u89e3\u91ca\u8d77\u6765\u90fd\u76f8\u5f53\u7e41\u7410\u4e14\u6280\u672f\u6027\uff1a\u957f\u8bdd\u77ed\u8bf4\uff0c\u6000\u5c14\u65af\u8bc1\u660e\u4e86\u300cR=T\u300d\u5b9a\u7406\uff0c\u800c\u5230\u76ee\u524d\u4e3a\u6b62\u7684\u5927\u90e8\u5206\u5de5\u4f5c\u90fd\u662f\u6559\u8ba1\u7b97\u673a\u7406\u89e3\u4ec0\u4e48\u662f R \u548c T\uff1b\u6211\u4eec\u4ecd\u7136\u8fd8\u6ca1\u6709\u5b8c\u6210\u8fd9\u4e24\u8005\u4e2d\u4efb\u4f55\u4e00\u4e2a\u7684\u5b9a\u4e49\u3002<\/p>\n<p>\u4f46\u662f\uff0c\u6211\u7684\u535a\u58eb\u751f Andrew Yang \u5df2\u7ecf\u8bc1\u660e\u4e86\u6211\u4eec\u9700\u8981\u7684\u62bd\u8c61\u53ef\u4ea4\u6362\u4ee3\u6570\u7ed3\u679c\uff08\u300c\u5982\u679c\u62bd\u8c61\u73af\uff08abstract rings\uff09R \u548c T \u6ee1\u8db3\u8bb8\u591a\u6280\u672f\u6761\u4ef6\uff0c\u5219\u5b83\u4eec\u76f8\u7b49\u300d\uff09\uff0c\u8fd9\u662f\u4ee4\u4eba\u5174\u594b\u7684\u7b2c\u4e00\u6b65\u3002<\/p>\n<p>\u6211\u4eec\u4f7f\u7528\u7684\u7cfb\u7edf\u662f Lean \u53ca\u5176\u6570\u5b66\u8f6f\u4ef6\u5e93 mathlib\uff0c\u8be5\u8f6f\u4ef6\u5e93\u7531 Lean \u8bc1\u660e\u5668\u793e\u533a\u7ef4\u62a4\u3002\u5982\u679c\u4f60\u5bf9 Lean \u548c\u6570\u8bba\u6709\u6240\u4e86\u89e3\uff0c\u53ef\u4ee5\u8003\u8651\u9605\u8bfb\u8d21\u732e\u6307\u5357\u3001\u67e5\u770b\u9879\u76ee\u4eea\u8868\u677f\u5e76\u8ba4\u9886\u4e00\u4e2a\u95ee\u9898\u3002<\/p>\n<p>\u4e0b\u9762\u662f\u4e00\u4e9b\u76f8\u5173\u94fe\u63a5\uff1a<\/p>\n<ul data-id=\"ua73dd4b-gh3N71bg\">\n<li data-id=\"ld70c578-G8Nga9MT\">\u84dd\u56fe\u548c\u8fdb\u5c55\uff1ahttps:\/\/imperialcollegelondon.github.io\/FLT\/blueprint\/<\/li>\n<li data-id=\"ld70c578-92PV14Jf\">Lean\uff1ahttps:\/\/lean-fro.org\/<\/li>\n<li data-id=\"ld70c578-G5el7RNR\">mathlib\uff1ahttps:\/\/github.com\/leanprover-community\/mathlib4<\/li>\n<li data-id=\"ld70c578-8MUeHZ9H\">\u8d21\u732e\u6307\u5357\uff1ahttps:\/\/github.com\/ImperialCollegeLondon\/FLT\/blob\/main\/CONTRIBUTING.md<\/li>\n<li data-id=\"ld70c578-9XBR7V6c\">\u9879\u76ee\u4eea\u8868\u76d8\uff1ahttps:\/\/github.com\/orgs\/ImperialCollegeLondon\/projects\/102<\/li>\n<li data-id=\"ld70c578-bKo111kk\">\u95ee\u9898\uff1ahttps:\/\/github.com\/ImperialCollegeLondon\/FLT\/issues<\/li>\n<\/ul>\n<p><img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s8.51cto.com\/oss\/202412\/28\/6411cf21956f895a04f70846593e70130f5e5c.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/><\/p>\n<p>\u84dd\u56fe\u9875\u9762\u622a\u56fe<\/p>\n<p>\u5982\u524d\u6240\u8ff0\uff0c\u6211\u4eec\u5df2\u7ecf\u8fdb\u884c\u4e86\u4e24\u4e2a\u6708\u3002\u4f46\u662f\uff0c\u6211\u4eec\u5df2\u7ecf\u6709\u4e00\u4e2a\u6211\u8ba4\u4e3a\u503c\u5f97\u5206\u4eab\u7684\u6709\u8da3\u6545\u4e8b\u4e86\u3002\u8c01\u77e5\u9053\u8fd9\u662f\u5426\u9884\u793a\u7740\u67d0\u4e2a\u672a\u6765\u3002<\/p>\n<p>\u6211\u4eec\u7684\u76ee\u7684\u5e76\u4e0d\u662f\u5f62\u5f0f\u5316 1990 \u5e74\u4ee3\u90a3\u4e2a FLT \u8bc1\u660e\u3002\u81ea\u90a3\u4ee5\u540e\uff0c\u5df2\u7ecf\u6709\u5f88\u591a\u4eba\uff08Diamond\/Fujiwara\u3001Kisin\u3001Taylor\u3001Scholze \u7b49\u4eba\uff09\u5bf9\u8be5\u8bc1\u660e\u8fdb\u884c\u4e86\u6cdb\u5316\u548c\u7b80\u5316\u3002\u6211\u7684\u90e8\u5206\u52a8\u673a\u662f\u8981\u8bc1\u660e\u8fd9\u4e9b\u66f4\u901a\u7528\u3001\u66f4\u6709\u529b\u7684\u7ed3\u679c\u3002\u4e3a\u4ec0\u4e48\u8fd9\u662f\u56e0\u4e3a\u5982\u679c AI \u771f\u7684\u53ef\u4ee5\u53d8\u9769\u6570\u5b66\uff08\u6709\u53ef\u80fd\uff09\uff0c\u5e76\u4e14 Lean \u88ab\u8bc1\u660e\u662f\u4e00\u4e2a\u91cd\u8981\u7684\u7ec4\u6210\u90e8\u5206\uff08\u4e5f\u6709\u53ef\u80fd\uff09\uff0c\u90a3\u4e48\u8ba1\u7b97\u673a\u5c06\u80fd\u591f\u66f4\u597d\u5730\u5e2e\u52a9\u4eba\u7c7b\u7a81\u7834\u73b0\u4ee3\u6570\u8bba\u7684\u754c\u9650\u3002\u5bf9\u4e8e\u8fd9\u79cd\u5f62\u5f0f\u5316\u5de5\u4f5c\uff0c\u8ba1\u7b97\u673a\u80fd\u591f\u4ee5\u5b83\u4eec\u7406\u89e3\u7684\u65b9\u5f0f\u6765\u83b7\u5f97\u5173\u952e\u7684\u73b0\u4ee3\u5b9a\u4e49\u3002<\/p>\n<p>\u6000\u5c14\u65af\u7684\u539f\u59cb\u8bc1\u660e\u4e2d\u6ca1\u6709\u4f7f\u7528\u7684\u4e00\u4e2a\u6982\u5ff5\uff0c\u5728\u6211\u4eec\u6b63\u5728\u5f62\u5f0f\u5316\u7684\u8bc1\u660e\u4e2d\u4f7f\u7528\u4e86\uff0c\u5b83\u5c31\u662f<strong>\u6676\u4f53\u4e0a\u540c\u8c03\uff08crystalline cohomology\uff09<\/strong>\u3002<\/p>\n<p>\u8fd9\u662f 20 \u4e16\u7eaa\u516d\u4e03\u5341\u5e74\u4ee3\u5728\u6cd5\u56fd\u5df4\u9ece\u53d1\u5c55\u8d77\u6765\u7684\u7406\u8bba\uff0c\u5176\u57fa\u7840\u662f\u7531\u6570\u5b66\u5bb6 Berthelot \u6839\u636e\u53e6\u4e00\u4f4d\u6570\u5b66\u5bb6 Grothendieck \u7684\u601d\u60f3\u642d\u5efa\u7684\u3002\u57fa\u672c\u601d\u60f3\u662f\u7ecf\u5178\u6307\u6570\u548c\u5bf9\u6570\u51fd\u6570\u5728\u5fae\u5206\u51e0\u4f55\uff08\u4f8b\u5982 Lie \u4ee3\u6570\u548c Lie \u7fa4\uff09\u53d1\u6325\u5173\u952e\u4f5c\u7528\uff0c\u7279\u522b\u662f\u5728\u7406\u89e3\u5fb7\u62c9\u59c6\u4e0a\u540c\u8c03\uff08de Rham cohomology,\uff09\u4e2d\uff0c\u4e0d\u8fc7\u5b83\u4eec\u5728\u66f4\u591a\u7684\u7b97\u672f\u60c5\u51b5\u4e0b\u4e0d\u8d77\u4f5c\u7528\uff08\u4f8b\u5982\u5728\u7279\u5f81 p \u4e2d\uff09\u3002<\/p>\n<p>20 \u4e16\u7eaa\u516d\u5341\u5e74\u4ee3\uff0cRoby \u5728\u4e00\u7cfb\u5217\u7cbe\u5f69\u7684\u8bba\u6587\u4e2d\u63d0\u51fa\u4e86\u300c\u9664\u5e42\u7ed3\u6784\u300d\uff08divided power structures\uff09\uff0c\u5728\u6784\u5efa\u53ef\u7528\u4e8e\u7b97\u672f\u60c5\u51b5\u7684\u7c7b\u51fd\u6570\u4e2d\u53d1\u6325\u4e86\u81f3\u5173\u91cd\u8981\u7684\u4f5c\u7528\u3002\u6ce8\uff1a\u6211\u4eec\u8981\u60f3\u6559\u8ba1\u7b97\u673a\u6676\u4f53\u4e0a\u540c\u8c03\uff0c\u9996\u5148\u9700\u8981\u6559\u5b83\u9664\u5e42\u7406\u8bba\u3002<\/p>\n<p>\u6570\u5b66\u9886\u57df\u7684\u7814\u7a76\u8005 Antoine Chambert-Loir\uff08\u7b80\u79f0 Antoine\uff09\u548c Maria Ines de Frutos Fernandez\uff08\u7b80\u79f0 Maria Ines\uff09\u4e00\u76f4\u5728\u6559 Lean \u9664\u5e42\u7406\u8bba\uff0c\u800c\u6574\u4e2a\u590f\u5929\uff0cLean \u90fd\u65f6\u800c\u51fa\u73b0\u4e00\u79cd\u4ee4\u4eba\u607c\u706b\u7684\u60c5\u51b5\uff1a\u5b83\u4f1a\u62b1\u6028\u6807\u51c6\u6587\u732e\u4e2d\u4eba\u4e3a\u63d0\u51fa\u7684\u8bba\u8bc1\uff0c\u5e76\u7ecf\u8fc7\u4ed4\u7ec6\u68c0\u67e5\u53d1\u73b0\u4eba\u4e3a\u8bba\u8bc1\u6709\u5f85\u6539\u8fdb\uff0c\u7279\u522b\u662f Roby \u7684\u5de5\u4f5c\u4e2d\u6709\u4e00\u4e2a\u5173\u952e\u5f15\u7406\u4f3c\u4e4e\u4e0d\u6b63\u786e\u3002\u5f53 Antoine \u544a\u8bc9\u6211\u8fd9\u4ef6\u4e8b\u65f6\uff0c\u4ed6\u89c9\u5f97\u6211\u4f1a\u8ba4\u4e3a\u8fd9\u5f88\u6709\u8da3\uff0c\u800c\u4ed6\u6536\u5230\u7684\u56de\u590d\u4e2d\u4e00\u957f\u4e32\u5927\u7b11\u7684\u8868\u60c5\u7b26\u53f7\u786e\u5b9e\u8bc1\u5b9e\u4e86\u8fd9\u4e00\u70b9\u3002<\/p>\n<p>\u7136\u800c\uff0cAntoine \u6bd4\u6211\u66f4\u4e13\u4e1a\uff0c\u8ba4\u4e3a\u6211\u4e0d\u5e94\u8be5\u53d1\u63a8\u8ba8\u8bba\u8fd9\u4e2a\u95ee\u9898\uff08\u53cd\u6b63\u6211\u4e5f\u4e0d\u53d1\uff0c\u6211\u5df2\u7ecf\u629b\u5f03\u4e86\u63a8\u7279\u5e76\u8f6c\u5411\u4e86\u793e\u4ea4\u5e73\u53f0 bluesky\uff09\uff0c\u800c\u5e94\u8be5\u5c1d\u8bd5\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u3002<\/p>\n<p>\u6211\u4eec\u4ee5\u5b8c\u5168\u4e0d\u540c\u7684\u65b9\u5f0f\u6765\u5904\u7406\u8fd9\u4e2a\u95ee\u9898\uff0cAntoine \u628a\u5b83\u5217\u5165\u4e86\u81ea\u5df1\u7684\u5de5\u4f5c\u6e05\u5355\uff0c\u800c\u6211\u5374\u5b8c\u5168\u5ffd\u7565\u4e86\u5b83\uff0c\u53ea\u662f\u5076\u5c14\u5411\u4eba\u4eec\u63d0\u53ca\u8fd9\u4e2a\u8bc1\u660e\u6709\u95ee\u9898\uff0c\u662f\u5f31\u8bc1\u660e\u3002\u6211\u4e4b\u6240\u4ee5\u8bf4\u662f\u5f31\u8bc1\u660e\uff0c\u662f\u56e0\u4e3a\u8fd9\u4e00\u89c2\u5bdf\u5fc5\u987b\u653e\u5728\u67d0\u79cd\u80cc\u666f\u4e0b\u3002<\/p>\n<p>\u6839\u636e\u6211\u76ee\u524d\u5bf9\u6570\u5b66\u7684\u89c2\u5bdf\uff08\u4f5c\u4e3a\u5f62\u5f0f\u4e3b\u4e49\u8005\uff09\uff0c\u5f53 Antoine \u53d1\u73b0\u8fd9\u4e2a\u95ee\u9898\u65f6\uff0c\u6574\u4e2a\u6676\u4f53\u4e0a\u540c\u8c03\u7406\u8bba\u5c31\u4ece\u6587\u732e\u4e2d\u6d88\u5931\u4e86\uff0c\u5e76\u5e26\u6765\u5de8\u5927\u7684\u9644\u5e26\u635f\u5bb3\uff08\u4f8b\u5982\u6570\u5b66\u5bb6 Scholze \u7684\u5927\u91cf\u5de5\u4f5c\u5c31\u6d88\u5931\u4e86\uff0c\u6574\u672c\u7684\u4e66\u7c4d\u548c\u8bba\u6587\u90fd\u5316\u4e3a\u4e4c\u6709\uff09\u3002\u4f46\u8fd9\u79cd\u6d88\u5931\u53ea\u662f\u6682\u65f6\u7684\uff0c\u6676\u4f53\u4e0a\u540c\u8c03\u5728\u5b9e\u9645\u610f\u4e49\u4e0a\u5e76\u6ca1\u6709\u9519\u8bef\u3002\u8fd9\u4e9b\u5b9a\u7406\u6beb\u65e0\u7591\u95ee\u4ecd\u7136\u662f\u6b63\u786e\u7684\uff0c\u53ea\u662f\u5c31\u6211\u800c\u8a00\uff0c\u8bc1\u660e\u662f\u4e0d\u5b8c\u6574\u7684\uff08\u6216\u8005\u81f3\u5c11 Antoine \u548c Maria Ines \u9075\u5faa\u7684\u8bc1\u660e\u4e0d\u5b8c\u6574\uff09\u3002\u56e0\u6b64\u6211\u4eec\u7684\u5de5\u4f5c\u5c31\u662f\u4fee\u6b63\u5b83\u4eec\u3002<\/p>\n<p>\u6211\u60f3\u5f3a\u8c03\u7684\u662f\uff0c\u6211\u548c Antoine \u90fd\u5f88\u6e05\u695a\uff0c\u5373\u4f7f\u4e2d\u95f4\u5f15\u7406\u662f\u9519\u8bef\u7684\uff0c\u4e3b\u8981\u7ed3\u679c\u7684\u8bc1\u660e\u5f53\u7136\u53ef\u4ee5\u4fee\u6b63\uff0c\u8fd9\u662f\u56e0\u4e3a\u4ece 20 \u4e16\u7eaa 70 \u5e74\u4ee3\u4ee5\u6765\u6676\u4f53\u4e0a\u540c\u8c03\u5c31\u5f97\u5230\u4e86\u5e7f\u6cdb\u4f7f\u7528\u3002\u5982\u679c\u5b83\u6709\u95ee\u9898\uff0c\u65e9\u5c31\u8be5\u66b4\u9732\u51fa\u6765\u4e86\u3002\u6211\u4ea4\u6d41\u8fc7\u7684\u6bcf\u4e2a\u4e13\u5bb6\u90fd\u540c\u610f\u8fd9\u4e00\u70b9\uff0c\u6709\u51e0\u4f4d\u751a\u81f3\u8ba4\u4e3a\u6211\u5728\u5c0f\u9898\u5927\u505a\u3002\u4f46\u4e5f\u8bb8\u4ed6\u4eec\u4e0d\u660e\u767d\u5f62\u5f0f\u5316\u5728\u5b9e\u8df5\u4e2d\u5230\u5e95\u610f\u5473\u7740\u4ec0\u4e48\uff1a\u4f60\u4e0d\u80fd\u53ea\u662f\u8bf4\u300c\u6211\u76f8\u4fe1\u5b83\u53ef\u4ee5\u4fee\u6b63\u300d\uff0c\u4f60\u5fc5\u987b\u771f\u6b63\u5730\u4fee\u6b63\u5b83\u3002\u53e6\u5916\uff0cRoby\u3001Grothendieck \u548c Berthelot \u90fd\u5df2\u7ecf\u53bb\u4e16\u4e86\uff0c\u6211\u4eec\u65e0\u6cd5\u4ece\u8fd9\u4e9b\u539f\u6765\u7684\u4e13\u5bb6\u90a3\u91cc\u76f4\u63a5\u5bfb\u6c42\u5e2e\u52a9\u3002<\/p>\n<p>\u5bf9\u66f4\u591a\u6280\u672f\u7ec6\u8282\u611f\u5174\u8da3\u7684\u4eba\u53ef\u4ee5\u5148\u770b\u8fd9\u91cc\uff1aBerthelot \u7684\u8bba\u6587\u5e76\u6ca1\u6709\u4ece\u5934\u5f00\u59cb\u53d1\u5c55\u9664\u5e42\u7406\u8bba\uff0c\u4ed6\u4f7f\u7528\u4e86 Roby \u7684\u300cLes algebres a puissances divisees\u300d\uff0c1965 \u5e74\u5728 Bull Sci Math \u4e0a\u53d1\u8868\u3002\u8be5\u8bba\u6587\u7684\u5f15\u7406 8 \u4f3c\u4e4e\u662f\u9519\u8bef\u7684\uff0c\u800c\u4e14\u5982\u4f55\u4fee\u6b63\u8bc1\u660e\u4e5f\u6ca1\u8bf4\u660e\u767d\u3002\u8be5\u5f15\u7406\u7684\u8bc1\u660e\u9519\u8bef\u5f15\u7528\u4e86 Roby 1963 \u5e74 Ann Sci ENS \u8bba\u6587\u4e2d\u7684\u53e6\u4e00\u4e2a\u5f15\u7406\u3002\u5176\u6b63\u786e\u7684\u8868\u8ff0\u662f\u300cGamma_A (M) tensor_A R = Gamma_R (M tensor_A R)\u300d\uff0c\u4f46\u5176\u4e2d\u4e00\u4e2a\u5f20\u91cf\u79ef\u5728\u5e94\u7528\u4e2d\u610f\u5916\u8131\u79bb\u3002\u8fd9\u5c31\u6253\u7834\u4e86 Roby \u5173\u4e8e\u300c\u6a21\uff08module\uff09\u7684\u9664\u5e42\u4ee3\u6570\u5177\u6709\u9664\u5e42\uff3d\u7684\u8bc1\u660e\uff0c\u4ece\u800c\u963b\u6b62\u6211\u4eec\u5b9a\u4e49\u73af A_{cris}\u3002<\/p>\n<p>\u6240\u4ee5\uff0c\u6b63\u5982\u6211\u6240\u8a00\uff0cAntoine \u6b63\u81f4\u529b\u4e8e\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u800c\u6211\u53ea\u662f\u5728\u5411\u4e13\u5bb6\u4eec\u516b\u5366\u95f2\u8c08\uff0c\u800c\u4e14\u6211\u72af\u4e86\u4e00\u4e2a\u9519\uff1a\u5728\u4f0a\u65af\u7075\u987f\u7684\u4e00\u5bb6\u5496\u5561\u5e97\u544a\u8bc9\u4e86\u6642\u679d\u6b63\uff08Tadashi Tokieda\uff09\u8fd9\u4ef6\u4e8b\uff0c\u4ed6\u56de\u5230\u65af\u5766\u798f\u540e\u5411 Brian Conrad \u63d0\u5230\u4e86\u8fd9\u4ef6\u4e8b\uff0c\u7136\u540e Conrad \u5c31\u5f00\u59cb\u5728\u6211\u7684\u6536\u4ef6\u7bb1\u91cc\u95ee\u6211\u6676\u4f53\u4e0a\u540c\u8c03\u6709\u95ee\u9898\u5230\u5e95\u662f\u600e\u4e48\u56de\u4e8b\u3002<\/p>\n<p>\u6211\u89e3\u91ca\u4e86\u8fd9\u4e2a\u95ee\u9898\u7684\u6280\u672f\u7ec6\u8282\uff0cConrad \u540c\u610f\u8fd9\u597d\u50cf\u786e\u5b9e\u662f\u4e00\u4e2a\u95ee\u9898\uff0c\u7136\u540e\u4ed6\u5f00\u59cb\u601d\u8003\u3002\u51e0\u4e2a\u5c0f\u65f6\u540e\uff0c\u4ed6\u56de\u590d\u4e86\u6211\uff0c\u5e76\u6307\u51fa\uff0c\u5728 Berthelot-Ogus \u7684\u5173\u4e8e\u6676\u4f53\u4e0a\u540c\u8c03\u7684\u8457\u4f5c\u7684\u9644\u5f55\u4e2d\uff0c\u5b58\u5728\u5bf9\u300c\u6a21\u7684\u4e00\u822c\u9664\u5e42\u4ee3\u6570\u5177\u6709\u9664\u5e42\u300d\u8fd9\u4e2a\u65ad\u8a00\u7684\u53e6\u4e00\u4e2a\u4e0d\u540c\u7684\u8bc1\u660e\uff0c\u800c\u4e14 Conrad \u8ba4\u4e3a\u8fd9\u4e2a\u65b9\u6cd5\u6ca1\u6709\u95ee\u9898\u3002\u8bc1\u660e\u53c8\u56de\u6765\u4e86\uff01<\/p>\n<p><img decoding=\"async\" title=\"\u56fe\u7247\" src=\"https:\/\/s6.51cto.com\/oss\/202412\/28\/0559ee374bc774600e0725d74fc721c43b215e.webp\" alt=\"\u56fe\u7247\" data-type=\"inline\" \/><\/p>\n<p>\u8fd9\u5dee\u4e0d\u591a\u5c31\u662f\u6545\u4e8b\u7684\u5168\u90e8\u3002\u4e0a\u4e2a\u6708\u6211\u8bbf\u95ee\u4e86\u4f2f\u514b\u5229\uff0c\u548c Arthur Ogus \u5171\u8fdb\u5348\u9910\uff0c\u6211 90 \u5e74\u4ee3\u5728\u90a3\u91cc\u505a\u535a\u58eb\u540e\u7684\u65f6\u5019\u5c31\u8ba4\u8bc6\u4ed6\u4e86\u3002\u6211\u7b54\u5e94\u8fc7 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\u2014\u2014 \u4e24\u5468\u524d\uff0cMaria Ines \u5728\u5251\u6865\u6570\u5b66\u5f62\u5f0f\u5316\u7814\u8ba8\u4f1a\uff08Cambridge Formalization of Mathematics seminar\uff09\u4e0a\u53d1\u8868\u4e86\u4e00\u4e2a\u5173\u4e8e\u9664\u5e42\u7684\u5f62\u5f0f\u5316\u7684\u6f14\u8bb2\u3002\u6839\u636e\u8fd9\u4e2a\u6f14\u8bb2\uff0c\u6211\u7684\u7406\u89e3\u662f\u8fd9\u4e9b\u95ee\u9898\u73b0\u5728\u5df2\u7ecf\u5f97\u5230\u89e3\u51b3\u4e86\u3002\u6240\u4ee5\u6211\u4eec\u5b9e\u9645\u4e0a\u53c8\u56de\u5230\u4e86\u6b63\u8f68\u3002\u76f4\u5230\u4e0b\u4e00\u6b21\u6587\u732e\u8ba9\u6211\u4eec\u5931\u671b\u2026\u2026<\/p>\n<p>\u53c2\u8003\u94fe\u63a5\uff1a<\/p>\n<p>https:\/\/xenaproject.wordpress.com\/2024\/12\/11\/fermats-last-theorem-how-its-going\/\u3002<\/p>\n<p>https:\/\/news.ycombinator.com\/item?id=42399397\u3002<\/p>\n<p>\u6587\u7ae0\u6765\u81ea\uff1a51CTO<\/p>\n<\/div>\n<\/div>\n<div class=\"pvc_clear\"><\/div>\n<p id=\"pvc_stats_23816\" class=\"pvc_stats total_only  \" data-element-id=\"23816\" 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