{"id":57398,"date":"2025-03-17T19:37:11","date_gmt":"2025-03-17T11:37:11","guid":{"rendered":"https:\/\/swarma.org\/?p=57398"},"modified":"2025-03-17T19:37:11","modified_gmt":"2025-03-17T11:37:11","slug":"%e7%99%be%e5%b9%b4%e4%b8%80%e9%81%87%e7%9a%84%e8%af%81%e6%98%8e%ef%bc%8c%e6%94%bb%e5%85%8b%e6%95%b0%e5%ad%a6%e7%95%8c%e7%9a%84%e6%8c%82%e8%b0%b7%e7%8c%9c%e6%83%b3","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=57398","title":{"rendered":"\u767e\u5e74\u4e00\u9047\u7684\u8bc1\u660e\uff0c\u653b\u514b\u6570\u5b66\u754c\u7684\u6302\u8c37\u731c\u60f3"},"content":{"rendered":"
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1917\u5e74\uff0c\u6302\u8c37\u5b97\u4e00<\/span>\uff08S\u014dichi Kakeya\uff09<\/span>\u63d0\u51fa\u4e86\u8fd9\u4e2a\u95ee\u9898\uff0c\u4f46\u5047\u8bbe\u94c5\u7b14\u662f\u65e0\u9650\u7ec6\u7684\u3002\u4ed6\u627e\u5230\u4e86\u4e00\u79cd\u6ed1\u52a8\u65e0\u9650\u7ec6\u94c5\u7b14\u7684\u65b9\u5f0f\uff0c\u4f7f\u5f97\u626b\u8fc7\u7684\u9762\u79ef\u6bd4\u51ed\u76f4\u89c9\u505a\u5706\u5468\u8fd0\u52a8\u626b\u8fc7\u7684\u9762\u79ef\u66f4\u5c0f\u3002<\/span><\/section>\n

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Mark Belan\/<\/span>Quanta Magazine<\/span><\/em><\/span><\/section>\n

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\u7ebd\u7ea6\u5927\u5b66\u67ef\u6717\u7814\u7a76\u6240\u7684\u738b\u8679\u8868\u793a\uff0c\u8fd9\u4e00\u8bc1\u660e\u5c06\u4e3a\u6570\u5b66\u5f00\u8f9f\u65b0\u9886\u57df\u3002\u201c\u8fd9\u4e2a\u95ee\u9898\u5fc5\u987b\u89e3\u51b3\uff0c\u201d\u5979\u8bf4\u3002\u4e28Rickinasia\/Wikimedia Commons<\/span><\/span><\/p>\n


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\u6302\u8c37\u5b97\u4e00\uff08S\u014dichi Kakeya\uff09\u57281917\u5e74\u63d0\u51fa\u4e86\u65e5\u540e\u4ee5\u4ed6\u540d\u5b57\u547d\u540d\u7684\u95ee\u9898\uff0c\u5f53\u65f6\u4ed631\u5c81\u3002\u4e28\u4e1c\u4eac\u5927\u5b66\u4f9b\u56fe<\/span><\/span><\/p>\n


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2022\u5e74\uff0c\u5728\u73b0\u4ee3\u7248\u672c\u6302\u8c37\u731c\u60f3\u63d0\u51fa\u4e94\u5341\u5468\u5e74\u4e4b\u9645\uff0c\u738b\u8679\u4e0e\u624e\u5c14\u53d6\u5f97\u4e86\u91cd\u5927\u8fdb\u5c55[7]\u3002\u4ed6\u4eec\u9075\u5faa\u5361\u8328<\/span>\uff08Katz\uff09<\/span>\u4e0e\u9676\u54f2\u8f69<\/span>\uff08Terence Tao\uff09<\/span>[8]2014\u5e74\u63d0\u51fa\u7684\u7814\u7a76\u6846\u67b6\uff0c\u5206\u6790\u4e86\u4e00\u7c7b\u68d8\u624b\u7684\u5361\u514b\u4e9a\u96c6\u3002\u4ed6\u4eec\u8bc1\u660e\u8fd9\u7c7b\u96c6\u5408\u7684\u7ef4\u6570\u5747\u4e3a3\uff0c\u8fd9\u4e2a\u8bc1\u660e\u9002\u7528\u4e8e\u95f5\u53ef\u592b\u65af\u57fa\u7ef4\u6570\u4ee5\u53ca\u4e00\u4e2a\u76f8\u8fd1\u7684\u53eb\u8c6a\u65af\u591a\u592b\u7ef4\u6570<\/span>\uff08Hausdorff dimension\uff09<\/span>\u7684\u6982\u5ff5\u3002\u6392\u9664\u8fd9\u4e00\u607c\u4eba\u7684\u7279\u6b8a\u7c7b\u522b\u540e\uff0c\u4ed6\u4eec\u9700\u8981\u8bc1\u660e\u6240\u6709\u5176\u4ed6\u5361\u514b\u4e9a\u96c6\u7684\u7ef4\u6570\u4e5f\u662f3\u3002<\/span><\/section>\n

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\u4ed6\u4eec\u91c7\u7528\u4e86\u5206\u6b65\u63a8\u8fdb\u7684\u7b56\u7565\uff1a\u9996\u5148\u7814\u7a76\u67d0\u4e2a\u72ed\u7a84\u7684\u7ef4\u6570\u533a\u95f4<\/span>\uff08\u59822.5\u81f32.6\uff09<\/span>\uff0c\u8bc1\u660e\u4e0d\u5b58\u5728\u8be5\u533a\u95f4\u5185\u7684\u5361\u514b\u4e9a\u96c6\u3002\u82e5\u80fd\u5bf9\u6240\u6709\u533a\u95f4\u91cd\u590d\u8fd9\u4e00\u8fc7\u7a0b\uff0c\u5373\u53ef\u8bc1\u660e\u6574\u4e2a\u731c\u60f3\u3002<\/span><\/section>\n

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\u5e78\u8fd0\u7684\u662f\uff0c\u738b\u8679\u4e0e\u624e\u5c14\u65e0\u9700\u4ece\u96f6\u5f00\u59cb\u3002\u6c64\u59c6\u00b7\u6c83\u5c14\u592b<\/span>\uff08Tom Wolff\uff09<\/span>\u57281995\u5e74\u5df2\u8bc1\u660e\uff1a\u4efb\u4f55\u4e09\u7ef4\u5361\u514b\u4e9a\u96c6\u7684\u8c6a\u65af\u591a\u592b\u7ef4\u6570\u6216\u95f5\u53ef\u592b\u65af\u57fa\u7ef4\u6570\u90fd\u4e0d\u53ef\u80fd\u4f4e\u4e8e2.5\u3002\u4f46\u7814\u7a76\u8005\u4eec\u9700\u8981\u627e\u5230\u4e00\u79cd\u65b9\u6cd5\uff0c\u8bc1\u660e\u4ecb\u4e8e2.5\u5230<\/span>\uff08\u4f8b\u5982\uff09<\/span>2.500001\u4e4b\u95f4\u7684\u7ef4\u6570\u540c\u6837\u4e0d\u53ef\u80fd\u5b58\u5728\u3002\u901a\u8fc7\u91cd\u590d\u8fd9\u4e00\u8bba\u8bc1\u8fc7\u7a0b\uff0c\u4ed6\u4eec\u53ef\u4ee5\u5c06\u7ef4\u5ea6\u4e0b\u9650\u9010\u6b65\u63a8\u5347\u81f32.500002\uff0c\u5e76\u4ee5\u6b64\u7c7b\u63a8\u3002\u6bcf\u6b21\u63a8\u8fdb\u672c\u8d28\u4e0a\u90fd\u5728\u8bc1\u660e\u2014\u2014\u5728\u5982\u6b64\u5fae\u5c0f\u7684\u589e\u91cf\u8303\u56f4\u5185\uff0c\u4e0d\u53ef\u80fd\u5b58\u5728\u6ee1\u8db3\u6761\u4ef6\u7684\u5361\u514b\u4e9a\u96c6\u3002<\/span><\/section>\n

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\u5b9e\u9645\u4e0a\uff0c\u4ed6\u4eec\u65e0\u9700\u9010\u4e00\u7e41\u7410\u5730\u8bc1\u660e\u8fd9\u6570\u767e\u4e07\u4e2a\u589e\u91cf\u533a\u95f4\u7684\u6bcf\u4e00\u4e2a\u3002\u4ed6\u4eec\u53ea\u9700\u8bc1\u660e\u7b2c\u4e00\u4e2a\u589e\u91cf\uff0c\u540c\u65f6\u5c55\u793a\u5f53\u524d\u8fb9\u754c\u80fd\u591f\u63a8\u5bfc\u51fa\u4e0b\u4e00\u4e2a\u7a0d\u5927\u7684\u8fb9\u754c\u3002\u6b64\u5916\uff0c\u4ed6\u4eec\u8fd8\u9700\u8981\u8bc1\u660e\u8fd9\u4e00\u63a8\u5bfc\u8fc7\u7a0b\u65e0\u8bba\u4ece\u54ea\u4e2a\u8d77\u59cb\u70b9\u5f00\u59cb\u90fd\u6210\u7acb\u3002\u901a\u8fc7\u8fd9\u79cd\u65b9\u5f0f\uff0c\u5c31\u8db3\u4ee5\u8bf4\u660e\u8fb9\u754c\u53ef\u4ee5\u88ab\u9010\u6b65\u63a8\u8fdb\uff0c\u6700\u7ec8\u8fbe\u52303\u8fd9\u4e2a\u76ee\u6807\u503c\u3002<\/span><\/section>\n

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\u4e0e2022\u5e74\u4f7f\u7528\u5361\u8328-\u9676\u6846\u67b6\u4e0d\u540c\uff0c\u8fd9\u6b21\u4ed6\u4eec\u6ca1\u6709\u73b0\u6210\u7684\u8def\u7ebf\u56fe\u3002\u4e8e\u662f\u4ed6\u4eec\u8f6c\u5411\u4e86”\u9897\u7c92\u6027”\u8fd9\u4e00\u7279\u6b8a\u6027\u8d28\u3002<\/span><\/section>\n

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2014\u5e74\uff0c\u9ebb\u7701\u7406\u5de5\u5b66\u9662\u7684\u62c9\u91cc\u00b7\u53e4\u65af<\/span>\uff08Larry Guth\uff09<\/span>[9]\u8bc1\u660e\uff0c\u4efb\u4f55\u5173\u4e8e\u6302\u8c37\u731c\u60f3\u7684\u53cd\u4f8b\u90fd\u5fc5\u987b\u5177\u6709”\u9897\u7c92\u72b6”\u7279\u5f81\u3002\u5728\u8fd9\u79cd\u9897\u7c92\u72b6\u96c6\u5408\u4e2d\uff0c\u5b58\u5728\u8bb8\u591a\u5fae\u5c0f\u7684\u4e09\u7ef4\u622a\u9762\u533a\u57df\uff0c\u5176\u4e2d\u5927\u91cf\u7ba1\u72b6\u7ed3\u6784\u4f1a\u76f8\u4e92\u91cd\u53e0\u3002\u6bcf\u4e2a\u8fd9\u6837\u7684”\u9897\u7c92”\u539a\u5ea6\u7ea6\u4e3a\u5355\u4e2a\u7ba1\u5b50\u7684\u76f4\u5f84\uff0c\u5bbd\u5ea6\u662f\u5176\u51e0\u500d<\/span>\uff08\u4f46\u957f\u5ea6\u8fdc\u4e0d\u53ca\u539f\u7ba1\u5b50\uff09<\/span>\uff0c\u5e76\u4e14\u6709\u5927\u91cf\u7ba1\u5b50\u6cbf\u7740\u5176\u7eb5\u5411\u8d2f\u7a7f\u5176\u4e2d\u3002<\/span><\/section>\n

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\u738b\u8679\u4e0e\u624e\u5c14\u610f\u8bc6\u5230\uff0c\u5b8c\u5168\u907f\u5f00\u590d\u6742\u7684\u7ba1\u72b6\u7ed3\u6784\uff0c\u8f6c\u800c\u5904\u7406\u8fd9\u4e9b\u66f4\u7b80\u5355\u7684\u9897\u7c92\u7ed3\u6784\u3002\u4ed6\u4eec\u53d1\u73b0\uff0c\u901a\u8fc7\u8fd9\u79cd\u65b9\u5f0f\u66f4\u5bb9\u6613\u5217\u4e3e\u5e76\u8ba1\u7b97\u9897\u7c92\u4e4b\u95f4\u4e0d\u540c\u91cd\u53e0\u65b9\u5f0f\u7684\u6570\u5b66\u5173\u7cfb\u3002<\/span><\/section>\n

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<\/section>\n

\u7ea6\u4e66\u4e9a\u00b7\u624e\u5c14\uff08Joshua Zahl\uff09\uff0c\u4e0d\u5217\u98a0\u54e5\u4f26\u6bd4\u4e9a\u5927\u5b66\u6570\u5b66\u5bb6\uff0c\u65b0\u8bc1\u660e\u7684\u5408\u8457\u8005\u3002\u4e28<\/span>Paul Joseph<\/span><\/p>\n

<\/section>\n
\u5373\u4f7f\u5728\u6240\u6709\u9897\u7c92\u90fd\u5c3d\u53ef\u80fd\u4ee5\u6700\u5927\u7a0b\u5ea6\u91cd\u53e0\u7684\u60c5\u51b5\u4e0b\uff0c\u7814\u7a76\u4eba\u5458\u53d1\u73b0\uff0c\u7ecf\u8fc7\u4efb\u610f\u7ed9\u5b9a\u70b9\u7684\u9897\u7c92\u6570\u91cf\u4e5f\u4e0d\u4f1a\u8fc7\u4e8e\u5e9e\u5927\u3002\u4ece2.5\u7ef4\u7684\u4e0b\u9650\u51fa\u53d1\uff0c\u4ed6\u4eec\u6210\u529f\u8bc1\u660e\u8fd9\u4e9b\u9897\u7c92\u7684\u91cd\u53e0\u7a0b\u5ea6\u65e0\u6cd5\u4f7f\u7ef4\u5ea6\u7565\u5fae\u7a81\u7834\u8be5\u754c\u9650\u3002\u968f\u540e\uff0c\u4ed6\u4eec\u4ece\u66f4\u9ad8\u7ef4\u5ea6\u51fa\u53d1\uff0c\u901a\u8fc7\u76f8\u540c\u7684\u8ba1\u7b97\u6b65\u9aa4\u5c06\u4e0b\u9650\u8fdb\u4e00\u6b65\u63d0\u5347\u3002\u8fd9\u79cd\u9012\u8fdb\u8fc7\u7a0b\u6301\u7eed\u8fdb\u884c\u3002<\/span><\/section>\n

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“\u8fd9\u5c31\u50cf\u5728\u5b8c\u5584\u4e00\u53f0\u6c38\u52a8\u673a\uff0c\u5145\u6ee1\u4e86\u9b54\u5e7b\u8272\u5f69\u3002”\u9676\u54f2\u8f69\u8bc4\u4ef7\u9053\uff0c”\u4ed6\u4eec\u7684\u7814\u7a76\u6210\u679c\u4ea7\u51fa\u8fdc\u8d85\u8fc7\u521d\u59cb\u6295\u5165\u3002”\u901a\u8fc7\u8fd9\u79cd\u9012\u63a8\u673a\u5236\uff0c\u7814\u7a76\u56e2\u961f\u6700\u7ec8\u5c06\u95f5\u53ef\u592b\u65af\u57fa\u7ef4\u6570<\/span>\uff08\u53ca\u8c6a\u65af\u591a\u592b\u7ef4\u6570\uff09<\/span>\u4e0b\u9650\u63a8\u81f3 3\uff0c\u6210\u529f\u8bc1\u660e\u4e863\u7ef4\u6302\u8c37\u731c\u60f3\u3002<\/span><\/section>\n
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\u9010\u68a6\u4e4b\u5854 \uff1a<\/strong><\/span><\/strong><\/strong><\/p>\n

\u8c03\u548c\u5206\u6790\u9886\u57df\u7684\u91cc\u7a0b\u7891\u4e0e\u9ad8\u7ef4\u731c\u60f3\u5c55\u671b<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n

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\u8fd9\u4e00\u731c\u60f3\u7684\u89e3\u51b3\u5bf9\u7814\u7a76\u5085\u91cc\u53f6\u53d8\u6362\u7ec6\u8282\u7684\u8c03\u548c\u5206\u6790<\/span>\uff08harmonic analysis\uff09<\/span>\u9886\u57df\u5177\u6709\u91cc\u7a0b\u7891\u610f\u4e49\u3002<\/span><\/section>\n

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\u8c03\u548c\u5206\u6790\u9886\u57df\u7684\u4e09\u5ea7\u91cd\u5927\u731c\u60f3[10]\u7684\u9ad8\u5854\u5efa\u7acb\u5728\u6302\u8c37\u731c\u60f3\u4e4b\u4e0a\u3002\u5854\u4e2d\u7684\u6bcf\u4e00\u5c42\u90fd\u5fc5\u987b\u8db3\u591f\u7a33\u56fa\uff0c\u5176\u4e0a\u7684\u697c\u5c42\u624d\u6709\u673a\u4f1a\u7acb\u7a33\u3002\u5982\u679c\u6302\u8c37\u731c\u60f3\u88ab\u8bc1\u4f2a\u2014\u2014\u5982\u679c\u738b\u8679\u548c\u624e\u5c14\u771f\u7684\u627e\u5230\u4e86\u53cd\u4f8b\u2014\u2014\u6574\u5ea7\u7406\u8bba\u4e4b\u5854\u90fd\u5c06\u8f70\u7136\u5d29\u584c\u3002<\/span><\/section>\n

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\u5982\u4eca\u8bc1\u660e\u6210\u7acb\u540e\uff0c\u6570\u5b66\u5bb6\u4eec\u6709\u671b\u501f\u52a9\u6302\u8c37\u731c\u60f3\u9010\u5c42\u653b\u514b\u8fd9\u4e9b\u66f4\u5b8f\u5927\u7684\u731c\u60f3\u3002\u201c\u6240\u6709\u6570\u5b66\u5bb6\u66fe\u7ecf\u68a6\u60f3\u89e3\u51b3\u7684\u95ee\u9898\uff0c\u73b0\u5728\u90fd\u53d8\u5f97\u89e6\u624b\u53ef\u53ca\uff0c\u201d\u53e4\u65af\u8868\u793a\u3002<\/span><\/section>\n

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\u8fd9\u4e00\u8fdb\u7a0b\u5df2\u6084\u7136\u542f\u52a8\u3002\u738b\u8679\u8fd1\u671f\u5408\u8457\u7684\u53e6\u4e00\u7bc7\u8bba\u6587\u5c06\u4e0b\u4e00\u5c42\u731c\u60f3\u7b80\u5316\u4e3a\u66f4\u5f3a\u7248\u672c\u7684\u6302\u8c37\u731c\u60f3\uff0c\u4e3a\u8fde\u63a5\u4e24\u5c42\u7406\u8bba\u8fc8\u51fa\u5173\u952e\u4e00\u6b65\u3002<\/span><\/section>\n

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\u5bf9\u4e8e\u8fd9\u4e2a\u4e00\u76f4\u56f0\u5728\u4e8c\u7ef4\u7a7a\u95f4\u4e2d\u7684\u6570\u5b66\u9886\u57df\u6765\u8bf4\uff0c\u8fd9\u4e5f\u662f\u4e00\u6b21\u7ef4\u5ea6\u4e0a\u7684\u98de\u8dc3\u3002\u201c\u5728\u4e8c\u7ef4\u60c5\u51b5\u4e0b\uff0c\u4eba\u4eec\u5df2\u7ecf\u6df1\u523b\u7406\u89e3<\/span>\uff08\u4e0eKakeya\u76f8\u5173\u7684\u95ee\u9898\uff09<\/span>\u7684\u8fd0\u884c\u673a\u5236\uff0c\u4f46\u6211\u4eec\u7f3a\u4e4f\u7814\u7a76\u66f4\u9ad8\u7ef4\u5ea6\u7684\u5de5\u5177\uff0c\u201d\u738b\u8679\u89e3\u91ca\u9053\uff0c\u201c\u56e0\u6b64\u6211\u8ba4\u4e3a\u8fd9\u9879\u7a81\u7834\u662f\u5fc5\u8981\u4e14\u5fc5\u987b\u5b9e\u73b0\u7684\u3002\u201d<\/span><\/section>\n
\u56db\u7ef4\u6302\u8c37\u731c\u60f3\u4ecd\u672a\u89e3\u51b3\uff0c\u5176\u4e0a\u8fd8\u77d7\u7acb\u7740\u4e00\u7cfb\u5217\u56db\u7ef4\u731c\u60f3\u3002\u53e4\u65af\u8868\u793a\uff0c\u867d\u7136\u672a\u6765\u4f1a\u9047\u5230\u65b0\u7684\u56f0\u96be\uff0c\u4f46\u4ed6\u8ba4\u4e3a\u4ece\u4e8c\u7ef4\u5230\u4e09\u7ef4\u7684\u8de8\u8d8a\u6700\u4e3a\u8270\u96be\uff0c\u800c\u738b\u8679\u548c\u624e\u5c14\u7684\u8bc1\u660e\u65b9\u6cd5\u5f88\u53ef\u80fd\u53ef\u4ee5\u5e94\u7528\u4e8e\u8fd9\u4e00\u7cfb\u5217\u731c\u60f3\uff0c\u751a\u81f3\u63a8\u5e7f\u5230\u66f4\u9ad8\u7ef4\u5ea6\u3002<\/span><\/section>\n

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\u201c\u5f53\u6211\u8fd8\u662f\u5e74\u8f7b\u6570\u5b66\u5bb6\u65f6\uff0c\u6211\u4e3a\u6302\u8c37\u95ee\u9898\u7740\u8ff7\u3002\u5b83\u770b\u4f3c\u5982\u6b64\u7b80\u5355\uff0c\u5145\u6ee1\u51e0\u4f55\u7f8e\u611f\uff0c\u5176\u5b9e\u9645\u96be\u5ea6\u4e4b\u9ad8\u8d85\u4e4e\u6211\u7684\u9884\u6599\uff0c\u201d\u53e4\u65af\u56de\u5fc6\u9053\u3002\u591a\u5e74\u540e\uff0c\u4ed6\u7684\u535a\u58eb\u751f\u738b\u8679\u540c\u6837\u88ab\u8fd9\u4e2a\u6570\u5b66\u8c1c\u9898\u8868\u9762\u7b80\u5355\u5b9e\u5219\u6df1\u5965\u7684\u7279\u6027\u6240\u5438\u5f15\u3002<\/span><\/section>\n

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\u201c\u8fd9\u4e9b\u5177\u4f53\u7684\u51e0\u4f55\u5bf9\u8c61\u6613\u4e8e\u60f3\u8c61\uff0c\u4e0d\u50cf\u5176\u4ed6\u6570\u5b66\u7406\u8bba\u90a3\u6837\u4ee4\u4eba\u671b\u800c\u751f\u754f\uff0c”\u738b\u8679\u8bf4\uff0c”\u6211\u53ea\u662f\u60f3\u5f04\u660e\u767d\u5b83\u4e3a\u4f55\u5982\u6b64\u56f0\u96be\u3002\u201d<\/span><\/section>\n

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\u5982\u4eca\uff0c\u5f97\u76ca\u4e8e\u738b\u8679\u4e0e\u624e\u5c14\u7684\u52aa\u529b\uff0c\u8fd9\u4e2a\u8c1c\u9898\u7684\u7b54\u6848\u5df2\u524d\u6240\u672a\u6709\u7684\u6e05\u6670\u3002\u201c\u6211\u771f\u5fc3\u8ba4\u4e3a\uff0c\u8fd9\u91cc\u6b63\u5728\u5b55\u80b2\u548c\u6d8c\u73b0\u7684\u5173\u952e\u601d\u60f3\uff0c\u8db3\u4ee5\u9769\u65b0\u6574\u4e2a\u4ece\u6b64\u5f00\u542f\u7684\u9886\u57df\uff0c”\u5e0c\u514b\u66fc<\/span>\uff08Hickman\uff09<\/span>\u8bf4\uff0c”\u8fd9\u662f\u4e00\u4e2a\u975e\u5e38\u3001\u975e\u5e38\u6fc0\u52a8\u4eba\u5fc3\u7684\u65f6\u523b\u3002\u201d<\/span><\/section>\n

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\u53c2\u8003\u8d44\u6599\uff1a<\/span><\/strong><\/span><\/section>\n
1.Jonathan Hickman:https:\/\/www.maths.ed.ac.uk\/~jhickman\/<\/span><\/section>\n
2.Hong Wang\uff1ahttps:\/\/sites.google.com\/view\/hongwang\/home<\/span><\/section>\n
3.Joshua Zahl\uff1ahttps:\/\/personal.math.ubc.ca\/~jzahl\/<\/span><\/section>\n
4.\u8bba\u6587\u5730\u5740\uff1ahttps:\/\/arxiv.org\/abs\/2502.17655<\/span><\/section>\n
5.Nets Katz:https:\/\/profiles.rice.edu\/faculty\/nets-katz<\/span><\/section>\n
6.Charles Fefferman:https:\/\/www.math.princeton.edu\/people\/charles-fefferman<\/span><\/section>\n
7.2022\u8fdb\u5c55\u7684\u6587\u7ae0\u5730\u5740\uff1aa significant step forward\uff1ahttps:\/\/www.quantamagazine.org\/new-proof-threads-the-needle-on-a-sticky-geometry-problem-20230711\/<\/span><\/section>\n
8.Terence Tao\uff1ahttps:\/\/www.math.ucla.edu\/~tao\/<\/span><\/section>\n
9.Larry Guth\uff1ahttps:\/\/math.mit.edu\/directory\/profile.html?pid=1461<\/span><\/section>\n
10.\u8c03\u548c\u5206\u6790\u4e09\u5927\u731c\u60f3\u7684\u6587\u7ae0\u5730\u5740\uff1arests atop the Kakeya conjecture:https:\/\/www.quantamagazine.org\/a-tower-of-conjectures-that-rests-upon-a-needle-20230912\/<\/span><\/section>\n
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\u539f\u6587\u5730\u5740\uff1a<\/span><\/section>\n
https:\/\/www.quantamagazine.org\/once-in-a-century-proof-settles-maths-kakeya-conjecture-20250314\/<\/span><\/section>\n<\/section>\n<\/section>\n<\/blockquote>\n

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\u4eba\u5de5\u667a\u80fd\u4e0e\u6570\u5b66\u8bfb\u4e66\u4f1a<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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\u6570\u5341\u5e74\u6765\uff0c\u4eba\u5de5\u667a\u80fd\u7684\u7406\u8bba\u53d1\u5c55\u548c\u6280\u672f\u5b9e\u8df5\u4e00\u76f4\u4e0e\u79d1\u5b66\u63a2\u7d22\u76f8\u4f34\u800c\u751f\uff0c\u5c24\u5176\u5728\u4ee5\u5927\u6a21\u578b\u4e3a\u4ee3\u8868\u7684\u4eba\u5de5\u667a\u80fd\u6280\u672f\u5e94\u7528\u96c6\u4e2d\u7206\u53d1\u7684\u5f53\u4e0b\uff0c\u4eba\u5de5\u667a\u80fd\u6b63\u5728\u52a0\u901f\u7269\u7406\u3001\u5316\u5b66\u3001\u751f\u7269\u7b49\u57fa\u7840\u79d1\u5b66\u7684\u9769\u65b0\uff0c\u800c\u8fd9\u4e9b\u5b66\u79d1\u4e5f\u5728\u53cd\u8fc7\u6765\u542f\u53d1\u4eba\u5de5\u667a\u80fd\u6280\u672f\u521b\u65b0\u3002\u5728\u6b64\u8fc7\u7a0b\u4e2d\uff0c\u6570\u5b66\u4f5c\u4e3a\u517c\u5177\u7406\u8bba\u5c5e\u6027\u4e0e\u5de5\u5177\u5c5e\u6027\u7684\u91cd\u8981\u57fa\u7840\u5b66\u79d1\uff0c\u4e0e\u4eba\u5de5\u667a\u80fd\u5173\u7cfb\u751a\u5bc6\uff0c\u76f8\u8f85\u76f8\u6210\u3002\u4e00\u65b9\u9762\uff0c\u4eba\u5de5\u667a\u80fd\u5728\u89e3\u51b3\u6570\u5b66\u9886\u57df\u7684\u8bf8\u591a\u5de5\u7a0b\u95ee\u9898\u3001\u7406\u8bba\u95ee\u9898\u4e43\u81f3\u5723\u676f\u96be\u9898\u4e0a\u5c61\u521b\u8bb0\u5f55\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u6570\u5b66\u6301\u7eed\u4e3a\u4eba\u5de5\u667a\u80fd\u6784\u7b51\u7406\u8bba\u57fa\u77f3\u5e76\u62d3\u5c55\u5176\u672a\u6765\u7a7a\u95f4\u3002\u8fd9\u4e24\u4e2a\u5173\u952e\u9886\u57df\u7684\u4ea4\u53c9\u878d\u5408\uff0c\u6b63\u5728\u63ed\u5f00\u4e0b\u4e2a\u65f6\u4ee3\u7684\u79d1\u5b66\u4e4b\u5e55\u3002<\/span><\/p>\n


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\u4e3a\u4e86\u63a2\u7d22\u6570\u5b66\u4e0e\u4eba\u5de5\u667a\u80fd\u6df1\u5ea6\u878d\u5408\u7684\u53ef\u80fd\u6027\uff0c\u96c6\u667a\u4ff1\u4e50\u90e8\u8054\u5408\u540c\u6d4e\u5927\u5b66\u7279\u8058\u7814\u7a76\u5458\u9648\u5c0f\u6768\u3001\u6e05\u534e\u5927\u5b66\u4ea4\u53c9\u4fe1\u606f\u5b66\u9662\u52a9\u7406\u6559\u6388\u8881\u6d0b\u3001\u5357\u6d0b\u7406\u5de5\u5927\u5b66\u526f\u6559\u6388\u590f\u514b\u6797\u4e09\u4f4d\u8001\u5e08\uff0c\u5171\u540c\u53d1\u8d77\u201c\u4eba\u5de5\u667a\u80fd\u4e0e\u6570\u5b66\u201d\u8bfb\u4e66\u4f1a\uff0c\u5e0c\u671b\u4ece AI\u3000for\u3000Math\uff0cMath\u3000for\u3000AI \u4e24\u4e2a\u65b9\u9762\u6df1\u5165\u63a2\u8ba8\u4eba\u5de5\u667a\u80fd\u4e0e\u6570\u5b66\u7684\u5bc6\u5207\u8054\u7cfb\u3002\u8bfb\u4e66\u4f1a\u5df2\u5b8c\u7ed3\uff0c\u73b0\u5728\u62a5\u540d\u53ef\u52a0\u5165\u793e\u7fa4\u5e76\u89e3\u9501\u56de\u653e\u89c6\u9891\u6743\u9650\u3002<\/span><\/span><\/p>\n

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\"\u56fe\u7247\"<\/span><\/a><\/section>\n
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\u8be6\u60c5\u8bf7\u89c1\uff1a<\/span><\/p>\n

\u4eba\u5de5\u667a\u80fd\u4e0e\u6570\u5b66\u8bfb\u4e66\u4f1a\u542f\u52a8\uff1aAI for Math\uff0cMath for AI<\/a><\/span>
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\u63a8\u8350\u9605\u8bfb<\/span><\/strong><\/strong><\/strong><\/section>\n
<\/strong><\/section>\n
1. <\/strong>\u901a\u5f80\u5b6a\u751f\u8d28\u6570\u731c\u60f3\u7684\u57ab\u811a\u77f3\uff1a\u56fe\u8bba\u5e2e\u52a9\u6570\u5b66\u5bb6\u7834\u89e3\u8d28\u6570\u7684\u9634\u8c0b<\/a><\/strong><\/span><\/strong><\/section>\n
2. <\/strong>\u8457\u540d\u6570\u5b66\u5bb6\u963f\u8482\u4e9a\u53bb\u4e16\uff0c\u9ece\u66fc\u731c\u60f3\u8bc1\u660e\u7ee7\u7eed\u60ac\u7f6e<\/a><\/strong><\/span><\/strong><\/strong><\/section>\n
3. <\/strong>\u6570\u5b66\u5bb6\u8bc1\u660e\u76f8\u53d8\u7684\u5bf9\u79f0\u6027\uff1a\u4ece\u65cb\u8f6c\u5bf9\u79f0\u6027\u5230\u6807\u5ea6\u4e0d\u53d8\u6027<\/a><\/strong><\/span><\/strong><\/section>\n
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4. <\/strong><\/span>\u5f20\u6c5f\uff1a\u7b2c\u4e09\u4ee3\u4eba\u5de5\u667a\u80fd\u6280\u672f\u57fa\u7840\u2014\u2014\u4ece\u53ef\u5fae\u5206\u7f16\u7a0b\u5230\u56e0\u679c\u63a8\u7406 | \u96c6\u667a\u5b66\u56ed\u5168\u65b0\u8bfe\u7a0b<\/a><\/strong><\/strong><\/span><\/section>\n
<\/strong>5. <\/strong>\u89e3\u9501\u96c6\u667a\u5168\u7ad9\u5185\u5bb9\uff0c\u5f00\u542f\u65b0\u5e74\u5b66\u4e60\u8ba1\u5212<\/a><\/strong><\/section>\n

6. <\/strong>\u52a0\u5165\u96c6\u667a\uff0c\u4e00\u8d77\u590d\u6742\uff01<\/strong><\/span><\/a><\/p>\n

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\u70b9\u51fb\u201c\u9605\u8bfb\u539f\u6587\u201d\uff0c\u62a5\u540d\u8bfb\u4e66\u4f1a<\/span><\/section>\n<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

\u5bfc\u8bed \u5982\u679c\u8ba9\u4e00\u6839\u9488\u5728\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u65cb\u8f6c\uff0c\u904d\u5386\u6240\u6709\u65b9\u5411\uff0c\u5176\u626b\u8fc7\u533a\u57df\u7684\u6700\u5c0f\u4f53\u79ef\u662f\u591a\u5c11\uff1f\u6302\u8c37\u731c\u60f3\u770b\u4f3c\u5f62\u5f0f\u7b80\u5355\uff0c\u5374\u5df2\u7ecf\u56f0\u6270\u4e86\u6570\u5b66\u5bb6\u4eec\u957f\u8fbe\u534a\u4e2a\u4e16\u7eaa\u4e4b\u4e45\u3002\u5982\u4eca\uff0c\u7ebd\u7ea6\u5927\u5b66\u7684\u738b\u8679\u4e0e\u4e0d\u5217\u98a0\u54e5\u4f26\u6bd4\u4e9a\u5927\u5b66\u7684Joshua Zahl\u6210\u529f\u8bc1\u660e\u4e09\u7ef4\u60c5\u5f62\u4e0b\u7684\u6302\u8c37\u731c\u60f3\uff0c\u4e3a\u4e00\u7cfb\u5217\u76f8\u5173\u96be\u9898\u7684\u89e3\u51b3\u5e26\u6765\u4e86\u66d9\u5149\u3002 \u7814\u7a76\u9886\u57df\uff1a\u6302\u8c37\u731c\u60f3\u3001\u95f5\u53ef\u592b\u65af\u57fa\u7ef4…<\/p>\n","protected":false},"author":1,"featured_media":57389,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"special":[],"_links":{"self":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/57398"}],"collection":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=57398"}],"version-history":[{"count":0,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/57398\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/media\/57389"}],"wp:attachment":[{"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=57398"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=57398"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=57398"},{"taxonomy":"special","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fspecial&post=57398"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}