{"id":4724,"date":"2026-10-04T21:00:00","date_gmt":"2026-10-04T13:00:00","guid":{"rendered":"https:\/\/www.huanqiukexue.com\/?p=4724"},"modified":"2026-10-14T17:34:04","modified_gmt":"2026-10-14T09:34:04","slug":"%e7%8e%8b%e8%99%b9%e7%8e%8b%e8%80%85%e7%9a%84%e8%b8%8c%e8%ba%87%e4%b8%8e%e6%89%a7%e7%9d%80","status":"publish","type":"post","link":"https:\/\/www.huanqiukexue.com\/?p=4724","title":{"rendered":"\u738b\u8679:\u738b\u8005\u7684\u8e0c\u8e87\u4e0e\u6267\u7740"},"content":{"rendered":"<!-- wechat-archive:post:97825d23d829f46937d04617c464d388e8cf7ffd55f24915270cf02965ccda63:98c082cc4b574e3fb9f842cedcf13ac5 -->\n<section data-autoskip=\"1\" style=\"overflow: auto; line-height: 2.45; padding: 20px; border-radius: 5px; overflow-wrap: normal; color: #010101; background-color: #d5dce1;\"><span style=\"font-size: large;\"><span style=\"letter-spacing: 1px;\">\u738b\u8679\u51ed\u501f\u4e13\u6ce8\u3001\u6267\u7740\u4e0e\u654f\u9510\u7684\u6d1e\u89c1\uff0c\u5b8c\u6210\u4e86\u4e00\u9879\u201c\u767e\u5e74\u4e00\u9047\u201d\u7684\u8bc1\u660e\u3002\u5728\u8fd9\u7bc7\u6765\u81ea\u300a\u73af\u7403\u79d1\u5b66\u300b2026\u5e7410\u6708\u65b0\u520a\u7684\u6587\u7ae0\u4e2d\uff0c\u4f5c\u8005\u7eb3\u5854\u8389\u00b7\u6c83\u5c14\u4e54\u97e6\u5c14\u901a\u8fc7\u91c7\u8bbf\u8fd9\u4f4d\u5386\u53f2\u4e0a\u7b2c\u4e09\u4f4d\u8363\u83b7\u83f2\u5c14\u5179\u5956\u7684\u5973\u6027\uff0c\u4e3a\u6211\u4eec\u5448\u73b0\u4e86\u5979\u7684\u6570\u5b66\u4e4b\u65c5\u3002<\/span><\/span><\/section><p class=\"hq-byline\" style=\"color: rgb(153, 153, 153); font-size: 16px; letter-spacing: 1px;\">\u64b0\u6587\u00a0|\u00a0\u7eb3\u5854\u8389\u00b7\u6c83\u5c14\u4e54\u97e6\u5c14\uff08Natalie Wolchover\uff09<\/p><p class=\"hq-byline\" style=\"color: rgb(153, 153, 153); font-size: 16px; letter-spacing: 1px;\">\u7ffb\u8bd1\uff5c\u90ed\u6b22\u5e86<\/p><p class=\"hq-byline\" style=\"color: rgb(153, 153, 153); font-size: 16px; letter-spacing: 1px;\">\u5ba1\u6821\uff5c\u82d7\u957f\u5174<\/p><p>\u5728\u4eba\u4eec\u60f3\u8c61\u4e2d\uff0c\u6570\u5b66\u5bb6\u8bc1\u660e\u4e00\u9879\u91cd\u5927\u5b9a\u7406\u540e\uff0c\u5fc5\u5b9a\u4f1a\u6c89\u6d78\u5728\u72c2\u559c\u4e4b\u4e2d\u3002\u738b\u8679\u5e76\u6ca1\u6709\u8fd9\u79cd\u4f53\u9a8c\u30022025\u5e742\u6708\uff0c\u5979\u4e0e\u5408\u4f5c\u8005\u4e54\u8212\u4e9a\u00b7\u624e\u5c14\uff08Joshua Zahl\uff09\u5171\u540c\u53d1\u8868\u4e86\u4e00\u4efd\u957f\u8fbe127\u9875\u7684\u8bba\u6587\uff0c\u8bc1\u660e\u4e86\u4e00\u4e2a\u6a2a\u8de8\u591a\u4e2a\u6570\u5b66\u5206\u652f\u7684\u957f\u671f\u731c\u60f3\u3002\u5728\u53d1\u8868\u524d\u7684\u51e0\u4e2a\u6708\u91cc\uff0c\u4e24\u4eba\u53cd\u590d\u6838\u67e5\u8bba\u8bc1\uff0c\u8fd8\u5148\u628a\u8bba\u6587\u53d1\u7ed9\u5c11\u6570\u540c\u884c\u5ba1\u9605\uff0c\u76f4\u5230\u6700\u540e\u624d\u9f13\u8d77\u52c7\u6c14\u5c06\u5b83\u516c\u5f00\u3002\u6bd4\u8d77\u8bba\u8bc1\u672c\u8eab\u53ef\u80fd\u5b58\u5728\u6f0f\u6d1e\uff0c\u738b\u8679\u66f4\u62c5\u5fc3\u81ea\u5df1\u7684\u8868\u8ff0\u4e0d\u591f\u5b8c\u5584\uff0c\u5bfc\u81f4\u522b\u4eba\u770b\u4e0d\u61c2\u3002\u6ca1\u6709\u4eba\u53d1\u73b0\u4efb\u4f55\u9519\u8bef\u3002\u968f\u7740\u540c\u884c\u9010\u6e10\u6d88\u5316\u5e76\u7cbe\u7b80\u8fd9\u5957\u8bc1\u660e\u903b\u8f91\uff0c\u6240\u6709\u4eba\u90fd\u786e\u4fe1\u5176\u6b63\u786e\u65e0\u8bef\u2014\u2014<strong>\u738b\u8679\u548c\u624e\u5c14\uff0c\u771f\u7684\u8bc1\u660e\u4e86\u4e09\u7ef4\u6302\u8c37\u96c6\u731c\u60f3<\/strong>\uff08three-dimensional Kakeya conjecture\uff09\u3002<\/p><p>\u8fd9\u9879\u8bc1\u660e\u4e3a\u8fd9\u4f4d\u6765\u81ea\u4e2d\u56fd\u6842\u6797\u7684\u6570\u5b66\u5bb6\u5e26\u6765\u4e86\u4e00\u8fde\u4e32\u8363\u8a89\u30022025\u5e74\uff0c\u738b\u8679\u65a9\u83b7\u8428\u52d2\u59c6\u5956\uff08Salem Prize\uff09\u3001\u5965\u65af\u7279\u6d1b\u592b\u65af\u57fa\u5956\uff08Ostrowski Prize\uff09\u4ee5\u53ca\u4e16\u754c\u534e\u4eba\u6570\u5b66\u5bb6\u5927\u4f1a\u6570\u5b66\u91d1\u5956\u30022026\u5e74\u4e0a\u534a\u5e74\uff0c\u5979\u53c8\u63a5\u8fde\u5c06\u5b89\u4e1c\u5c3c\u5965\u00b7\u5b89\u5e03\u7f57\u585e\u8482\u5956\u7ae0\uff08Antonio Ambrosetti Medal\uff09\u3001\u8428\u591a\u65af\u57fa\u5956\uff08Sadosky Prize\uff09\u3001\u514b\u83b1\u7814\u7a76\u5956\uff08Clay Research Award\uff09\u548c\u6570\u5b66\u65b0\u89c6\u91ce\u5956\uff08New Horizons in Mathematics Prize\uff09\u6536\u5165\u56ca\u4e2d\u3002<strong>\u6700\u7ec8\uff0c\u5979\u6458\u5f97\u4e862026\u5e74\u83f2\u5c14\u5179\u5956\u7684\u6842\u51a0<\/strong>\u3002\u83f2\u5c14\u5179\u5956\u88ab\u516c\u8ba4\u4e3a\u6570\u5b66\u754c\u7684\u6700\u9ad8\u8363\u8a89\uff0c\u4e13\u95e8\u6388\u4e8840\u5c81\u4ee5\u4e0b\u6210\u5c31\u5353\u8457\u7684\u6570\u5b66\u5bb6\u300235\u5c81\u7684\u738b\u8679\u73b0\u4efb\u7f8e\u56fd\u7ebd\u7ea6\u5927\u5b66\u548c\u6cd5\u56fd\u9ad8\u7b49\u79d1\u5b66\u7814\u7a76\u9662\u6570\u5b66\u6559\u6388\uff0c\u4e5f\u662f\u83f2\u5c14\u5179\u595690\u5e74\u5386\u53f2\u4e0a\u7684\u7b2c\u4e09\u4f4d\u5973\u6027\u5f97\u4e3b\u3002<\/p><p>\u8363\u8a89\u5e26\u6765\u4e86\u5173\u6ce8\uff0c\u6f14\u8bb2\u3001\u5dee\u65c5\u548c\u91c7\u8bbf\u9080\u8bf7\u4e5f\u7eb7\u81f3\u6c93\u6765\uff0c\u5979\u5f88\u96be\u4e00\u4e00\u63a8\u8f9e\uff0c\u800c\u8fd9\u4e9b\u4e8b\u52a1\u4e0d\u53ef\u907f\u514d\u5730\u6324\u5360\u4e86\u5979\u505a\u7814\u7a76\u7684\u65f6\u95f4\u2014\u2014\u5979\u672c\u9700\u8981\u7528\u8fd9\u4e9b\u65f6\u95f4\u53bb\u601d\u8003\uff0c\u90a3\u4e9b\u6307\u5411\u4e0d\u540c\u65b9\u5411\u7684\u7ba1\u72b6\u96c6\uff08tube\uff09\u7a76\u7adf\u80fd\u91cd\u53e0\u5230\u4ec0\u4e48\u7a0b\u5ea6\u3002<\/p><p>\u8fd9\u6b63\u662f<strong>\u738b\u8679\u4e13\u653b\u7684\u201c\u6302\u8c37\u578b\u95ee\u9898\u201d<\/strong>\u7684\u6838\u5fc3\u6240\u5728\u3002\u8fd9\u7c7b\u95ee\u9898\u5904\u4e8e\u591a\u4e2a\u9886\u57df\u7684\u4ea4\u6c47\u4e2d\u5fc3\uff1a\u8c03\u548c\u5206\u6790\uff08\u7814\u7a76\u4fe1\u53f7\u5982\u4f55\u5206\u89e3\u4e3a\u4e0d\u540c\u9891\u7387\uff09\u3001\u51e0\u4f55\u6d4b\u5ea6\u8bba\uff08\u7814\u7a76\u975e\u5149\u6ed1\u7269\u4f53\u7684\u5f62\u72b6\u4e0e\u5c3a\u5bf8\uff09\u4ee5\u53ca\u504f\u5fae\u5206\u65b9\u7a0b\uff08\u63cf\u8ff0\u591a\u53d8\u91cf\u540c\u65f6\u53d8\u5316\u7684\u7cfb\u7edf\uff09\uff0c\u5e76\u4e0e\u6570\u8bba\u3001\u7ec4\u5408\u6570\u5b66\u7b49\u65b9\u5411\u606f\u606f\u76f8\u5173\u3002\u201c\u6b63\u662f\u8fd9\u79cd\u5e7f\u6cdb\u7684\u8054\u7cfb\uff0c\u4f7f\u5f97\u8be5\u9886\u57df\u5904\u4e8e\u5982\u6b64\u6838\u5fc3\u7684\u5730\u4f4d\uff0c\u4e5f\u8ba9\u738b\u8679\u7684\u5de5\u4f5c\u5907\u53d7\u91cd\u89c6\uff0c\u201d\u52a0\u62ff\u5927\u4e0d\u5217\u98a0\u54e5\u4f26\u6bd4\u4e9a\u5927\u5b66\u6570\u5b66\u5bb6\u5df4\u52c3\u7f57\u00b7\u65bd\u9ed8\u91d1\uff08Pablo Shmerkin\uff09\u8bc4\u4ef7\u9053\u3002<\/p><p>\u65e0\u9700\u5916\u51fa\u65f6\uff0c\u738b\u8679\u51e0\u4e4e\u5168\u8eab\u5fc3\u6295\u5165\u6570\u5b66\u7814\u7a76\uff0c\u4fdd\u6301\u7740\u8fd1\u4e4e\u82e6\u884c\u822c\u7684\u4e13\u6ce8\u548c\u81ea\u5f8b\u3002\u201c<strong>\u5979\u5bf9\u6570\u5b66\u7b80\u76f4\u5230\u4e86\u75f4\u8ff7\u7684\u5730\u6b65<\/strong>\uff0c\u201d\u5979\u7684\u5408\u4f5c\u8005\u3001\u7f8e\u56fd\u5370\u7b2c\u5b89\u7eb3\u5927\u5b66\u7684\u5434\u6f8d\u5764\u8bf4\uff0c\u201c\u5979\u7edd\u5bf9\u662f\u6211\u89c1\u8fc7\u6700\u62fc\u547d\u7684\u4eba\u4e4b\u4e00\u3002\u201d\u5979\u820d\u4e0d\u5f97\u628a\u65f6\u95f4\u82b1\u5728\u8bfb\u4e66\u6216\u517b\u72d7\u8fd9\u7c7b\u201c\u8017\u65f6\u201d\u7684\u7231\u597d\u4e0a\uff0c\u4f46\u4f1a\u62bd\u51fa\u65f6\u95f4\u966a\u4f34\u670b\u53cb\u3001\u7ec3\u4e60\u745c\u4f3d\uff0c\u4ee5\u53ca\u6e05\u6668\u53bb\u534e\u76db\u987f\u5e7f\u573a\u516c\u56ed\u6563\u6b65\uff0c\u770b\u4e00\u770b\u90a3\u91cc\u7684\u72d7\u3002<strong>\u8fd9\u4e9b\u7247\u523b\u80fd\u7a0d\u7a0d\u7f13\u89e3\u6570\u5b66\u7814\u7a76\u5e26\u7ed9\u5979\u7684\u538b\u529b\uff0c\u4ee5\u53ca\u4e0d\u65f6\u88ad\u6765\u7684\u81ea\u6211\u6000\u7591\u3002<\/strong><\/p><p><figure class=\"hq-figure\"><img decoding=\"async\" alt=\"\" class=\"wp-image-4725\" height=\"350\" loading=\"lazy\" src=\"https:\/\/www.huanqiukexue.com\/wp-content\/uploads\/2026\/10\/6afe354dc69e579b27f241a81c2a56d6306821634f19e467a3068813823016cb.png\" width=\"600\" srcset=\"https:\/\/www.huanqiukexue.com\/wp-content\/uploads\/2026\/10\/6afe354dc69e579b27f241a81c2a56d6306821634f19e467a3068813823016cb.png 600w, https:\/\/www.huanqiukexue.com\/wp-content\/uploads\/2026\/10\/6afe354dc69e579b27f241a81c2a56d6306821634f19e467a3068813823016cb-300x175.png 300w\" sizes=\"auto, (max-width: 600px) 100vw, 600px\" \/><\/figure>\u738b\u8679\u4e13\u6ce8\u7684\u201c\u6302\u8c37\u578b\u95ee\u9898\u201d\u4e0e\u8c03\u548c\u5206\u6790\u3001\u51e0\u4f55\u6d4b\u5ea6\u8bba\u3001\u504f\u5fae\u5206\u65b9\u7a0b\u4ee5\u53ca\u6570\u8bba\u3001\u7ec4\u5408\u6570\u5b66\u7b49\u65b9\u5411\u90fd\u6709\u8054\u7cfb\u3002\u56fe\u7247\u6765\u6e90\uff1a\u6731\u5229\u5b89 \u00b7 \u4f69\u5e03\u96f7\u5c14\uff08Julien Pebrel\uff09\/M.Y.O.P.<\/p><p>\u5bf9\u4ece\u77e5\u8bc6\u548c\u80fd\u529b\u4e0a\u83b7\u5f97\u786e\u5b9a\u611f\u7684\u6e34\u671b\uff0c\u4f3c\u4e4e\u5851\u9020\u4e86\u738b\u8679\u7684\u4eba\u751f\u8f68\u8ff9\u3002\u8fd9\u4e5f\u662f\u6570\u5b66\u5438\u5f15\u5979\u7684\u5730\u65b9\uff1a<strong>\u5728\u5979\u770b\u6765\uff0c\u6570\u5b66\u662f\u4e16\u4e0a\u6700\u4e0d\u5bb9\u7f6e\u7591\u7684\u4e8b\u7269<\/strong>\u3002\u5b8c\u6210\u8fd9\u9879\u91cc\u7a0b\u7891\u5f0f\u7684\u8bc1\u660e\u540e\uff0c\u738b\u8679\u6ca1\u6709\u4e13\u95e8\u82b1\u65f6\u95f4\u5e86\u795d\uff0c\u4e5f\u6ca1\u6709\u56e0\u6b64\u611f\u5230\u81ea\u8d1f\u3002\u4f46\u81f3\u5c11\u73b0\u5728\uff0c\u5979\u53ef\u4ee5\u65e0\u6bd4\u7b03\u5b9a\u5730\u8bf4\uff1a\u5728\u4e09\u7ef4\u7a7a\u95f4\u4e2d\uff0c\u6307\u5411\u5404\u4e2a\u65b9\u5411\u7684\u7ba1\u72b6\u96c6\u4e0d\u53ef\u80fd\u91cd\u53e0\u5f97\u592a\u5389\u5bb3\u3002<\/p><p class=\"has-text-align-center has-medium-font-size\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0);\"><span style=\"font-size: 24px; text-decoration: overline; caret-color: rgb(8,124,186); color: rgb(8,124,186);\"><strong><br\/><br\/>\u65e0\u5fe7\u5c11\u5e74\u65f6<\/strong><\/span><\/mark><\/strong><\/p><p>\u738b\u8679\u521d\u63a5\u89e6\u65f6\u6709\u4e9b\u6162\u70ed\uff0c\u4f46\u5f88\u5feb\u5c31\u80fd\u653e\u677e\u4e0b\u6765\u3002\u5979\u6234\u7740\u4e00\u526f\u73b3\u7441\u8272\u5706\u6846\u773c\u955c\uff0c\u89c6\u9891\u901a\u8bdd\u65f6\uff0c\u5979\u7684\u53cc\u624b\u5076\u5c14\u4f1a\u95ef\u5165\u753b\u9762\u2014\u2014\u4e24\u6839\u98df\u6307\u4e0a\u5404\u6234\u7740\u4e00\u679a\u6212\u6307\uff0c\u5de6\u624b\u94f6\u8272\uff0c\u53f3\u624b\u91d1\u8272\u3002\u63a5\u53d7\u91c7\u8bbf\u65f6\uff0c\u5979\u6b63\u5728\u7f8e\u56fd\u897f\u6d77\u5cb8\u62dc\u8bbf\u5408\u4f5c\u8005\u4e0e\u670b\u53cb\uff0c\u8ba1\u5212\u5728\u90a3\u91cc\u5f85\u4e0a\u51e0\u4e2a\u6708\u3002<strong>\u5979\u5766\u8a00\uff0c\u81ea\u5df1\u5c0f\u65f6\u5019\u7684\u751f\u6d3b\u5176\u5b9e\u65e0\u5fe7\u65e0\u8651\u5f97\u591a\u3002<\/strong><\/p><p>\u4e0a\u4e16\u7eaa90\u5e74\u4ee3\uff0c\u738b\u8679\u5728\u6842\u6797\u957f\u5927\u3002\u653e\u5b66\u56de\u5bb6\u540e\uff0c\u5979\u4f1a\u770b\u770b\u4e66\uff0c\u6bd4\u5982\u5e0c\u814a\u795e\u8bdd\u3001\u300a\u54c8\u5229\u00b7\u6ce2\u7279\u300b\u548c\u300a\u6307\u73af\u738b\u300b\uff0c\u4e5f\u4f1a\u770b\u770b\u7535\u89c6\uff0c\u6253\u6253\u4e52\u4e53\u7403\u6216\u8005\u7fbd\u6bdb\u7403\u3002\u5c3d\u7ba1\u7236\u6bcd\u90fd\u662f\u6559\u5e08\uff0c\u5374\u4ece\u672a\u5728\u5b66\u4e1a\u4e0a\u7ed9\u5979\u65bd\u52a0\u538b\u529b\u3002\u508d\u665a\uff0c\u4e00\u5bb6\u4e09\u53e3\u5e38\u4f1a\u5728\u6842\u6797\u8857\u5934\u6563\u6b65\u3002\u6842\u6797\u7fa4\u5cf0\u82cd\u7fe0\uff0c\u6f13\u6c5f\u7a7f\u57ce\u800c\u8fc7\uff0c\u5e38\u88ab\u8a89\u4e3a\u201c\u4e2d\u56fd\u6700\u7f8e\u201d\u7684\u57ce\u5e02\u4e4b\u4e00\u3002<\/p><p>\u8d77\u521d\uff0c\u6570\u5b66\u53ea\u662f\u5979\u4f17\u591a\u7231\u597d\u4e2d\u7684\u4e00\u9879\u3002\u6bcf\u6b21\u62ff\u5230\u65b0\u6570\u5b66\u8bfe\u672c\uff0c\u5979\u603b\u4f1a\u5728\u5f00\u5b66\u524d\u628a\u8bfe\u540e\u4e60\u9898\u5168\u90e8\u505a\u5b8c\uff0c\u4e4b\u540e\u518d\u53bb\u4e66\u5e97\u4e70\u66f4\u591a\u7684\u6570\u5b66\u4e66\uff0c\u628a\u91cc\u9762\u7684\u9898\u76ee\u4e5f\u4e00\u4e00\u89e3\u5f00\u3002<\/p><p>\u5979\u81f3\u4eca\u4ecd\u8bb0\u5f97\uff0c\u67d0\u4e00\u7ae0\u672b\u5c3e\u6709\u4e00\u9053\u8111\u7b4b\u6025\u8f6c\u5f2f\uff1a\u600e\u6837\u79cd7\u68f5\u6811\uff0c\u624d\u80fd\u6392\u51fa\u6700\u591a\u7684\u201c\u4e09\u6811\u4e00\u7ebf\u201d\uff1f<strong>\u8fd9\u4e2a\u95ee\u9898\u4e0e\u5979\u65e5\u540e\u7814\u7a76\u7684\u6302\u8c37\u578b\u95ee\u9898\u5f62\u6210\u4e86\u5947\u5999\u7684\u547c\u5e94<\/strong>\u3002\u5b83\u4eec\u90fd\u5c5e\u4e8e\u201c\u5173\u8054\u51e0\u4f55\u201d\uff08incidence geometry\uff09\u8303\u7574\uff0c\u63a2\u8ba8\u7684\u662f\u51e0\u4f55\u5bf9\u8c61\u5982\u4f55\u76f8\u4ea4\u3001\u91cd\u53e0\u2014\u2014\u5728\u8fd9\u9053\u9898\u91cc\u662f\u7ebf\uff08\u4e09\u68f5\u6811\u6392\u5217\u7684\u4e00\u884c\uff09\u4e0e\u70b9\uff08\u6811\uff09\u7684\u5173\u7cfb\u3002\u738b\u8679\u5f88\u5feb\u60f3\u51fa\u4e86\u7b54\u6848\uff1a\u79cd\u6210\u4e00\u4e2a\u7b49\u8fb9\u4e09\u89d2\u5f62\uff0c\u4e09\u4e2a\u9876\u70b9\u5404\u79cd\u4e00\u68f5\uff0c\u4e09\u6761\u8fb9\u7684\u4e2d\u70b9\u5404\u79cd\u4e00\u68f5\uff0c\u7b2c\u4e03\u68f5\u79cd\u5728\u6b63\u4e2d\u5fc3\u3002\u8fd9\u6837\u5c31\u80fd\u5f62\u62106\u884c\u6811\uff0c\u4e09\u6761\u8fb9\u5404\u4e00\u884c\uff0c\u4e2d\u95f4\u7a7f\u8fc7\u4e09\u884c\u3002<strong>\u5979\u6bd4\u8eab\u4e3a\u6570\u5b66\u6559\u5e08\u7684\u7236\u4eb2\u66f4\u5feb\u627e\u51fa\u4e86\u7b54\u6848\uff0c\u90a3\u65f6\u5979\u624d6\u5c81<\/strong>\u3002<\/p><p>\u968f\u7740\u65f6\u95f4\u63a8\u79fb\uff0c\u738b\u8679\u8d8a\u6765\u8d8a\u6b23\u8d4f\u6570\u5b66\u7684\u6c38\u6052\u6027\u3002\u5386\u53f2\u603b\u5728\u88ab\u4e0d\u65ad\u6539\u5199\uff0c\u5b66\u82f1\u8bed\u4e5f\u8ba9\u5979\u611f\u5230\u632b\u8d25\uff0c\u56e0\u4e3a\u4f8b\u5916\u4f3c\u4e4e\u548c\u89c4\u5219\u672c\u8eab\u4e00\u6837\u591a\u3002\u76f8\u6bd4\u4e4b\u4e0b\uff0c<strong>\u6570\u5b66\u5b9a\u7406\u663e\u5f97\u575a\u4e0d\u53ef\u6467<\/strong>\u3002\u201c\u4e0d\u4f1a\u6709\u4eba\u8dd1\u8fc7\u6765\u544a\u8bc9\u4f60\uff0c\u2018\u54e6\uff0c\u8fd9\u4e2a\u5b9a\u7406\u5176\u5b9e\u662f\u9519\u7684\u2019\uff0c\u201d\u5979\u8bf4\u3002<\/p><p>\u738b\u8679\u56de\u5fc6\u8bf4\uff0c\u7236\u6bcd\u4e00\u76f4\u5e0c\u671b\u5979\u80fd\u5c3d\u91cf\u8fc7\u666e\u901a\u4eba\u7684\u751f\u6d3b\u3002\u53ef\u5979\u53ea\u60f3\u5c3d\u53ef\u80fd\u591a\u5730\u5b66\u4e60\uff0c\u4e8e\u662f\u8fde\u8df3\u4e86\u51e0\u7ea7\u3002\u5230\u4e86\u521d\u4e2d\u5feb\u6bd5\u4e1a\u65f6\uff0c\u4e3a\u4e86\u8003\u8fdb\u6842\u6797\u7684\u4e00\u6240\u597d\u9ad8\u4e2d\uff0c\u6210\u7ee9\u53d8\u5f97\u81f3\u5173\u91cd\u8981\u3002\u738b\u8679\u5c06\u76ee\u6807\u9501\u5b9a\u5728\u5317\u4eac\u5927\u5b66\u6570\u5b66\u7cfb\u3002\u636e\u5979\u6240\u8bf4\uff0c2007\u5e74\u5317\u5927\u6570\u5b66\u7cfb\u5728\u5979\u6240\u5728\u7684\u7701\u4efd\u4ec5\u62db\u6536\u4e00\u540d\u5b66\u751f\uff0c\u5f55\u53d6\u5b8c\u5168\u4f9d\u636e\u9ad8\u8003\u6210\u7ee9\u3002\u9057\u61be\u7684\u662f\uff0c\u5979\u5e76\u6ca1\u6709\u5728\u540c\u5fd7\u613f\u7684\u8003\u751f\u4e2d\u62ff\u5230\u6700\u9ad8\u5206\u3002<\/p><p>\u4e0d\u8fc7\uff0c<strong>\u5979\u7684\u5206\u6570\u8db3\u4ee5\u8ba9\u5979\u8fdb\u5165\u5317\u4eac\u5927\u5b66\u5730\u7403\u79d1\u5b66\u7cfb\u5c31\u8bfb\uff0c\u5979\u8ba1\u5212\u5165\u5b66\u540e\u518d\u8f6c\u5230\u6570\u5b66\u7cfb<\/strong>\u3002\u5979\u7684\u5730\u7403\u7269\u7406\u5b66\u6559\u6388\u5f88\u652f\u6301\u5979\uff0c\u5e76\u5411\u5979\u5f3a\u8c03\u4e86\u6570\u5b66\u5bf9\u79d1\u5b66\u7684\u91cd\u8981\u6027\u3002\u4f8b\u5982\uff0c\u79d1\u5b66\u5bb6\u53ef\u4ee5\u5229\u7528\u5730\u9707\u6ce2\u7ed8\u5236\u5730\u7403\u5185\u90e8\u7ed3\u6784\u2014\u2014\u8fd9\u80cc\u540e\u7684\u90e8\u5206\u6570\u5b66\u5176\u5b9e\u4e5f\u4e0e\u6302\u8c37\u95ee\u9898\u606f\u606f\u76f8\u5173\uff0c\u53ea\u662f\u5979\u5f53\u65f6\u5e76\u4e0d\u77e5\u60c5\u3002\u5979\u523b\u82e6\u7528\u529f\uff0c\u6700\u7ec8\u5982\u613f\u4ee5\u507f\u8f6c\u4e86\u4e13\u4e1a\u3002\u5979\u8fd8\u8bb0\u5f97\uff0c\u7236\u4eb2\u66fe\u968f\u53e3\u8bc4\u4ef7\uff1a\u7814\u7a76\u53d8\u5316\u91cf\u3001\u6781\u9650\u3001\u6d4b\u5ea6\u548c\u903c\u8fd1\u7684\u5206\u6790\u5b66\uff0c\u8981\u6bd4\u6ee1\u662f\u62bd\u8c61\u7b26\u53f7\u7684\u4ee3\u6570\u5b66\u5bb9\u6613\u5f97\u591a\u3002\u738b\u8679\u504f\u504f\u751f\u51fa\u51e0\u5206\u9006\u53cd\u4e4b\u5fc3\uff0c\u9009\u62e9\u4e86\u4e3b\u653b\u4ee3\u6570\u3002<\/p><p>\u7531\u4e8e\u672c\u79d1\u6210\u7ee9\u5e76\u975e\u62d4\u5c16\uff0c\u5979\u4e00\u5ea6\u6000\u7591\u81ea\u5df1\u80fd\u5426\u8003\u4e0a\u7814\u7a76\u751f\u3002\u5c31\u5728\u8fd9\u65f6\uff0c\u6cd5\u56fd\u58f0\u671b\u6781\u9ad8\u3001\u9009\u62d4\u6781\u4e25\u683c\u7684\u5df4\u9ece\u7efc\u5408\u7406\u5de5\u5b66\u9662\u6d3e\u4ee3\u8868\u6765\u5230\u5317\u4eac\uff0c\u4e3a\u5176\u5b66\u58eb\u540e\u9879\u76ee\u7ec4\u7ec7\u62db\u751f\u8003\u8bd5\u30022011\u5e74\uff0c\u5979\u52a8\u8eab\u524d\u5f80\u6cd5\u56fd\u3002<\/p><p>\u95ee\u9898\u662f\uff0c\u5b66\u6821\u6240\u6709\u8bfe\u7a0b\u5747\u7528\u6cd5\u8bed\u6388\u8bfe\uff0c\u800c\u738b\u8679\u5f53\u65f6\u4e00\u53e5\u6cd5\u8bed\u4e5f\u4e0d\u4f1a\u3002\u5e78\u8fd0\u7684\u662f\uff0c\u7b2c\u4e00\u5b66\u671f\u6d89\u53ca\u7684\u6570\u5b66\u5185\u5bb9\u5979\u5927\u591a\u5df2\u7ecf\u5b66\u8fc7\u3002\u5979\u5e38\u548c\u8bf4\u6cd5\u8bed\u7684\u540c\u5b66\u4e00\u8d77\u5403\u996d\uff0c\u5b89\u9759\u5730\u503e\u542c\uff0c\u4e0d\u61c2\u5c31\u793c\u8c8c\u8bf7\u6559\u3002\u6e10\u6e10\u5730\uff0c\u5979\u542c\u61c2\u7684\u5185\u5bb9\u8d8a\u6765\u8d8a\u591a\u3002\u4e0e\u6b64\u540c\u65f6\uff0c<strong>\u5979\u5f00\u59cb\u4fee\u8bfb\u5206\u6790\u5b66\u8bfe\u7a0b\uff0c\u5e76\u53d1\u73b0\u81ea\u5df1\u5728\u8fd9\u4e2a\u9886\u57df\u6bd4\u4ee3\u6570\u66f4\u6709\u5929\u8d4b<\/strong>\u3002<\/p><figure class=\"hq-figure\"><img decoding=\"async\" alt=\"\" class=\"wp-image-4726\" height=\"289\" loading=\"lazy\" src=\"https:\/\/www.huanqiukexue.com\/wp-content\/uploads\/2026\/10\/7ac38394a88d12e8d9f2de0f96a1dee237dea81fcb40e73a21ef12758b2048ea.png\" width=\"600\" srcset=\"https:\/\/www.huanqiukexue.com\/wp-content\/uploads\/2026\/10\/7ac38394a88d12e8d9f2de0f96a1dee237dea81fcb40e73a21ef12758b2048ea.png 600w, https:\/\/www.huanqiukexue.com\/wp-content\/uploads\/2026\/10\/7ac38394a88d12e8d9f2de0f96a1dee237dea81fcb40e73a21ef12758b2048ea-300x145.png 300w\" sizes=\"auto, (max-width: 600px) 100vw, 600px\" \/><figcaption style=\"color: rgb(153, 153, 153); font-size: 16px; letter-spacing: 1px;\">\u5728\u6cd5\u56fd\u6c42\u5b66\u671f\u95f4\uff0c\u5979\u66fe\u77ed\u6682\u8f6c\u5411\u5efa\u7b51\u5b66\uff0c\u4f46\u6570\u5b66\u90a3\u4efd\u6e05\u6670\u800c\u7b03\u5b9a\u7684\u76ee\u6807\u611f\uff0c\u5f88\u5feb\u53c8\u5c06\u5979\u62c9\u56de\u4e86\u5206\u6790\u5b66\u7684\u4e16\u754c\u3002\u56fe\u7247\u6765\u6e90\uff1a\u6731\u5229\u5b89 \u00b7 \u4f69\u5e03\u96f7\u5c14\uff08Julien Pebrel\uff09\/M.Y.O.P.<\/figcaption><\/figure><p><strong>\u5c3d\u7ba1\u8bfe\u4e1a\u8868\u73b0\u4f18\u5f02\uff0c\u5979\u4ecd\u7136\u4e0d\u76f8\u4fe1\u81ea\u5df1\u6709\u80fd\u529b\u771f\u6b63\u4ece\u4e8b\u6570\u5b66\u7814\u7a76<\/strong>\u3002\u6709\u4e00\u4e2a\u5b66\u671f\uff0c<strong>\u5979\u751a\u81f3\u8f6c\u53bb\u5b66\u4e60\u5efa\u7b51<\/strong>\uff0c\u8fd8\u5230\u5df4\u9ece\u7684\u4e00\u5bb6\u5efa\u7b51\u4e8b\u52a1\u6240\u5b9e\u4e60\u3002\u201c\u90a3\u6bb5\u65e5\u5b50\u6ca1\u4ec0\u4e48\u538b\u529b\uff0c\u201d\u5979\u8bf4\uff0c\u201c\u4f46\u6211\u627e\u4e0d\u5230\u76ee\u6807\u3002\u201d<strong>\u4e8e\u662f\uff0c\u5979\u91cd\u65b0\u56de\u5230\u4e86\u6570\u5b66\u7684\u6000\u62b1<\/strong>\u3002\u201c\u6211\u51b3\u5b9a\u4e0d\u518d\u7ea0\u7ed3\u81ea\u5df1\u7a76\u7adf\u591f\u4e0d\u591f\u597d\uff0c\u53ea\u662f\u4e00\u5fc3\u628a\u95ee\u9898\u7406\u89e3\u900f\u5f7b\uff0c\u201d\u5979\u8bf4\u3002<\/p><p class=\"has-text-align-center has-medium-font-size\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0);\"><span style=\"font-size: 24px; text-decoration: overline; caret-color: rgb(8,124,186); color: rgb(8,124,186);\"><strong><br\/><br\/>\u7c98\u6027\u56f0\u5883<\/strong><\/span><\/mark><\/strong><\/p><p>2013\u5e74\uff0c\u738b\u8679\u5728\u9ebb\u7701\u7406\u5de5\u5b66\u9662\u505a\u7814\u7a76\u5b9e\u4e60\u65f6\uff0c\u542c\u4e86\u5206\u6790\u5b66\u5bb6\u62c9\u91cc\u00b7\u53e4\u601d\uff08Larry Guth\uff09\u7684\u62a5\u544a\u3002\u53e4\u601d\u8bb2\u8ff0\u4e86\u4ed6\u4e0e\u83b1\u65af\u5927\u5b66\u6570\u5b66\u5bb6\u5185\u8328\u00b7\u5361\u8328\uff08Nets Katz\uff09\u5408\u4f5c\u8bc1\u660e\u7684\u57c3\u5c14\u5fb7\u4ec0\u4e0d\u540c\u8ddd\u79bb\u95ee\u9898\uff08Erd\u0151s distinct distances problem\uff09\uff1a\u5e73\u9762\u4e0a\u4efb\u610f\u6709\u9650\u70b9\u96c6\u4e2d\uff0c\u70b9\u5bf9\u4e4b\u95f4\u6709\u591a\u5c11\u79cd\u4e0d\u540c\u7684\u8ddd\u79bb\uff1f\u53e4\u601d\u5c06\u95ee\u9898\u4e0e\u89e3\u6cd5\u5256\u6790\u5f97\u6781\u4e3a\u6e05\u6670\u3002\u738b\u8679\u53d1\u73b0\u81ea\u5df1\u80fd\u9886\u4f1a\u5176\u4e2d\u76f8\u5f53\u4e00\u90e8\u5206\u8bc1\u660e\uff0c\u8fd9\u8ba9\u5979\u6df1\u53d7\u9f13\u821e\u3002\u5979\u4e86\u89e3\u5230\uff0c\u8fd9\u4e2a\u95ee\u9898\u4e0e\u8bb8\u591a\u6027\u8d28\u76f8\u4f3c\u7684\u96be\u9898\u606f\u606f\u76f8\u5173\uff0c\u800c\u5b83\u4eec\u7684\u6838\u5fc3\u90fd\u662f\u5173\u8054\u51e0\u4f55\u3002\u6b21\u5e74\uff0c<strong>\u5979\u987a\u5229\u8fdb\u5165\u9ebb\u7701\u7406\u5de5\u5b66\u9662\u653b\u8bfb\u535a\u58eb\uff0c\u5e76\u9009\u62e9\u53e4\u601d\u4f5c\u4e3a\u5bfc\u5e08\uff0c\u4e00\u8d77\u653b\u514b\u6302\u8c37\u95ee\u9898\u7684\u76f8\u5173\u96be\u9898<\/strong>\u3002<\/p><p><strong>\u4e0d\u5230\u4e00\u5e74\uff0c\u4ed6\u4eec\u4fbf\u89e3\u51b3\u4e86\u6cd5\u5c14\u79d1\u7eb3\u8ddd\u79bb\u96c6\u95ee\u9898\uff08Falconer distance problem\uff09\u7684\u4e00\u4e2a\u7279\u4f8b\u3002<\/strong>\u8fd9\u4e2a\u95ee\u9898\u6bd4\u53e4\u601d\u548c\u5361\u8328\u66fe\u7814\u7a76\u8fc7\u7684\u57c3\u5c14\u5fb7\u4ec0\u8ddd\u79bb\u96c6\u95ee\u9898\u66f4\u96be\u3002\u738b\u8679\u8fd8\u5c06\u5085\u91cc\u53f6\u9650\u5236\u6027\u95ee\u9898\u7f6e\u4e8e\u5173\u8054\u51e0\u4f55\u7684\u6846\u67b6\u4e0b\u8fdb\u884c\u63a2\u7d22\uff0c\u5e76\u53d6\u5f97\u4e86\u65b0\u8fdb\u5c55\u3002\u201c\u8fd9\u4e2a\u95ee\u9898\u592a\u96be\u4e86\uff0c\u6781\u5c11\u6709\u4eba\u80fd\u63d0\u51fa\u65b0\u89c1\u89e3\uff0c\u6240\u4ee5\u4e00\u4e2a\u535a\u58eb\u751f\u80fd\u505a\u5230\uff0c\u5b9e\u5728\u4ee4\u4eba\u60ca\u8bb6\uff0c\u201d\u82f1\u56fd\u7231\u4e01\u5821\u5927\u5b66\u6570\u5b66\u5bb6\u4e54\u7eb3\u68ee\u00b7\u5e0c\u514b\u66fc\uff08Jonathan Hickman\uff09\u56de\u5fc6\u9053\uff0c\u201c\u6211\u5f53\u65f6\u7ed9\u5979\u53d1\u4e86\u5c01\u90ae\u4ef6\uff0c\u5c31\u5199\u4e86\u4e00\u4e2a\u5b57\u2018\u54c7\u2019\u3002\u201d<\/p><p>\u540c\u6837\u7814\u7a76\u8fc7\u6cd5\u5c14\u79d1\u7eb3\u8ddd\u79bb\u96c6\u95ee\u9898\u7684\u65bd\u9ed8\u91d1\uff0c\u5728\u9ebb\u7701\u7406\u5de5\u5b66\u9662\u62dc\u8bbf\u53e4\u601d\u65f6\u6ce8\u610f\u5230\u4e86\u738b\u8679\u7684\u624d\u534e\u3002\u4ed6\u8ba4\u4e3a\u738b\u8679\u4e0d\u4ec5\u6781\u5177\u521b\u9020\u529b\uff0c\u800c\u4e14\u5438\u6536\u65b0\u6280\u672f\u7684\u80fd\u529b\u6781\u5f3a\u3002\u5c3d\u7ba1\u63a5\u89e6\u5173\u8054\u51e0\u4f55\u624d\u4e0d\u4e45\uff0c\u5979\u5bf9\u8fd9\u4e2a\u9886\u57df\u4f3c\u4e4e\u5df2\u7ecf\u6709\u76f8\u5f53\u6df1\u5165\u7684\u7406\u89e3\u3002<\/p><p>\u5173\u8054\u51e0\u4f55\u9886\u57df\u672c\u5c31\u5728\u4e0d\u65ad\u6d8c\u73b0\u65b0\u5de5\u5177\uff0c\u738b\u8679\u5f88\u5feb\u53c8\u4ece\u51e0\u4f55\u6d4b\u5ea6\u8bba\u4e2d\u5f15\u5165\u4e86\u66f4\u591a\u5de5\u5177\uff0c\u8fd9\u4e9b\u662f\u5979\u5728\u4e0e\u65bd\u9ed8\u91d1\u5408\u4f5c\u7814\u7a76\u6cd5\u5c14\u79d1\u7eb3\u8ddd\u79bb\u96c6\u95ee\u9898\u65f6\u5b66\u5230\u7684\u3002\u65bd\u9ed8\u91d1\u7684\u591a\u5c3a\u5ea6\u5206\u6790\uff08multiscale analysis\uff09\u65b9\u6cd5\u7ed9\u4e86\u5979\u6781\u5927\u542f\u53d1\uff0c\u8fd9\u79cd\u65b9\u6cd5\u901a\u8fc7\u6bd4\u8f83\u4e0d\u540c\u5c3a\u5ea6\u4e0a\u7684\u73b0\u8c61\u6765\u5bfb\u627e\u77db\u76fe\u3002\u201c\u5979\u603b\u662f\u975e\u5e38\u8c26\u900a\uff0c\u627f\u8ba4\u6709\u4e9b\u60f3\u6cd5\u6e90\u81ea\u6211\u7684\u5de5\u4f5c\uff0c\u4f46\u5979\u4f1a\u4ee5\u6211\u5b8c\u5168\u65e0\u6cd5\u60f3\u8c61\u7684\u65b9\u5f0f\u5de7\u5999\u5e94\u7528\u5b83\u4eec\uff0c\u201d\u65bd\u9ed8\u91d1\u8bf4\u3002<\/p><p>2019\u5e74\uff0c\u738b\u8679\u4e0e\u53e4\u601d\u53ca\u7f8e\u56fd\u52a0\u5229\u798f\u5c3c\u4e9a\u5927\u5b66\u4f2f\u514b\u5229\u5206\u6821\u7684\u5f20\u745e\u7965\uff08Ruixiang Zhang\uff09\u5408\u4f5c\uff0c\u5171\u540c\u8bc1\u660e\u4e86\u5c40\u90e8\u5149\u6ed1\u6027\u731c\u60f3\uff08local smoothing conjecture\uff09\u7684\u4e8c\u7ef4\u60c5\u5f62\uff0c\u8fd9\u662f\u8c03\u548c\u5206\u6790\u7684\u201c\u5723\u676f\u201d\u4e4b\u4e00\uff0c\u8be5\u731c\u60f3\u65ad\u8a00\u6ce2\u52a8\u65b9\u7a0b\u7684\u89e3\u65e0\u6cd5\u5728\u957f\u65f6\u95f4\u5185\u5c06\u80fd\u91cf\u96c6\u4e2d\u5728\u4e00\u4e2a\u5c0f\u533a\u57df\u3002\u5979\u4e5f\u7531\u6b64\u5728\u6570\u5b66\u754c\u83b7\u5f97\u66f4\u5e7f\u6cdb\u7684\u5173\u6ce8\u3002<strong>\u540c\u5e74\uff0c\u535a\u58eb\u6bd5\u4e1a\u7684\u5979\u524d\u5f80\u666e\u6797\u65af\u987f\u9ad8\u7b49\u7814\u7a76\u9662\u505a\u535a\u58eb\u540e\u7814\u7a76\u5458\u3002<\/strong><\/p><p><strong>\u79bb\u5f00\u53e4\u601d\u540e\uff0c\u738b\u8679\u4e00\u5ea6\u62c5\u5fc3\u65e0\u6cd5\u72ec\u7acb\u505a\u51fa\u6210\u679c<\/strong>\u3002\u4f46\u6e10\u6e10\u5730\uff0c\u5979\u5f00\u59cb\u5efa\u7acb\u65b0\u7684\u5408\u4f5c\uff0c\u5e76\u5728\u66f4\u591a\u6302\u8c37\u578b\u95ee\u9898\u4e0a\u53d6\u5f97\u7a81\u7834\u3002\u6559\u804c\u62db\u8058\u59d4\u5458\u4f1a\u5f88\u5feb\u6ce8\u610f\u5230\u4e86\u5979\u30022021\u5e74\uff0c\u5979\u83b7\u5f97\u52a0\u5229\u798f\u5c3c\u4e9a\u5927\u5b66\u6d1b\u6749\u77f6\u5206\u6821\u7684\u6559\u804c\u30022023\u5e74\uff0c\u5979\u6210\u4e3a\u7ebd\u7ea6\u5927\u5b66\u7684\u526f\u6559\u6388\u3002<strong>\u5165\u804c\u4ec5\u4e00\u4e2a\u6708\uff0c\u5979\u629b\u51fa\u4e00\u9879\u91cd\u78c5\u6210\u679c<\/strong>\uff1a\u4e0e\u51ef\u6587\u00b7\u4efb\uff08Kevin Ren\uff09\u5171\u540c\u8bc1\u660e\u4e86\u4e8c\u7ef4\u5f17\u65af\u6ed5\u4f2f\u683c\u96c6\u731c\u60f3\uff082D Furstenberg set conjecture\uff09\uff0c\u8be5\u731c\u60f3\u523b\u753b\u4e86\u5e73\u9762\u4e0a\u5305\u542b\u6240\u6709\u65b9\u5411\u7ebf\u6bb5\u7684\u70b9\u96c6\u7684\u7ef4\u6570\u3002<strong>\u5c3d\u7ba1\u6210\u5c31\u6590\u7136\uff0c\u738b\u8679\u5374\u59cb\u7ec8\u89c9\u5f97\u81ea\u5df1\u4e0d\u591f\u4f18\u79c0<\/strong>\u3002\u201c\u6bcf\u6b21\u90fd\u89c9\u5f97\u53ea\u662f\u8fd0\u6c14\u597d\uff0c\u201d\u5979\u8fd9\u6837\u8bc4\u4ef7\u81ea\u5df1\u7684\u5404\u9879\u5de5\u4f5c\u3002<\/p><p>\u6b63\u662f\u5728\u75ab\u60c5\u671f\u95f4\uff0c\u8fd8\u5728\u666e\u6797\u65af\u987f\u9ad8\u7b49\u7814\u7a76\u9662\u65f6\uff0c<strong>\u738b\u8679\u51b3\u5b9a\u5c06\u76ee\u5149\u8f6c\u5411\u4e09\u7ef4\u6302\u8c37\u96c6\u731c\u60f3<\/strong>\u3002\u51e0\u5341\u5e74\u6765\uff0c\u8fd9\u4e2a\u95ee\u9898\u96be\u5012\u4e86\u65e0\u6570\u6311\u6218\u8005\u3002\u751a\u81f3\u66fe\u6709\u4eba\u5ba3\u5e03\u5df2\u5b8c\u6210\u8bc1\u660e\uff0c\u6700\u540e\u5374\u88ab\u53d1\u73b0\u5176\u4e2d\u5b58\u5728\u9519\u8bef\u3002\u201c\u6211\u4e00\u76f4\u6ca1\u80fd\u89e3\u51b3\u6302\u8c37\u731c\u60f3\uff0c\u4f46\u6709\u56db\u4e94\u6b21\uff0c\u6211\u90fd\u4ee5\u4e3a\u81ea\u5df1\u5feb\u505a\u5230\u4e86\uff0c\u201d\u53e4\u601d\u8bf4\u3002\u6bcf\u4e00\u6b21\uff0c\u4ed6\u90fd\u5728\u516c\u5f00\u53d1\u8868\u524d\u53d1\u73b0\u4e86\u9519\u8bef\u3002<\/p><p><figure class=\"hq-figure\"><img decoding=\"async\" alt=\"\" class=\"wp-image-4727\" height=\"450\" loading=\"lazy\" src=\"https:\/\/www.huanqiukexue.com\/wp-content\/uploads\/2026\/10\/e793a981c91658da6472418427b2d461bdcb59c3c04988294c2ecb3186214aa0.png\" width=\"600\" srcset=\"https:\/\/www.huanqiukexue.com\/wp-content\/uploads\/2026\/10\/e793a981c91658da6472418427b2d461bdcb59c3c04988294c2ecb3186214aa0.png 600w, https:\/\/www.huanqiukexue.com\/wp-content\/uploads\/2026\/10\/e793a981c91658da6472418427b2d461bdcb59c3c04988294c2ecb3186214aa0-300x225.png 300w\" sizes=\"auto, (max-width: 600px) 100vw, 600px\" \/><\/figure>\u738b\u8679\u4e0e\u6570\u5b66\u5bb6\u5f17\u5170\u514b \u00b7 \u6885\u5c14\uff08Frank Merle\uff09\u8fb9\u559d\u8336\u8fb9\u4ea4\u8c08\u3002\u5728\u8bc1\u660e\u4e09\u7ef4\u6302\u8c37\u96c6\u731c\u60f3\u4e4b\u524d\uff0c\u5979\u5df2\u901a\u8fc7\u4e00\u8fde\u4e32\u91cd\u78c5\u5408\u4f5c\u6210\u679c\u5efa\u7acb\u8d77\u81ea\u5df1\u7684\u58f0\u8a89\u3002\u56fe\u7247\u6765\u6e90\uff1a\u6731\u5229\u5b89 \u00b7 \u4f69\u5e03\u96f7\u5c14\uff08Julien Pebrel\uff09\/M.Y.O.P.<\/p><p><strong>\u738b\u8679\u8bfb\u5230\u4e86\u52a0\u5229\u798f\u5c3c\u4e9a\u5927\u5b66\u6d1b\u6749\u77f6\u5206\u6821\u6570\u5b66\u5bb6\u9676\u54f2\u8f69\uff08Terence Tao\uff09\u57282014\u5e74\u53d1\u8868\u7684\u4e00\u7bc7\u535a\u5ba2<\/strong>\uff0c\u6587\u4e2d\u9610\u8ff0\u4e86\u4e00\u5957\u9676\u54f2\u8f69\u548c\u5361\u8328\u6784\u601d\u5374\u672a\u7ee7\u7eed\u63a8\u8fdb\u7684\u8bc1\u660e\u7b56\u7565\u3002\u738b\u8679\u89c9\u5f97\u8fd9\u6761\u601d\u8def\u5f88\u6709\u5e0c\u671b\uff0c\u4e8e\u662f\u5979\u8054\u7cfb\u4e86\u5f53\u65f6\u5728\u4e0d\u5217\u98a0\u54e5\u4f26\u6bd4\u4e9a\u5927\u5b66\u7684\u624e\u5c14\u2014\u2014\u4ed6\u7684\u535a\u58eb\u8bba\u6587\u540c\u6837\u6d89\u53ca\u6302\u8c37\u578b\u95ee\u9898\u7684\u82e5\u5e72\u65b9\u9762\u3002<strong>\u4e24\u4eba\u51b3\u5b9a\u8054\u624b\uff0c\u6cbf\u7740\u9676\u54f2\u8f69\u548c\u5361\u8328\u7684\u8bbe\u60f3\u6df1\u5165\u63a2\u7d22\u3002<\/strong><\/p><p>\u8fd9\u6761\u8def\u7ebf\u6700\u7ec8\u9700\u8981\u52a8\u7528\u5e9e\u5927\u7684\u6570\u5b66\u5de5\u5177\u5e93\u3002\u4f46\u5176\u6838\u5fc3\u601d\u8def\u662f\u8bc1\u660e\uff1a\u4efb\u4f55\u9488\u5bf9\u8be5\u731c\u60f3\u7684\u5047\u8bbe\u6027\u53cd\u4f8b\u2014\u2014\u5373\u4e00\u79cd\u53ef\u80fd\u5c06\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u6307\u5411\u5404\u4e2a\u65b9\u5411\u7684\u7ebf\u6bb5\u6324\u538b\u5230\u5c0f\u4e8e\u4e09\u4e2a\u7ef4\u5ea6\u7684\u65b9\u6cd5\u2014\u2014\u90fd\u5fc5\u987b\u5177\u5907\u6781\u5176\u521a\u6027\u4e14\u6709\u6548\u7684\u7ed3\u6784\uff0c\u4ee5\u81f3\u4e8e\u4f1a\u4e0e\u652f\u914d\u52a0\u6cd5\u4e0e\u4e58\u6cd5\u76f8\u4e92\u4f5c\u7528\u7684\u5b9a\u7406\uff08sum-product 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class=\"hq-figure\"><img decoding=\"async\" alt=\"\" class=\"wp-image-4728\" height=\"431\" loading=\"lazy\" src=\"https:\/\/www.huanqiukexue.com\/wp-content\/uploads\/2026\/10\/fd767263c850439c8bbbdec97fec95363bfe6f6ef0ee98cbaa5123fd5c5017cb.png\" width=\"600\" srcset=\"https:\/\/www.huanqiukexue.com\/wp-content\/uploads\/2026\/10\/fd767263c850439c8bbbdec97fec95363bfe6f6ef0ee98cbaa5123fd5c5017cb.png 600w, https:\/\/www.huanqiukexue.com\/wp-content\/uploads\/2026\/10\/fd767263c850439c8bbbdec97fec95363bfe6f6ef0ee98cbaa5123fd5c5017cb-300x216.png 300w\" sizes=\"auto, (max-width: 600px) 100vw, 600px\" \/><figcaption style=\"color: rgb(153, 153, 153); font-size: 16px; letter-spacing: 1px;\">\u56fe\u7247\u6765\u6e90\uff1a\u6731\u5229\u5b89 \u00b7 \u4f69\u5e03\u96f7\u5c14\uff08Julien Pebrel\uff09\/M.Y.O.P.<\/figcaption><\/figure><p>2024\u5e74\u521d\uff0c\u8ddd\u79bb\u4e24\u4eba\u6b63\u5f0f\u5f00\u542f\u8fd9\u9879\u7814\u7a76\u5df2\u8fc7\u53bb\u56db\u5e74\uff0c\u8fd9\u5957\u590d\u6742\u7684\u5f52\u7eb3\u903b\u8f91\u4f3c\u4e4e\u771f\u7684\u8d70\u901a\u4e86\uff0c\u4f46\u738b\u8679\u548c\u624e\u5c14\u8c01\u4e5f\u4e0d\u6562\u8f7b\u6613\u4e0b\u7ed3\u8bba\u3002\u201c\u8fd9\u4e48\u56f0\u96be\u7684\u95ee\u9898\uff0c\u6211\u51ed\u4ec0\u4e48\u80fd\u89e3\u51fa\u6765\uff1f\u201d\u738b\u8679\u8bf4\uff0c\u201c\u4f60\u5f53\u7136\u4f1a\u6000\u7591\u3002\u4f46\u8bba\u8bc1\u7684\u8fc7\u7a0b\u53c8\u663e\u5f97\u90a3\u4e48\u81ea\u7136\u3002\u201d<strong>\u5979\u80fd\u5728\u8111\u6d77\u4e2d\u6e05\u6670\u5730\u63a8\u6f14\u6574\u4e2a\u903b\u8f91<\/strong>\uff1a\u67d0\u4e00\u5c3a\u5ea6\u7684\u7ba1\u72b6\u96c6\uff0c\u5728\u66f4\u5927\u5c3a\u5ea6\u4e0a\u53d8\u6210\u677f\u6761\uff08plank\uff09\uff0c\u518d\u6269\u5c55\u4e3a\u586b\u6ee1\u6574\u4e2a\u4f53\u79ef\u7684\u5e73\u677f\u5c42\uff08slab\uff09\u3002<strong>\u8fd9\u4e9b\u5f62\u72b6\u76f8\u4e92\u6f14\u5316\u7684\u65b9\u5f0f\u8ba9\u5979\u786e\u4fe1\uff0c\u6302\u8c37\u96c6\u5fc5\u7136\u662f\u4e09\u7ef4\u7684<\/strong>\u3002\u4e0d\u8fc7\uff0c\u53c8\u8fc7\u4e86\u4e00\u5e74\uff0c\u738b\u8679\u548c\u624e\u5c14\u624d\u5c06\u8bc1\u660e\u516c\u4e4b\u4e8e\u4f17\u3002<\/p><p 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