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\r\n\u671b\u6708\u65b0\u4e00\u9047\u5230\u7684\u60c5\u51b5\u5374\u6709\u70b9\u4e0d\u540c\u3002\u4ed6\u5df2\u7ecf\u5728ABC\u731c\u60f3\u7684\u8bc1\u660e\u5de5\u4f5c\u4e0a\u72ec\u81ea\u601d\u8003\u4e8620\u5e74\uff0c\u5efa\u7acb\u8d77\u4e86\u4ed6\u79f0\u4e4b\u4e3a\u201c\u5b87\u5b99\u969bTeichm\u00fcller\u7406\u8ad6\u201d\u7684\u65b0\u4e16\u754c\uff0c\u5b9a\u4e49\u4e86\u5404\u79cd\u524d\u6240\u672a\u6709\u7684\u795e\u79d8\u672f\u8bed\uff0c\u6bd4\u5982\u7b2c\u4e00\u7bc7\u8bba\u6587\u8bb2\u4e86\u201c\u970d\u5947\u5f71\u9662\u201d\uff08Hodge Theater\uff09\u7684\u6784\u9020\uff0c\u7b2c\u4e8c\u7bc7\u8bba\u6587\u5219\u5f15\u5165\u4e86\u201c\u5916\u661f\u7b97\u6570\u5168\u7eaf\u7ed3\u6784\u201d\uff08alien arithmetic holomorphic structures\uff09\u3002
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\r\n\r\n\u8d28\u6570\u87ba\u65cb
\r\n\u518d\u8005\uff0cABC\u731c\u60f3\u548c\u5176\u4ed6\u5f88\u591a\u6570\u8bba\u4e2d\u7684\u672a\u89e3\u95ee\u9898\u6709\u7740\u91cd\u5927\u8054\u7cfb\u3002
\r\n\r\n\u6bd4\u5982\u521a\u624d\u63d0\u5230\u7684\u4e22\u756a\u56fe\u65b9\u7a0b\u95ee\u9898\u3001\u8d39\u9a6c\u6700\u540e\u5b9a\u7406\u7684\u63a8\u5e7f\u731c\u60f3\u3001Mordell\u731c\u60f3\u3001Erd\u0151s\u2013Woods\u731c\u60f3\uff0c\u7b49\u7b49\u7b49\u7b49\u3002\u800c\u4e14\uff0cABC\u731c\u60f3\u8fd8\u80fd\u95f4\u63a5\u63a8\u5bfc\u51fa\u5f88\u591a\u5df2\u88ab\u8bc1\u660e\u7684\u91cd\u8981\u7ed3\u679c\uff0c\u6bd4\u5982\u8d39\u9a6c\u6700\u540e\u5b9a\u7406\u3002\u4ece\u8fd9\u4e2a\u89d2\u5ea6\u6765\u8bb2\uff0cABC\u731c\u60f3\u662f\u8d28\u6570\u7ed3\u6784\u7684\u672a\u77e5\u5b87\u5b99\u7684\u5f3a\u529b\u63a2\u6d4b\u5668\uff0c\u4ec5\u6b21\u4e8e\u9ece\u66fc\u731c\u60f3\u3002
\r\n\r\n\u5176\u6b21\uff0c\u6211\u4eec\u6765\u770b\u671b\u6708\u7528\u4e86\u4ec0\u4e48\u6570\u5b66\u5de5\u5177\u6765\u89e3\u51b3ABC\u731c\u60f3\u3002
\r\n\r\n\u671b\u6708\u5f00\u59cb\u57cb\u5934\u7814\u7a76ABC\u731c\u60f3\u7684\u8bc1\u660e\u65f6\uff0c\u8ddd\u731c\u60f3\u63d0\u51fa\u4e0d\u8fc710\u5e74\uff0c\u800c\u4e14\u51e0\u4e4e\u6ca1\u6709\u4efb\u4f55\u8fdb\u5c55\uff0c\u671b\u6708\u53ef\u4ee5\u8bf4\u662f\u51e0\u4e4e\u4ece\u96f6\u5f00\u59cb\u7684\u3002\u4e4b\u6240\u4ee5\u8bf4 \u201c\u51e0\u4e4e\u201d\uff0c\u662f\u56e0\u4e3a\u671b\u670820\u591a\u5c81\u65f6\uff0c\u5728\u201c\u8fdc\u963f\u8d1d\u5c14\u51e0\u4f55\u201d[1]\u9886\u57df\u4e2d\u4f5c\u51fa\u8fc7\u8d85\u5353\u8d21\u732e\uff0c\u8fd8\u88ab\u9080\u8bf7\u52304\u5e74\u4e00\u5c4a\u7684\u56fd\u9645\u6570\u5b66\u5bb6\u5927\u4f1a\u4e0a\u6f14\u8bb2\u3002\u7136\u800c\uff0c1988\u5e74\u67cf\u6797\u7684\u6570\u5b66\u5bb6\u5927\u4f1a\u7ed3\u675f\u4e4b\u540e\uff0c\u671b\u6708\u5c31\u4ece\u5b66\u672f\u754c\u6d88\u5931\uff0c\u6f5c\u5fc3\u4e8e\u4ed6\u81ea\u5df1\u7684\u5b87\u5b99\u53bb\u8bc1\u660eABC\u731c\u60f3\u4e86\u3002\u4ed6\u7528\u7684\u7406\u8bba\u5de5\u5177\uff0c\u6b63\u662f\u201c\u8fdc\u963f\u8d1d\u5c14\u51e0\u4f55\u201d\u3002
\r\n\r\n\u53ef\u4ee5\u8bf4\uff0c\u671b\u6708\u8bc1\u660eABC\u731c\u60f3\u7684\u76ee\u7684\u4e4b\u4e00\uff0c\u5c31\u662f\u8981\u628a\u8fdc\u963f\u8d1d\u5c14\u51e0\u4f55\u53d1\u626c\u5149\u5927\u3002\u8fdc\u963f\u8d1d\u5c14\u51e0\u4f55\u8fd9\u4e2a\u6570\u5b66\u5206\u652f\uff0c\u7531\u4ee3\u6570\u51e0\u4f55\u6559\u7687\u683c\u7f57\u817e\u8fea\u514b\u4e8e\u4e0a\u4e2a\u4e16\u7eaa80\u5e74\u4ee3\u521b\u5efa\uff0c\u7814\u7a76\u5bf9\u8c61\u662f\u4e0d\u540c\u51e0\u4f55\u7269\u4f53\u4e0a\u7684\u4ee3\u6570\u7c07\u7684\u57fa\u672c\u7fa4\u7684\u7ed3\u6784\u76f8\u4f3c\u6027\u3002
\r\n\r\n\u5728\u5bcc\u6709\u4f20\u5947\u8272\u5f69\u7684\u4e3d\u6c83\u592b\u5496\u5561\u9986\uff0c\u8fd1\u4ee3\u5206\u6790\u5b66\u4e4b\u7236\u5df4\u7eb3\u8d6b\u8bf4\uff1a\u201c\u6570\u5b66\u5bb6\u80fd\u627e\u5230\u5b9a\u7406\u4e4b\u95f4\u7684\u76f8\u4f3c\u4e4b\u5904\uff0c\u4f18\u79c0\u7684\u6570\u5b66\u5bb6\u80fd\u770b\u5230\u8bc1\u660e\u4e4b\u95f4\u7684\u76f8\u4f3c\u4e4b\u5904\uff0c\u5353\u8d8a\u7684\u6570\u5b66\u5bb6\u80fd\u5bdf\u89c9\u5230\u6570\u5b66\u5206\u652f\u4e4b\u95f4\u7684\u76f8\u4f3c\u4e4b\u5904\u3002\u6700\u540e\uff0c\u7a76\u7ea7\u7684\u6570\u5b66\u5bb6\u80fd\u4fef\u77b0\u8fd9\u4e9b\u76f8\u4f3c\u4e4b\u5904\u4e4b\u95f4\u7684\u76f8\u4f3c\u4e4b\u5904\u3002\u201d \u683c\u7f57\u817e\u8fea\u514b\uff0c\u4fbf\u843d\u5165\u4e86\u5df4\u7eb3\u8d6b\u5206\u7c7b\u7684\u7a76\u7ea7\u6570\u5b66\u5bb6\u4e4b\u5217\uff0c\u8fdc\u963f\u8d1d\u5c14\u51e0\u4f55\u4fbf\u662f\u4e00\u95e8\u7814\u7a76\u201c\u76f8\u4f3c\u4e4b\u76f8\u4f3c\u201d\u7684\u6570\u5b66\u5206\u652f\uff1a 16\u4e16\u7eaa\uff0c\u7684\u5361\u5c14\u8fbe\u8bfa\u7814\u7a763\u6b21\u65b9\u7a0b\u6c42\u6839\uff1b19\u4e16\u7eaa\uff0c\u4f3d\u7f57\u74e6\u53d1\u73b0\u7279\u6b8a\u9ad8\u6b21\u65b9\u7a0b\u89e3\u7684\u7fa4\u7ed3\u6784\uff1b\u4ee3\u6570\u51e0\u4f55\u4e2d\u7684\u4ee3\u6570\u7c07\uff0c\u5219\u662f\u4e00\u5927\u7c7b\u65b9\u7a0b\u7684\u516c\u5171\u89e3\uff1b\u4ee3\u6570\u7c07\u7684\u57fa\u672c\u7fa4\uff0c\u5219\u662f\u5bf9\u4e8e\u5df2\u7ecf\u7efc\u5408\u4e86\u4e00\u5927\u7c7b\u7406\u8bba\u7684\u4ee3\u6570\u7c07\u7406\u8bba\u7684\u518d\u4e00\u6b21\u7efc\u5408\uff0c\u5173\u5fc3\u4ec0\u4e48\u6837\u7684\u7ed3\u6784\u72ec\u7acb\u4e8e\u51e0\u4f55\u7269\u4f53\u7684\u4ee3\u6570\u7c07\u7684\u8868\u8c61\u4e4b\u5916\u3002
\r\n\r\n\u7403\u5c04\u5f71\u7a7a\u95f4\u4e0a\u7684\u4ee3\u6570\u7c07
\r\n\u4e8e\u662f\u4e4e\uff0c\u5bf9\u4e8e\u6570\u5b66\u5bb6\u6765\u8bf4\uff0c\u68c0\u67e5\u671b\u6708\u7684\u8bc1\u660e\u662f\u5426\u5b58\u5728\u9519\u6f0f\u7684\u53e6\u5916\u4e00\u4e2a\u96be\u9898\u5c31\u662f\uff1a\u8981\u900f\u5f7b\u7406\u89e3\u671b\u6708\u90a3512\u9875\u7684ABC\u731c\u60f3\u7684\u8bc1\u660e\uff0c\u9700\u8981\u5148\u5f04\u61c2\u671b\u6708\u5173\u4e8e\u8fdc\u963f\u8d1d\u5c14\u51e0\u4f55\u7684750\u9875\u7684\u8457\u4f5c\uff01\u5168\u4e16\u754c\u603b\u5171\u53ea\u6709\u7ea650\u540d\u6570\u5b66\u5bb6\u5728\u8fd9\u65b9\u9762\u6709\u8db3\u591f\u7684\u80cc\u666f\u77e5\u8bc6\u53bb\u901a\u8bfb\u671b\u6708\u8fd9\u672c\u8fdc\u963f\u8d1d\u5c14\u51e0\u4f55\u8457\u4f5c\uff0c\u66f4\u522b\u63d0\u671b\u6708\u5728\u8bc1\u660e\u731c\u60f3\u4e2d\u5efa\u7acb\u8d77\u6765\u7684\u201c\u5b87\u5b99\u969bTeichm\u00fcller\u7406\u8ad6\u201d\u4e86\u3002\u76ee\u524d\u4e3a\u6b62\uff0c\u81ea\u79f0\u201c\u5b87\u5b99\u969b\u5e7e\u4f55\u5b78\u8005\u201d\u7684\u671b\u6708\uff0c\u662f\u4ed6\u81ea\u5df1\u521b\u9020\u51fa\u7684\u5b87\u5b99\u4e2d\u7684\u72ec\u884c\u8005\u3002
\r\n\r\n\u4e4b\u524d\u63d0\u5230\u7684\u671b\u6708\u7684\u597d\u53cb\u3001\u725b\u6d25\u5927\u5b66\u6559\u6388\u91d1\u660e\u8fe5\u8bf4\uff1a\u201c\u8bfb\u8bc1\u660e\uff0c\u5bf9\u6570\u5b66\u5bb6\u6765\u8bf4\uff0c\u4e5f\u662f\u975e\u5e38\u75db\u82e6\u7684\u3002\u8bf4\u670d\u5927\u591a\u6570\u4ee3\u6570\u51e0\u4f55\u5b66\u8005\u53bb\u9605\u8bfb\u9700\u8981\u5982\u6b64\u4e4b\u591a\u57fa\u7840\u77e5\u8bc6\u7684\u8bc1\u660e\uff0c\u66f4\u662f\u4e00\u4ef6\u96be\u4e8b\u3002\u201d \u5f53\u7136\uff0c\u8fd9\u5e76\u4e0d\u4ee3\u8868\u6ca1\u6709\u6570\u5b66\u5bb6\u5728\u68c0\u67e5\u671b\u6708\u7684\u8bc1\u660e\uff0c2012\u5e7410\u6708\uff0c\u65af\u5766\u798f\u5927\u5b66\u6559\u6388Akshay Venkatesh\u51fd\u81f3\u671b\u6708\uff0c\u6307\u51fa\u7b2c3\u7bc7\u548c\u7b2c4\u7bc7\u8bba\u6587\u4e2d\u7684\u9519\u8bef\u3002\u671b\u6708\u4e5f\u8fc5\u901f\u7b54\u590d\uff0c\u627f\u8ba4\u4e86\u9519\u8bef\uff0c\u5e76\u8bf4\u660e\u8be5\u9519\u8bef\u5bf9\u6574\u4f53\u7406\u8bba\u5e76\u65e0\u5f71\u54cd\u3002
\r\n\r\n\u8bc1\u660e\u53d1\u8868\u4e4b\u540e\uff0c\u6000\u7591\u4e4b\u58f0\u4e0d\u7edd\u4e8e\u8033\u3002\u56e0\u4e3a\u4ece\u76f4\u89c9\u4e0a\u6765\u8bb2\uff0cABC\u731c\u60f3\u5982\u679c\u88ab\u8bc1\u660e\u6b63\u786e\uff0c\u5bf9\u4e8e\u6570\u8bba\u7684\u5f71\u54cd\u4e4b\u5de8\u5927\uff0c\u65e0\u5f02\u4e8e\u76f8\u5bf9\u8bba\u548c\u91cf\u5b50\u7269\u7406\u4e4b\u4e8e\u73b0\u4ee3\u7269\u7406\u5b66\u3002\u6709\u4e9b\u4eba\u8ba4\u4e3a\uff0c\u8981\u662fABC\u731c\u60f3\u88ab\u8bc1\u660e\uff0c\u4e16\u754c\u5c31\u592a\u7f8e\u597d\u4e86\uff0c\u4eff\u4f5b\u8eab\u5904\u5e7b\u5883\u3002
\r\n\r\n\u5927\u591a\u6570\u6570\u8bba\u5de5\u4f5c\u8005\u5e0c\u671b\uff0c\u671b\u6708\u80fd\u591f\u5c31\u4ed6\u7684\u8bc1\u660e\u5199\u51fa\u4e00\u4e2a\u7efc\u8ff0\uff0c\u5c06\u6574\u5957\u7406\u8bba\u7684\u903b\u8f91\u8109\u7edc\u5c55\u73b0\u7ed9\u5927\u5bb6\uff0c\u6bd4\u5982\u4e3a\u4ec0\u4e48\u8981\u5f15\u5165\u5b9a\u7406X\u548c\u6982\u5ff5Y\uff0c\u600e\u4e48\u5c42\u5c42\u63a8\u8fdb\u5230\u6700\u7ec8\u731c\u60f3\u7684\u8bc1\u660e\u3002\u8bbe\u7acb\u5343\u79a7\u5e74\u5927\u5956\u7684\u514b\u96f7\u6570\u5b66\u7814\u7a76\u6240\u4e5f\u5728\u8003\u8651\u9080\u8bf7\u671b\u6708\u5f00\u529e\u4e00\u4e2a\u8ba8\u8bba\u73ed\uff0c\u9080\u8bf7\u4e16\u754c\u4e0a\u6700\u4f18\u79c0\u7684\u6570\u8bba\u548c\u4ee3\u6570\u51e0\u4f55\u5b66\u5bb6\u53c2\u52a0\uff0c\u5927\u5bb6\u4e00\u540c\u5b66\u4e60\u8fd9\u4e2a\u65b0\u7406\u8bba\u3002
\r\n\r\n\u4e0d\u8fc7\uff0c\u5173\u4e8e\u671b\u6708\u65b0\u4e00\u672c\u4eba\uff0c\u4ed6\u5728\u53d1\u5e03\u8bc1\u660e\u4e4b\u540e\u62d2\u7edd\u4e86\u4efb\u4f55\u91c7\u8bbf\uff0c\u800c\u4e14\u4ed6\u4e0d\u559c\u597d\u793e\u4ea4\u3002\u5728Google\u4e0a\u641c\u7d22\u5173\u4e8e\u671b\u6708\u65b0\u4e00\u7684\u80cc\u666f\u4ecb\u7ecd\uff0c\u4e2d\u6587\u94fe\u63a5\u4e2d\u53ef\u8bfb\u7684\uff0c\u552f\u6709\u5362\u660c\u6d77\u53d1\u5e03\u5728\u4ed6\u4e2a\u4eba\u4e3b\u9875\u4e0a\u7684 \u6587\u7ae0 \uff1a\u201c\u671b\u6708\u65b0\u4e00 1969 \u5e74 3 \u6708 29 \u65e5\u51fa\u751f\u4e8e\u65e5\u672c\u4e1c\u4eac\uff0c 16 \u5c81\u8fdb\u5165\u7f8e\u56fd\u666e\u6797\u65af\u987f\u5927\u5b66\u5c31\u8bfb\u672c\u79d1\uff0c \u4e09\u5e74\u540e\u8fdb\u5165\u7814\u7a76\u751f\u9662\uff0c\u5e08\u4ece\u8457\u540d\u5fb7\u56fd\u6570\u5b66\u5bb6\u3001 1986 \u5e74\u83f2\u5c14\u8328\u5956\u5f97\u4e3b\u6cd5\u5c14\u5ef7\u65af\uff0c 23 \u5c81 \uff08\u5373 1992 \u5e74\uff09 \u83b7\u5f97\u6570\u5b66\u535a\u58eb\u5b66\u4f4d\u3002 \u6b64\u540e\uff0c \u4ed6\u5148\u662f \u3001\u2018\u6d77\u5f52\u2019 \u6210\u4e86\u4eac\u90fd\u5927\u5b66 \u6570\u7406\u89e3\u6790\u7814\u7a76\u6240 \u7684\u7814\u7a76\u52a9\u7406\uff0c\u51e0\u4e2a\u6708\u540e\u53c8\u524d\u5f80\u7f8e\u56fd\u54c8\u4f5b\u5927\u5b66\u4ece\u4e8b\u4e86\u8fd1\u4e24\u5e74\u7684\u7814\u7a76\uff0c \u7136\u540e\u91cd\u8fd4\u4eac\u90fd\u5927\u5b66\u3002 2002 \u5e74\uff0c 33 \u5c81\u7684\u671b\u6708\u65b0\u4e00\u6210\u4e3a\u4e86\u4eac\u90fd\u5927\u5b66\u6570\u7406\u89e3\u6790\u7814\u7a76\u6240\u7684\u6559\u6388\u3002 \u671b\u6708\u65b0\u4e00\u7684\u5b66\u672f\u58f0\u8a89\u9887\u4f73\uff0c \u66fe\u83b7\u5f97\u8fc7\u65e5\u672c\u5b66\u672f\u5956\u7ae0\u7b49\u8363\u8a89\u3002\u201d
\r\n\r\n\u5173\u4e8e\u671b\u6708\u7684\u8fd9\u79cd\u51fa\u4e16\u7684\u884c\u4e8b\u65b9\u6cd5\uff0c\u91d1\u660e\u8fe5\u4f5c\u51fa\u7684\u8bc4\u4ef7\u662f\uff1a\u201c\u5f53\u4f60\u6c89\u6d78\u5728\u81ea\u5df1\u7684\u7406\u8bba\u5b87\u5b99\u4e2d\u592a\u4e45\uff0c\u4f60\u4f1a\u5bdf\u89c9\u4e0d\u5230\u4ed6\u4eba\u5bf9\u4e8e\u4f60\u7684\u7406\u8bba\u7684\u56f0\u60d1\uff0c\u56e0\u4e3a\u4f60\u5148\u5165\u4e3a\u4e3b\u5730\u5047\u8bbe\u4e86\u6240\u6709\u4eba\u90fd\u660e\u767d\u5f88\u591a\u57fa\u7840\u77e5\u8bc6\u3002\u201d
\r\n\r\n\u6545\u4e8b\u5230\u6b64\u5c31\u544a\u4e00\u6bb5\u843d\u4e86\uff0c\u5927\u5bb6\u90fd\u5728\u89c1\u8bc1\u5386\u53f2\u3002
\r\n\r\n\u672c\u6587\u7f16\u8bd1\u81ea\u6ce2\u58eb\u987f\u73af\u7403\u4e13\u680f\u6587\u7ae0: | \r\n\t\t\tAn ABC proof too tough even for mathematicians | \r\n\t\t
---|
[1] | \r\n\t\t\t\u8fdc\u963f\u8d1d\u5c14\u51e0\u4f55\u7684\u82f1\u6587\u662fAnabelian geometry\u3002\u5728\u4ee3\u6570\u4e2d\uff0cAbelian\u662f\u53ef\u4ea4\u6362\u4e4b\u610f\uff0c\u5b57\u9762\u610f\u601d\u52a0\u4e0a\u524d\u7f00an\uff0c\u5c31\u662f\u53cd\u4ea4\u6362\u51e0\u4f55\uff0c\u4f46\u548c\u975e\u4ea4\u6362Non-commutative\u7814\u7a76\u7684\u5bf9\u8c61\u5b8c\u5168\u4e0d\u540c\uff0c\u671b\u6708\u79f0\u8fd9\u4e3a\u201c\u9060\u30a2\u30fc\u30d9\u30eb\u5e7e\u4f55\u201d\uff0c\u8868\u8fbe\u4e0e\u4ea4\u6362\u51e0\u4f55\u4e2d\u7684\u7814\u7a76\u5bf9\u8c61\u76f8\u53bb\u751a\u8fdc\u4e4b\u610f\u3002 | \r\n\t\t