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\n\u4f46\u6587\u9898\u7684\u54e5\u5c3c\u65af\u5821\u5e76\u975e\u6b64\u54e5\u5c3c\u65af\u5821\u3002 \u800c\u662f\u5982\u4eca\u7684\u4fc4\u7f57\u65af\u57ce\u5e02\uff0c\u52a0\u91cc\u5b81\u683c\u52d2\u3002 \u5148\u524d\u51fa\u4e8e\u597d\u5947\u8c37\u6b4c\u4e86\u4e00\u4e0b\uff0c\u53d1\u73b0\u5f88\u591a\u4e0a\u53e4\u5927\u795e(\u6bd4\u5982\u5e0c\u5c14\u4f2f\u7279)\u7684\u5c65\u5386\u91cc\u9762\u5c61\u5c61\u63d0\u5230\u8fd9\u4e2a\u5730\u65b9\u3002\u4e8e\u662f\u627e\u5230\u8fd9\u4e48\u4e00\u7bc7\u6587\u7ae0\uff0c\u4f9b\u6709\u5171\u540c\u559c\u597d\u7684\u4eba\u5206\u4eab\u3002\u4ee5\u4e0b\u4e3a\u8f6c\u6587:<\/p>\n
\u6458\u81ea\uff1a\u56fd\u5bb6\u5730\u7406 \u4f5c\u8005\uff1a\u4e0d\u8be6\u7ec6
\n\u5728\u6ce2\u7f57\u7684\u6d77\u4e1c\u5cb8\uff0c\u7acb\u9676\u5b9b\u4e0e\u6ce2\u5170\u4e4b\u95f4\uff0c\u6709\u4e00\u5757\u9762\u79ef1.51\u4e07\u5e73\u65b9\u516c\u91cc\u7684\u571f\u5730\uff0c\u8fd9\u91cc\u662f\u4fc4\u7f57\u65af\u76f4\u8f96\u5e02\u4ee5\u5916\u6700\u5c0f\u7684\u4e00\u4e2a\u8054\u90a6\u4e3b\u4f53\u2015\u2015\u52a0\u91cc\u5b81\u683c\u52d2\u5dde\u3002\u8fd9\u4e2a\u4fc4\u6700\u897f\u90e8\u7684\u5dde\u867d\u7136\u5c5e\u4e8e\u4fc4\u8054\u90a6\u7ba1\u8f96\uff0c\u5374\u8ddd\u4fc4\u8054\u90a6\u672c\u571f\u6709600\u516c\u91cc\u4e4b\u9065\uff0c\u6d77\u9646\u7a7a\u5b8c\u5168\u4e0e\u672c\u571f\u9694\u5f00\uff0c\u662f\u4e00\u5757\u5b9e\u5b9e\u5728\u5728\u7684\u98de\u5730\u3002\u52a0\u91cc\u5b81\u683c\u52d2\u72ec\u7279\u7684\u5730\u7406\u4f4d\u7f6e\u548c\u5386\u53f2\u80cc\u666f\u4ee4\u4eba\u5bf9\u5b83\u5145\u6ee1\u597d\u5947\u3002<\/p>\n
\u4e00\u3001\u66fe\u7ecf\u662f\u4e1c\u666e\u9c81\u58eb\u7684\u9996\u90fd
\n\u3000\u3000\u4eca\u5e746\u6708\u52a0\u91cc\u5b81\u683c\u52d2\u5e02\u5c06\u5e86\u795d\u5efa\u57ce750\u5468\u5e74\uff0c\u8fd9\u4e0d\u7981\u8ba9\u4eba\u518d\u6b21\u56de\u5fc6\u8d77\u8fd9\u5ea7\u57ce\u5e02\u4e0d\u5e73\u51e1\u7684\u5386\u53f2\u3002\u52a0\u91cc\u5b81\u683c\u52d2\u5e02\u539f\u540d\u54e5\u5c3c\u65af\u5821\uff0c\u66fe\u662f\u5fb7\u56fd\u4e1c\u666e\u9c81\u58eb\u7684\u4e00\u90e8\u5206\uff0c1772\u5e74\u6210\u4e3a\u4e1c\u666e\u9c81\u58eb\u738b\u56fd\u7684\u9996\u90fd\u3002<\/p>\n
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\u4e09\u3001 \u7ec8\u8eab\u72ec\u5904\u7684\u54f2\u5b66\u5bb6\u5eb7\u5fb7<\/p>\n
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\u5eb7\u5fb7\u4e00\u751f\u4e2d\u51e0\u4e4e\u6ca1\u6709\u79bb\u5f00\u8fc7\u54e5\u5c3c\u65af\u5821\uff0c\u4ed6\u7684\u6d3b\u52a8\u8303\u56f4\u6700\u8fdc\u4e0d\u8d85\u8fc7100\u516c\u91cc\u3002\u6709\u4eba\u63d0\u51fa\u7591\u95ee\uff0c\u4e00\u4e2a\u65e2\u77e5\u5929\u6587\u5730\u7406\uff0c\u53c8\u638c\u63e1\u6df1\u5965\u54f2\u5b66\u7684\u4f1f\u4eba\u5c45\u7136\u4e00\u751f\u672a\u79bb\u4e61\u571f\uff0c\u8fd9\u771f\u4ee4\u4eba\u4e0d\u53ef\u601d\u8bae\u3002\u665a\u5e74\u7684\u5eb7\u5fb7\u5df2\u53d8\u6210\u4e86\u4e00\u4f4d\u75b2\u60eb\u7684\u8001\u4eba\uff0c\u4ed6\u7ecf\u5e38\u6c89\u6d78\u5728\u6df1\u601d\u4e2d\uff0c\u5bf9\u5ba2\u4eba\u5f88\u51b7\u6de1\u3002\u4ed6\u81ea\u5df1\u66fe\u8bf4\u8fc7\uff1a\u201c\u6211\u73b0\u5728\u8d8a\u6765\u8d8a\u611f\u5230\u8870\u8001\u548c\u75b2\u60eb\uff0c\u4f60\u4eec\u6700\u597d\u628a\u6211\u5f53\u6210\u4e00\u4e2a\u5b69\u5b50\u6765\u770b\u5f85\u3002\u201d1804\u5e742\u670812\u65e5\u4e0a\u534811\u65f6\uff0c\u5eb7\u5fb7\u5728\u5bb6\u4e61\u54e5\u5c3c\u65af\u5821\u53bb\u4e16\uff0c\u79bb\u4ed680\u5bff\u8fb0\u53ea\u5dee\u4e0d\u5230\u4e24\u4e2a\u6708\u3002\u5eb7\u5fb7\u53bb\u4e16\u65f6\u5168\u8eab\u9aa8\u7626\u5982\u67f4\uff0c\u9057\u4f53\u50cf\u4e00\u5177\u5b58\u653e\u4e86\u4e0a\u767e\u5e74\u7684\u6728\u4e43\u4f0a\u3002<\/p>\n
\u5eb7\u5fb7\u901d\u4e16\u7684\u6d88\u606f\u4f20\u51fa\u540e\uff0c\u54e5\u5c3c\u65af\u5821\u7684\u5c45\u6c11\u6392\u7740\u957f\u961f\u6765\u4e0e\u8fd9\u4e2a\u57ce\u5e02\u7684\u6700\u4f1f\u5927\u7684\u513f\u5b50\u544a\u522b\u3002\u5f53\u65f6\u5929\u6c14\u5bd2\u51b7\uff0c\u571f\u5730\u51bb\u5f97\u65e0\u6cd5\u6316\u6398\uff0c\u6574\u657416\u5929\u8fc7\u53bb\u540e\u5eb7\u5fb7\u7684\u9057\u4f53\u624d\u88ab\u4e0b\u846c\u3002\u5728\u5eb7\u5fb7\u7684\u5893\u524d\u9c9c\u82b1\u7ec8\u5e74\u4e0d\u65ad\uff0c\u56e0\u4e3a\u54e5\u5c3c\u65af\u5821\u5373\u52a0\u91cc\u5b81\u683c\u52d2\u7684\u5e74\u8f7b\u4eba\u6709\u4e00\u4e2a\u7ea6\u5b9a\u4fd7\u6210\u7684\u4e60\u60ef\uff0c\u7ed3\u5a5a\u65f6\u90fd\u8981\u5e26\u4e0a\u4e00\u675f\u82b1\u653e\u5728\u5eb7\u5fb7\u5893\u524d\u3002\u4eba\u4eec\u7ecf\u5e38\u80fd\u770b\u5230\uff0c\u624e\u7740\u9c9c\u82b1\u7684\u5f69\u8f66\u8f7d\u7740\u65b0\u5a18\u65b0\u90ce\u5728\u53bb\u5a5a\u793c\u7684\u8def\u4e0a\u7ed5\u9053\u6765\u770b\u671b\u5eb7\u5fb7\u3002<\/p>\n
\u56db\u3001 \u6570\u5b66\u5e0c\u5c14\u4f2f\u7279(David Hilbert)\u3002
\n\u5e0c\u5c14\u4f2f\u7279\u8ba4\u4e3a\uff0c\u6570\u5b66\u7684\u53d1\u5c55\u5728\u4e8e\u95ee\u9898\u7684\u63d0\u51fa\u4e0e\u89e3\u51b3\u3002<\/p>\n
\u5e0c\u5c14\u4f2f\u7279\u662f\u4e50\u89c2\u7684\u6570\u5b66\u5bb6\uff0c\u4ed6\u66fe\u8bf4\u8fc7\uff1a\u300e\u4efb\u4f55\u4e00\u4e2a\u95ee\u9898\u90fd\u6709\u89e3\uff0c\u53ea\u9700\u63a8\u6f14\uff0c\u5c31\u53ef\u4ee5\u5f97\u89e3\uff0c\u6570\u5b66\u4e2d\u6c38\u8fdc\u6ca1\u6709\u6211\u4eec\u77e5\u9053\u7684\u3002\u300f\u8fd9\u662f\u8db3\u4ee5\u632f\u594b\u4eba\u5fc3\u7684\u4e00\u756a\u8bdd\uff0c\u7ecf\u8fc7\u6709\u9650\u6b65\u9aa4\u7684\u4e25\u683c\u63a8\u8bba\uff0c\u5c31\u53ef\u4ee5\u627e\u51fa\u6570\u5b66\u95ee\u9898\u7684\u89e3\u6765\uff0c\u5373\u4f7f\u662f\u6ca1\u6709\u89e3\uff0c\u80fd\u591f\u4e25\u683c\u8bc1\u660e\uff0c\u4e5f\u7b97\u662f\u4e00\u79cd\u89e3\u3002\u5728\u5e0c\u5c14\u4f2f\u7279\u5d2d\u9732\u5934\u89d2\u7684\u4ee3\u6570\u4e0d\u53d8\u91cf\u7406\u8bba\uff08invariant
\ntheory\uff09\u4e2d\uff0c\u4ed6\u8bc1\u660e\u4e86\u4efb\u610f\u6b21\u6570\u5f62\u5f0f\u7684\u4e0d\u53d8\u91cf\u90fd\u662f\u6709\u9650\u751f\u6210\u7684\uff1b\u800c\u4e0d\u662f\u5efa\u6784\u5f0f\u7684\uff0c\u5f97\u5230\u7684\u662f\u4e00\u822c\u7684\u5b58\u5728\u6027\u5b9a\u7406\uff08existence theorem\uff09\u3002
\n\u3000\u3000\u5728\u5f53\u65f6\uff0c\u5982\u679c\u4e00\u4e2a\u6570\u5b66\u5bb6\u8981\u8bc1\u660e\u67d0\u4e2a\u7ed3\u679c\u662f\u5426\u6210\u7acb\uff0c\u4ee5\u53ca\u95ee\u9898\u662f\u5426\u89e3\u51b3\u4e86\uff0c\u6700\u4e3b\u6d41\u4e14\u660e\u663e\u7684\u65b9\u5f0f\uff0c\u4fbf\u662f\u660e\u786e\u5730\u7ed9\u51fa\u7b54\u6848\uff0c\u53ef\u662f\u6709\u4e9b\u95ee\u9898\u662f\u6781\u5176\u590d\u6742\u7684\uff0c\u8981\u76f4\u63a5\u5730\u627e\u51fa\u7b54\u6848\u662f\u5f88\u56f0\u96be\u7684\uff1b\u800c\u4e14\u5f80\u5f80\u5728\u65b0\u7684\u9886\u57df\u4e2d\uff0c\u7b26\u53f7\u7684\u8fd0\u7528\u5e38\u6beb\u65e0\u65b9\u5411\uff0c\u4e0d\u77e5\u8be5\u4ece\u4f55\u4e0b\u624b\uff1b\u56e0\u6b64\uff0c\u5982\u679c\u80fd\u7528\u95f4\u63a5\u8bc1\u660e\u7684\u65b9\u5f0f\uff0c\u7528\u5df2\u77e5\u7684\u4e8b\u5b9e\u7ed9\u51fa\u7ed3\u679c\uff0c\u8fd9\u4e2a\u4e1c\u897f\u662f\u5426\u5b58\u5728\uff1f\u5b58\u5728\uff0c\u6216\u8bb8\u6211\u4eec\u80fd\u5bf9\u8fd9\u4e1c\u897f\u6709\u4e86\u6e05\u695a\u7684\u4e86\u89e3\uff0c\u8fdb\u800c\u53bb\u627e\u51fa\u95ee\u9898\u7684\u89e3\u7b54\u3002\u5e0c\u5c14\u4f2f\u7279\u4fbf\u662f\u627e\u5230\u4e86\u8fd9\u6837\u4e00\u822c\u7684\u65b9\u6cd5\uff0c\u5bf9\u4e0d\u53d8\u91cf\u7406\u8bba\u505a\u51fa\u4e86\u7a81\u7834\uff0c\u8fd9\u5bf9\u5f53\u65f6\u662f\u4e00\u4e2a\u5f88\u5927\u7684\u51b2\u51fb\uff0c\u5f15\u8d77\u4e86\u5f88\u5927\u7684\u4e89\u8bae\u3002\u4f46\u662f\uff0c\u9010\u6e10\u5730\u88ab\u5927\u5bb6\u63a5\u53d7\u4ed6\u90a3\u6709\u5982\u795e\u8ff9\u822c\u7684\u65b9\u6cd5\uff0c\u6211\u4eec\u53ef\u4ee5\u77e5\u9053\uff0c\u8fd9\u575a\u56fa\u4e86\u5e0c\u5c14\u4f2f\u7279\u7684\u4fe1\u5ff5\uff0c\u90a3\u5c31\u662fWir
\nmussen wissen, wir werden wissen.\uff08\u6211\u4eec\u4e00\u5b9a\u8981\u77e5\u9053\uff1b\u6211\u4eec\u7ec8\u5c06\u4f1a\u77e5\u9053\uff09\u3002
\n\u3000\u3000\u770b\u5230\u8fd9\u91cc\uff0c\u5927\u5bb6\u4f1a\u4e0d\u4f1a\u5bf9\u4e8e\u8fd9\u6837\u7684\u4e00\u4e2a\u4e50\u89c2\u7684\u6570\u5b66\u5bb6\u597d\u5947\u5462\uff1f\u6211\u4eec\u73b0\u5728\u5c31\u6765\u7a0d\u7a0d\u4ecb\u7ecd\u4ed6\u7684\u751f\u5e73 \u3002
\n\u3000\u3000\u5e0c\u5c14\u4f2f\u7279\u751f\u4e8e\u666e\u9c81\u58eb\u54e5\u5c3c\u65af\u5821\uff0c\u5eb7\u5fb7\u662f\u54e5\u5c3c\u65af\u5821\u4eba\u7684\u9a84\u50b2\uff0c\u4e5f\u662f\u5e0c\u5c14\u4f2f\u7279\u5c11\u5e74\u65f6\u5fc3\u76ee\u4e2d\u7684\u5076\u50cf\u3002
\n\u3000\u3000\u5e0c\u5c14\u4f2f\u7279\u7236\u4eb2\u662f\u6cd5\u5b98\uff0c\u4e00\u76f4\u5e0c\u671b\u5e0c\u5c14\u4f2f\u7279\u80fd\u7ee7\u627f\u4ed6\u7684\u8863\u94b5\u3002\u6bcd\u4eb2\u53d7\u8fc7\u826f\u597d\u7684\u6559\u80b2\uff0c\u975e\u5e38\u666f\u4ef0\u5eb7\u5fb7\uff0c\u5bf9\u6570\u5b66\u3001\u5929\u6587\u5b66\u90fd\u6709\u7814\u7a76\u3002\u5979\u662f\u5e0c\u5c14\u4f2f\u7279\u7684\u542f\u8499\u8001\u5e08\uff0c\u5bf9\u4e8e\u542f\u53d1\u5e0c\u5c14\u4f2f\u7279\u5bf9\u79d1\u5b66\u7684\u5174\u8da3\u6709\u76f8\u5f53\u5f71\u54cd\u3002<\/p>\n
\u3000\u30001872\u5e74\u5e0c\u5c14\u4f2f\u7279\u8fdb\u5165\u666e\u9c81\u58eb\u8457\u540d\u7684\u83f2\u7279\u7acb\u6587\u79d1\u4e2d\u5b66\uff0c\u7531\u4e8e\u5fd7\u8da3\u4e0d\u5408\uff0c\u5728\u8fd9\u91cc\u5e0c\u5c14\u4f2f\u7279\u8868\u73b0\u5e76\u4e0d\u4f73\u30021880\u5e74\uff0c18\u5c81\u7684\u5e0c\u5c14\u4f2f\u7279\u8003\u4e0a\u4e86\u54e5\u5c3c\u65af\u5821\u5927\u5b66\uff0c\u5728\u81ea\u7531\u7684\u5b66\u672f\u98ce\u6c14\u91cc\uff0c\u5e0c\u5c14\u4f2f\u7279\u5982\u9c7c\u5f97\u6c34\uff0c\u4e13\u5fc3\u653b\u8bfb\u4ed6\u6700\u7231\u7684\u6570\u5b66\uff0c\u5728\u8fd9\u91cc\uff0c\u5e0c\u5c14\u4f2f\u7279\u548c\u4ed6\u4e00\u751f\u7684\u5bc6\u53cb
\nMinkowski \u76f8\u9047\u30021884\u5e74\uff0c25\u5c81\u7684 Hurwitz
\n\u6765\u5230\u54e5\u5c3c\u5821\u5927\u5b66\u62c5\u4efb\u6570\u5b66\u526f\u6559\u6388\uff0c\u4ed6\u4eec\u4e09\u4eba\u5fd7\u8da3\u76f8\u6295\uff0c\u5f88\u5feb\u7ed3\u4e0b\u4eb2\u5bc6\u53cb\u8c0a\uff0c\u4ed6\u4eec\u7684\u53cb\u8c0a\u6210\u4e3a\u6570\u5b66\u53f2\u4e0a\u7684\u4e00\u6bb5\u4f73\u8bdd\u3002
\n\u3000\u30001884\u5e74\uff0c\u5e0c\u5c14\u4f2f\u7279\u5728\u6570\u5b66\u6559\u6388 Lindemann
\n\u7684\u5efa\u8bae\u4e0b\uff0c\u4ee5\u4ee3\u6570\u4e0d\u53d8\u91cf\u4e3a\u9898\uff0c\u5b8c\u6210\u4ed6\u7684\u535a\u58eb\u8bba\u6587\u3002\u4e4b\u540e\uff0c\u5e0c\u5c14\u4f2f\u7279\u65c5\u884c\u83b1\u6bd4\u9521\u3001\u5df4\u9ece\u3001\u54e5\u5ef7\u6839\u5404\u5730\uff0c\u62dc\u8bbf\u5404\u5730\u6570\u5b66\u5bb6\uff0c\u65c1\u542c\u6570\u5b66\u5927\u5e08\u7684\u8bfe\uff0c\u4ed6\u62dc\u8bbf\u8fc7 Klein,
\nPoincare, Jordan, Hermite, Kronecker \u7b49\u4eba\uff0c\u8fd9\u4e3a\u4ed6\u65e5\u540e\u5728\u6570\u5b66\u4e0a\u7684\u53d1\u5c55\u6253\u4e0b\u4e86\u826f\u597d\u7684\u57fa\u7840\u3002
\n\u3000\u30001887\u5e74\uff0c\u5e0c\u5c14\u4f2f\u7279\u56de\u5230\u54e5\u5c3c\u65af\u5821\u5927\u5b66\u62c5\u4efb\u6570\u5b66\u8bb2\u5e08\uff0c\u540c\u65f6\u5168\u529b\u94bb\u7814\u4e0d\u53d8\u91cf\u7684\u7406\u8bba\u3002\u57281888\u5e74\u5e0c\u5c14\u4f2f\u7279\u63d0\u51fa\u4e86\u4ed6\u8457\u540d\u7684 Basis Theorem
\n\u7684\u8bc1\u660e\uff0c\u5f7b\u5e95\u89e3\u51b3\u4e86\u4e0d\u53d8\u91cf\u7406\u8bba\u7684\u95ee\u9898\u3002<\/p>\n
\u3000\u3000\u4e0d\u4e45\u4e4b\u540e\uff0cHerwitz \u8c03\u5230\u745e\u58eb\u8054\u90a6\u5de5\u4e1a\u5927\u5b66\u62c5\u4efb\u6570\u5b66\u6559\u6388\uff0c \u5e0c\u5c14\u4f2f\u7279\u4fbf\u63a5\u66ff\u4e86\u4ed6\u7684\u804c\u52a1\uff0c\u6210\u4e3a\u526f\u6559\u6388\u30021892\u5e74 \u5e0c\u5c14\u4f2f\u7279\u7ed3\u5a5a\u4e86\u3002
\n\u3000\u30001893\u5e74\u5e0c\u5c14\u4f2f\u7279\u5ba3\u5e03\u8131\u79bb\u4e0d\u53d8\u91cf\u9886\u57df\uff0c\u5f00\u59cb\u7814\u7a76\u6570\u5b66\u5973\u7687\u7684\u738b\u51a0\uff0d\uff0d\u6570\u8bba\uff0c\u540c\u5e74,\u5e0c\u5c14\u4f2f\u7279\u63a5\u66ffLindemann\u6210\u4e3a\u54e5\u5c3c\u65af\u5821\u5927\u5b66\u7684\u6570\u5b66\u6559\u6388\uff0c
\n1895\u5e74\uff0c\u5728Klein\u7684\u5954\u8d70\u4e0b\uff0c\u5e0c\u5c14\u4f2f\u7279\u5230\u5fb7\u56fd\u7684\u6570\u5b66\u4e2d\u5fc3\uff0d\uff0d\u54e5\u5ef7\u6839\u5927\u5b66\u62c5\u4efb\u6570\u5b66\u6559\u6388\u3002
\n\u3000\u3000\u5230\u4e86\u54e5\u5ef7\u6839\uff0c\u5e0c\u5c14\u4f2f\u7279\u4ecd\u5728\u6570\u8bba\u4e0a\u5de5\u4f5c\uff0c\u5e76\u8d77\u8349\u5fb7\u56fd\u6570\u5b66\u5b66\u4f1a\u6240\u59d4\u6258\u7684\u6570\u8bba\u7efc\u5408\u62a5\u544a\uff0c\u4ed6\u67e5\u9605\u4e86\u81eaGauss\u4ee5\u6765\u4e00\u5207\u6709\u5173\u6570\u7684\u8bba\u6587\u548c\u8457\u4f5c\uff0c\u4e25\u683c\u5ba1\u67e5\u6240\u6709\u5df2\u77e5\u5b9a\u7406\u7684\u8bc1\u660e\uff0c\u4fee\u6b63\u524d\u4eba\u7f3a\u5931\uff0c\u8865\u8db3\u4e0d\u5b8c\u6574\u7684\u7406\u8bba\uff0c\u5c06\u6574\u4e2a\u6570\u8bba\u7edf\u4e00\u8d77\u6765\u3002\u4ed6\u8fd8\u7edf\u4e00\u4e86\u5f53\u65f6\u767e\u5bb6\u4e89\u9e23\u7684\u6570\u5b66\u7b26\u53f7\uff0c 1897\u5e74\uff0c\u8fd9\u4efd\u62a5\u544a\u300a\u4ee3\u6570\u6570\u57df\u7684\u7406\u8bba\u300b(Zahlbericht) \u6b63\u5f0f\u51fa\u7248\uff0c\u8fd9\u90e8\u8457\u4f5c\u4e00\u95ee\u4e16\uff0c\u7acb\u523b\u5f15\u8d77\u5de8\u5927\u7684\u56de\u54cd\uff0c\u88ab\u79f0\u4e3a\u5341\u4e5d\u4e16\u7eaa\u4ee3\u6570\u6570\u8bba\u7684\u9876\u5cf0\uff0c\u81f3\u4eca\u4ecd\u662f\u4e00\u90e8\u7ecf\u5178\u8457\u4f5c\u3002<\/p>\n
\u3000\u3000\u7edf\u4e00\u4e86\u6570\u8bba\uff0c\u5e0c\u5c14\u4f2f\u7279\u628a\u4ed6\u7684\u77db\u5934\u6307\u5411\u4e86\u51e0\u4f55\u3002\u7ee7Euclid\u4e4b\u540e\uff0c\u5e0c\u5c14\u4f2f\u7279\u53c8\u8ba9\u51e0\u4f55\u4f5c\u4e86\u4e00\u6b21\u7684\u5927\u4e00\u7edf\u3002\u5341\u4e5d\u4e16\u7eaa\u7684\u6570\u5b66\u5bb6\u53d1\u73b0\uff1a\u770b\u4f3c\u65e0\u61c8\u53ef\u51fb\u7684\u6b27\u6c0f\u51e0\u4f55\uff0c\u4ecd\u5b58\u6709\u91cd\u5927\u7f3a\u9677\u3002
\nEuclid \u5bf9\u70b9\u3001\u7ebf\u3001\u9762\u6ca1\u6709\u4e0b\u8fc7\u660e\u786e\u7684\u5b9a\u4e49\uff0c\u800c\u4e14\u6709\u4e9b\u8bc1\u660e\u4e0d\u77e5\u4e0d\u89c9\u7528\u4e86\u4e00\u4e9b\u5047\u8bbe\u3002
\n\u5e0c\u5c14\u4f2f\u7279\u91cd\u65b0\u5ba1\u89c6\u6b27\u6c0f\u51e0\u4f55\uff0c\u63d0\u51fa\u4e8621\u6761\u516c\u7406\u5e76\u4e14\u5206\u6790\u5b83\u4eec\u7684\u91cd\u8981\u6027\u3002\u5e0c\u5c14\u4f2f\u7279\u8fd8\u4ece\u6b27\u6c0f\u51e0\u4f55\u51fa\u53d1\uff0c\u70b9\u51fa\u4e86\u301d\u516c\u7406\u5316\u301e\u65b9\u6cd5\u7684\u5b9e\u8d28\u3002\u5176\u5b9e\u6240\u8c13\u7684\u516c\u7406\uff0c\u53ea\u662f\u4e00\u4e9b\u5047\u8bbe\uff0c\u5e76\u975e\u4e0d\u8bc1\u81ea\u660e\u7684\u771f\u7406\u3002\u6839\u636e\u4e0d\u540c\u7684\u5047\u8bbe\uff0c\u4fbf\u53ef\u5efa\u7acb\u4e0d\u540c\u7684\u516c\u7406\u7cfb\u7edf\uff0c\u521b\u7acb\u4e0d\u540c\u7684\u51e0\u4f55\u5206\u652f\u3002\u7531\u301d\u5b9a\u4e49\u301e\u5230\u301d\u516c\u7406\u301e\u518d\u5230\u301d\u5b9a\u7406\u301e\u7684\u9636\u68af\uff0c\u4fbf\u662f\u516c\u7406\u5316\u65b9\u6cd5\u7684\u5b9e\u8d28\u3002
\n1899\u5e74\u5e0c\u5c14\u4f2f\u7279\u51fa\u7248\u4e86\u300a\u51e0\u4f55\u57fa\u7840\u300b(Grundlagender
\nGeometrie)\u4e00\u4e66\uff0c\u518d\u4e00\u6b21\u9020\u6210\u8f70\u52a8\u3002\u8fd9\u672c\u4e66\u4e0d\u4f46\u6210\u4e3a\u5fb7\u56fd\u6700\u7545\u9500\u7684\u6559\u79d1\u4e66\uff0c\u800c\u4e14\u5e7f\u4e3a\u7ffb\u8bd1\u6d41\u4f20\u3002\u800c\u5e0c\u5c14\u4f2f\u7279\u7684\u52aa\u529b\u4e5f\u4f7f\u6570\u5b66\u7684\u516c\u7406\u5316\u5411\u524d\u8fc8\u8fdb\u4e00\u5927\u6b65\u3002
\n\u3000\u30001900\u5e74\uff0c\u5728\u5df4\u9ece\u7684\u7b2c\u4e8c\u5c4a\u56fd\u9645\u6570\u5b66\u5bb6\u5927\u4f1a\u4e0a\uff0c\u5e0c\u5c14\u4f2f\u7279\u53d1\u8868\u4e86\u4ed6\u8457\u540d\u7684\u6f14\u8bf4 The Problem of Mathematics
\n\u5217\u51fa\u65b0\u4e16\u7eaa\u7684\u6570\u5b66\u5bb6\u6240\u5e94\u52aa\u529b\u89e3\u51b3\u7684 23 \u4e2a\u95ee\u9898\uff0c\u8fd9 23 \u4e2a\u95ee\u9898\u88ab\u79f0\u4e3a Hilbert\u2019s Problems
\n\uff0c\u5305\u542b\u4e86\u8fde\u7eed\u7edf\u5047\u8bbe\u3001\u54e5\u5fb7\u5df4\u8d6b\u731c\u60f3\u3001\u9ece\u66fc\u5047\u8bbe\u3001Dirichlet\u2019s Principle \u7684\u63a8\u5e7f\u7b49\u3002\u8fd9\u4e9b\u95ee\u9898\u534a\u6570\u4ee5\u4e0a\u90fd\u5df2\u5728\u8fd9\u4e2a\u4e16\u7eaa\u89e3\u51b3\uff0c\u800c\u6bcf\u5f53\u6709 \u5e0c\u5c14\u4f2f\u7279\u2019s
\nProblem \u88ab\u89e3\u51b3\uff0c\u90fd\u662f\u6570\u5b66\u754c\u60ca\u5929\u52a8\u5730\u7684\u5927\u4e8b\u3002
\n\u3000\u3000\u5e0c\u5c14\u4f2f\u7279\u4e0d\u53ea\u662f\u4e2a\u4f1f\u5927\u7684\u6570\u5b66\u5bb6\uff0c\u4e5f\u662f\u4e2a\u4f1f\u5927\u7684\u6559\u80b2\u5bb6\u3002\u4ed6\u7684\u6f14\u8bb2\u98ce\u8da3\u5e7d\u9ed8\uff0c\u800c\u4e14\u7531\u4e8e\u4ed6\u7684\u7814\u7a76\u6210\u679c\u4e30\u7855\uff0c\u8bfe\u7a0b\u4e2d\u603b\u7a7f\u63d2\u4e00\u4e9b\u4ed6\u6700\u65b0\u7684\u7814\u7a76\u6210\u679c\uff0c\u628a\u5b66\u751f\u6df1\u6df1\u5730\u5438\u5f15\u4f4f\u4e86\u3002
\n\u4ed6\u7684\u8bfe\u7ecf\u5e38\u6709\u51e0\u767e\u4eba\uff0c\u6709\u65f6\u8fde\u7a97\u53f0\u4e5f\u5750\u6ee1\u4e86\u4eba\u3002\u8bb8\u591a\u9752\u5e74\u4ec5\u4ec5\u56e0\u542c\u4e86\u5e0c\u5c14\u4f2f\u7279\u51e0\u5802\u8bfe\u3001\u6216\u8005\u770b\u4e86\u4ed6\u7684\u51e0\u672c\u6570\u5b66\u8457\u4f5c\uff0c\u4fbf\u6df1\u6df1\u5730\u88ab\u6570\u5b66\u6240\u5438\u5f15\uff0c\u628a\u6bd5\u751f\u7684\u7cbe\u529b\u732e\u7ed9\u4e86\u6570\u5b66\u3002\u4ed6\u8fd8\u7ec4\u7ec7\u4e86\u6570\u5b66\u8ba8\u8bba\u73ed\u8ba9\u5b66\u751f\u81ea\u7531\u53c2\u52a0\uff0c\u5b9a\u671f\u8fdb\u884c\u6570\u5b66\u62a5\u544a\u6d3b\u52a8\uff0c\u4e92\u76f8\u4ea4\u6d41\u7814\u7a76\u5fc3\u5f97\u3002\u4ed6\u672c\u4eba\u4e5f\u5e38\u628a\u6700\u65b0\u7814\u7a76\u6210\u679c\u5728\u8ba8\u8bba\u73ed\u4e0a\u62a5\u544a\uff0c\u7136\u540e\u8ba9\u9752\u5e74\u4eba\u63a5\u7740\u505a\u4e0b\u53bb\u3002\u4ed6\u4eec\u5f62\u6210\u4e86\u4e00\u4e2a\u56e2\u4f53\uff0c\u4e00\u7bc7\u7bc7\u8bba\u6587\u7531\u8fd9\u4e2a\u8ba8\u8bba\u73ed\u4e2d\u51fa\u6765\u3002\u8457\u540d\u7684
\nHilbert space\uff0c\u4fbf\u662f\u8fd9\u4e2a\u8ba8\u8bba\u73ed\u7684\u6210\u679c\uff0c\u8fd9\u4e2a\u7406\u8bba\u540e\u6765\u6210\u4e3a\u91cf\u5b50\u7406\u8bba\u7684\u6570\u5b66\u5de5\u5177\u3002\u4e8c\u5341\u4e16\u7eaa\u7684\u6570\u5b66\u5bb6 Weyl\u3001Blumenthal\u3001Von Neumann
\n\u8bfa\u8d1d\u5c14\u7269\u7406\u5956\u5f97\u4e3b Von Laue \u7b49\uff0c\u90fd\u662f\u4ed6\u7684\u5b66\u751f\u3002
\n\u3000\u3000\u4ec5\u7ba1\u5e0c\u5c14\u4f2f\u7279\u6b64\u65f6\u7684\u7814\u7a76\u6210\u679c\u5df2\u7ecf\u8db3\u4ee5\u786e\u7acb\u4ed6\u5728\u6570\u5b66\u4e0a\u7684\u5d07\u9ad8\u5730\u4f4d\uff0c\u4f46\u662f\u4e00\u4e2a\u4f18\u79c0\u7684\u6570\u5b66\u5bb6\u603b\u4e0d\u4f1a\u6ee1\u8db3\u4e8e\u5df2\u6709\u7684\u6210\u5c31\uff0c\u4ed6\u4e00\u76f4\u4e0d\u65ad\u5730\u5728\u4e00\u4e2a\u4e2a\u65b0\u9886\u57df\u4e2d\u8fdb\u884c\u5f00\u62d3\u7684\u5de5\u4f5c\u3002\u4ed6\u56db\u5341\u5e74\u7684\u6559\u4e66\u751f\u6daf\u91cc\uff0c\u9664\u4e86\u6700\u540e\u4e00\u5e74\u5916\uff0c\u6ca1\u6709\u5f00\u8fc7\u91cd\u590d\u7684\u8bfe\u7a0b\u3002\u6bcf\u5e74\u7684\u8bfe\u7a0b\uff0c\u90fd\u968f\u7740\u4ed6\u6700\u65b0\u7684\u7814\u7a76\u800c\u4e0d\u540c\u3002\u4ed6\u548c\u4ed6\u7684\u5b66\u751f\u4eec\u7814\u7a76\u4e86\u79ef\u5206\u65b9\u7a0b\uff0c\u521b\u7acb\u4e86
\nHilbert Space
\n\u7684\u7b97\u5b50\u8c31\u7406\u8bba\u3002\u5728\u63a8\u5e7f\u79ef\u5206\u65b9\u7a0b\u7684\u5e94\u7528\u4e2d\uff0c\u4ed6\u63a5\u89e6\u5230\u4e86\u8bb8\u591a\u7269\u7406\u95ee\u9898\uff0c\u53c8\u5fcd\u4e0d\u4f4f\u60f3\u7528\u516c\u7406\u5316\u65b9\u6cd5\u53bb\u89e3\u51b3\u7269\u7406\u4e2d\u7684\u6df7\u4e71\u72b6\u6001\u3002\u4ed6\u5b8c\u6210\u4e86\u8f90\u5c04\u7406\u8bba\u516c\u7406\u5316\u7684\u5de5\u4f5c\uff0c\u5bf9\u91cf\u5b50\u529b\u5b66\u548c\u70ed\u529b\u5b66\u7684\u516c\u7406\u5316\u4e5f\u505a\u4e86\u5f88\u591a\u6709\u76ca\u7684\u5de5\u4f5c\u3002<\/p>\n
\u3000\u30001915\u5e74 Einstein \u53d1\u8868\u4e86\u5e7f\u4e49\u76f8\u5bf9\u8bba\uff0c\u51e0\u4e4e\u540c\u65f6\u5e0c\u5c14\u4f2f\u7279\u4e5f\u5f97\u51fa\u4e86\u5e7f\u4e49\u76f8\u5bf9\u8bba\u7684\u573a\u65b9\u7a0b
\n(field equations)\u3002\u5982\u540c Newton \u548c
\nLibnitz \u5404\u81ea\u72ec\u7acb\u53d1\u5c55\u51fa\u5fae\u79ef\u5206\u3002\u7136\u800c\u4ec5\u7ba1\u5e0c\u5c14\u4f2f\u7279\u7684\u6210\u679c\u53ef\u548c Einstein\u5ab2\u7f8e\uff0c\u4f46\u4ed6\u8fd8\u662f\u627f\u8ba4\u5e7f\u4e49\u76f8\u5bf9\u8bba\u7684\u521b\u5efa\u5e94\u5f52\u529f\u4e8e Einstein\u3002
\n\u3000\u3000\u4e8c\u5341\u4e16\u7eaa\u7684\u4e8c\u25cb\u5e74\u4ee3\uff0c\u5e0c\u5c14\u4f2f\u7279\u81f4\u529b\u4e8e\u6570\u5b66\u57fa\u7840\u7684\u5de5\u4f5c\u4e0a\uff0c\u5f53\u65f6\u6570\u5b66\u754c\u4e3a\u4e86\u96c6\u5408\u8bba\u51fa\u73b0\u6096\u8bba\u7126\u5934\u70c2\u989d\u3002\u4e3a\u4e86\u4fee\u8865\u8fd9\u4e2a\u5927\u6f0f\u6d1e\uff0c\u5e0c\u5c14\u4f2f\u7279\u63d0\u51fa\u4e00\u4e2a\u8ba1\u5212\uff0c\u5e0c\u671b\u80fd\u7528\u6709\u7a77\u7684\u63a8\u7406\u6765\u7814\u7a76\u6570\u5b66\u5f62\u5f0f\u7cfb\u7edf\u4e2d\u7684\u517c\u5bb9\u6027\u95ee\u9898\u3002\u4e0d\u5e78\uff0c\u57281931\u5e74
\nGodel \u8bc1\u660e\u4e86\u4e0d\u53ef\u80fd\u7528\u6570\u5b66\u65b9\u6cd5\u5efa\u7acb\u6570\u5b66\u7684\u517c\u5bb9\u6027\uff0c\u5e0c\u5c14\u4f2f\u7279\u7684\u5e0c\u671b\u7ec8\u7a76\u6ca1\u80fd\u5b9e\u73b0\u3002
\n\u3000\u30001930\u5e74\uff0c68\u5c81\u7684\u5e0c\u5c14\u4f2f\u7279\u7531\u54e5\u5ef7\u6839\u5927\u5b66\u9000\u4f11\uff0c\u4ed6\u7684\u5de5\u4f5c\u7531\u4ed6\u7684\u5f97\u610f\u95e8\u751f Weyl \u63a5\u4efb\u3002
\n1933\u5e74\uff0c\u5e0c\u7279\u52d2\u4e0a\u53f0\uff0c\u60c5\u52bf\u6025\u8f6c\u76f4\u4e0b\u3002\u4e0d\u4e45\u4e4b\u540e\uff0c\u8bb8\u591a\u72b9\u592a\u79d1\u5b66\u5bb6\u88ab\u8feb\u79bb\u5f00\u5fb7\u56fd\uff0c\u6700\u540e\uff0c\u6240\u6709\u5916\u56fd\u7c4d\u7684\u6559\u6388\u90fd\u88ab\u89e3\u9664\u804c\u52a1\uff0c\u745e\u58eb\u7c4d\u7684 Weyl \u4e5f\u4e0d\u4f8b\u5916\u3002\u6b64\u65f6\uff0c\u5bc6\u53cb
\nMinkowski\u3001Hurwitz\u3001\u826f\u5e08\u517c\u76ca\u53cb Klein \u90fd\u5df2\u5148\u4ed6\u79bb\u5f00\u4eba\u4e16\uff0c\u66fe\u7ecf\u76db\u6781\u4e00\u65f6\u7684\u6570\u5b66\u4e2d\u5fc3\u54e5\u5ef7\u6839\uff0c\u51e0\u4e4e\u53ea\u5269\u5e0c\u5c14\u4f2f\u7279\u5b64\u5355\u4e00\u4eba\u3002
\n\u3000\u30001942 \u5e74 1\u670823\u65e5\u662f\u5e0c\u5c14\u4f2f\u7279\u516b\u5341\u5c81\u751f\u65e5\uff0c\u54e5\u5ef7\u6839\u6ca1\u6709\u4efb\u4f55\u8868\u793a\uff0c\u5c31\u5728\u8fd9\u4e00\u5929\uff0c\u5e0c\u5c14\u4f2f\u7279\u5728\u54e5\u5ef7\u6839\u5927\u8857\u4e0a\u8dcc\u5012\uff0c\u4ece\u6b64\u957f\u5367\u4e0d\u8d77\u3002
\n\u3000\u3000\u5373\u4f7f\u4ed6\u53bb\u4e16\u4e86\uff0c\u4f46\u662f\u4ed6\u57281900\u5e74\u5728\u5df4\u9ece\u63d0\u51fa\u7684\u95ee\u9898\uff0c\u6301\u7eed\u5e26\u7ed9\u6570\u5b66\u8fdb\u5c55\uff0c\u5f71\u54cd\u6df1\u8fdc\uff0c\u50cf\u662f\u524d\u51e0\u671f\u4ecb\u7ecd\u7684\u8d39\u5c14\u5179\u5956\uff0c\u5f88\u591a\u8d39\u5c14\u5179\u5956\u5f97\u4e3b\u4fbf\u662f\u56e0\u4e3a\u5728\u5e0c\u5c14\u4f2f\u7279\u95ee\u9898\u4e0a\uff0c\u505a\u51fa\u4e86\u6210\u679c\uff1b\u4e00\u4e9b\u4e8c\u5341\u4e16\u7eaa\u65b0\u53d1\u5c55\u7684\u6570\u5b66\u9886\u57df\uff0c\u4e5f\u591a\u591a\u5c11\u5c11\u53ef\u7531\u5e0c\u5c14\u4f2f\u7279\u95ee\u9898\u7aa5\u89c1\u5176\u8109\u7edc\u3002<\/p>\n
\u4e94\u3001\u201c\u4e03\u6865\u95ee\u9898\u201d\u4e0e\u6b27\u62c9\u3001\u62d3\u6251\u5b66<\/p>\n
\u54e5\u5c3c\u65af\u5821\u6fd2\u4e34\u84dd\u8272\u7684\u6ce2\u7f57\u7684\u6d77\uff0c\u662f\u4e00\u5ea7\u53e4\u8001\u800c\u7f8e\u4e3d\u7684\u57ce\u5e02\uff0c\u5e03\u52d2\u683c\u5c14\u6cb3\u7684\u4e24\u6761\u652f\u6d41\u5728\u8fd9\u91cc\u6c47\u5408\uff0c\u7136\u540e\u6a2a\u8d2f\u5168\u57ce\uff0c\u6d41\u5165\u5927\u6d77\u3002\u6cb3\u5fc3\u6709\u4e00\u4e2a\u5c0f\u5c9b\u3002\u6cb3\u6c34\u628a\u57ce\u5e02\u5206\u6210\u4e86\uff14\u5757\uff0c\u4e8e\u662f\uff0c\u4eba\u4eec\u5efa\u9020\u4e86\uff17\u5ea7\u5404\u5177\u7279\u8272\u7684\u6865\uff0c\u628a\u54e5\u5c3c\u65af\u5821\u8fde\u6210\u4e00\u4f53\u3002<\/p>\n
\u3000\u3000\u4e00\u5929\u53c8\u4e00\u5929\uff0c\uff17\u5ea7\u6865\u4e0a\u8d70\u8fc7\u4e86\u65e0\u6570\u7684\u884c\u4eba\u3002\u4e0d\u77e5\u4ece\u4ec0\u4e48\u65f6\u5019\u8d77\uff0c\u811a\u4e0b\u7684\u6865\u6881\u89e6\u53d1\u4e86\u4eba\u4eec\u7684\u7075\u611f\uff0c\u4e00\u4e2a\u6709\u8da3\u7684\u95ee\u9898\u5728\u5c45\u6c11\u4e2d\u4f20\u5f00\u4e86\uff1a\u8c01\u80fd\u591f\u4e00\u6b21\u8d70\u904d\u6240\u6709\u7684\uff17\u5ea7\u6865\uff0c\u800c\u4e14\u6bcf\u5ea7\u6865\u90fd\u53ea\u901a\u8fc7\u4e00\u6b21\uff1f<\/p>\n
\u3000\u3000\u8fd9\u4e2a\u95ee\u9898\u4f3c\u4e4e\u4e0d\u96be\uff0c\u8c01\u90fd\u4e50\u610f\u7528\u5b83\u6765\u6d4b\u8bd5\u4e00\u4e0b\u81ea\u5df1\u7684\u667a\u529b\u3002\u53ef\u662f\uff0c\u8c01\u4e5f\u6ca1\u6709\u627e\u5230\u4e00\u6761\u8fd9\u6837\u7684\u8def\u7ebf\u3002\u8fde\u4ee5\u535a\u5b66\u8457\u79f0\u7684\u5927\u5b66\u6559\u6388\u4eec\uff0c\u4e5f\u611f\u5230\u4e00\u7b79\u83ab\u5c55\u3002\u201d\u4e03\u6865\u95ee\u9898\u201d\u96be\u4f4f\u4e86\u54e5\u5c3c\u65af\u5821\u7684\u6240\u6709\u5c45\u6c11\u3002\u54e5\u5c3c\u65af\u5821\u4e5f\u56e0\u201d\u4e03\u6865\u95ee\u9898\u201d\u800c\u51fa\u4e86\u540d\u3002<\/p>\n
\u3000\u3000\u54e5\u5c3c\u65af\u5821\u4e03\u6865\u95ee\u9898\u4f20\u5f00\u540e\uff0c\u5f15\u8d77\u4e86\u5927\u6570\u5b66\u5bb6\u6b27\u62c9\u7684\u5174\u8da3\u3002\u6b27\u62c9\u6ca1\u6709\u53bb\u8fc7\u54e5\u5c3c\u65af\u5821\uff0c\u8fd9\u4e00\u6b21\uff0c\u4ed6\u4e5f\u6ca1\u6709\u53bb\u4eb2\u81ea\u6d4b\u8bd5\u53ef\u80fd\u7684\u8def\u7ebf\u3002\u4ed6\u77e5\u9053\uff0c\u5982\u679c\u6cbf\u7740\u6240\u6709\u53ef\u80fd\u7684\u8def\u7ebf\u90fd\u8d70\u4e00\u6b21\u7684\u8bdd\uff0c\u4e00\u5171\u8981\u8d705040\u6b21\u3002\u5c31\u7b97\u662f\u4e00\u5929\u8d70\u4e00\u6b21\uff0c\u4e5f\u9700\u898113\u5e74\u591a\u7684\u65f6\u95f4\uff0c\u5b9e\u9645\u4e0a\uff0e\u6b27\u62c9\u53ea\u7528\u4e86\u51e0\u5929\u7684\u65f6\u95f4\u5c31\u89e3\u51b3\u4e86\u4e03\u6865\u95ee\u9898\u3002<\/p>\n
\u3000\u3000\u5256\u6790\u4e00\u4e0b\u6b27\u62c9\u7684\u89e3\u6cd5\u662f\u9976\u6709\u8da3\u5473\u7684\u3002
\n\u3000\u3000\u7b2c\u4e00\u6b65\uff0c\u6b27\u62c9\u628a\u4e03\u6865\u95ee\u9898\u62bd\u8c61\u6210\u4e00\u4e2a\u5408\u9002\u7684\u201d\u6570\u5b66\u6a21\u578b\u201d\u3002\u4ed6\u60f3\uff1a\u4e24\u5cb8\u7684\u9646\u5730\u4e0e\u6cb3\u4e2d\u7684\u5c0f\u5c9b\uff0c\u90fd\u662f\u6865\u6881\u7684\u8fde\u63a5\u70b9\uff0c\u5b83\u4eec\u7684\u5927\u5c0f\u3002\u5f62\u72b6\u5747\u4e0e\u95ee\u9898\u672c\u8eab\u65e0\u5173\u3002\u56e0\u6b64\uff0c\u4e0d\u59a8\u628a\u5b83\u4eec\u770b\u4f5c\u662f4\u4e2a\u70b9\u30027\u5ea7\u6865\u662f7\u6761\u5fc5\u987b\u7ecf\u8fc7\u7684\u8def\u7ebf\uff0c\u5b83\u4eec\u7684\u957f\u77ed\u3001\u66f2\u76f4\uff0c\u4e5f\u4e0e\u95ee\u9898\u672c\u8eab\u65e0\u5173\u3002\u56e0\u6b64\uff0c\u4e0d\u59a8\u4efb\u610f\u753b7\u6761\u7ebf\u6765\u8868\u793a\u5b83\u4eec\u3002\u5c31\u8fd9\u6837\uff0c\u6b27\u62c9\u5c06\u4e03\u6865\u95ee\u9898\u62bd\u8c61\u6210\u4e86\u4e00\u4e2a\u201d\u4e00\u7b14\u753b\u201d\u95ee\u9898\u3002\u600e\u6837\u4e0d\u91cd\u590d\u5730\u901a\u8fc77\u5ea7\u6865\uff0c\u53d8\u6210\u4e86\u600e\u6837\u4e0d\u91cd\u590d\u5730\u753b\u51fa\u4e00\u4e2a\u51e0\u4f55\u56fe\u5f62\u7684\u95ee\u9898\u3002\u539f\u5148\uff0c\u4eba\u4eec\u662f\u8981\u6c42\u627e\u51fa\u4e00\u6761\u4e0d\u91cd\u590d\u7684\u8def\u7ebf\uff0c\u6b27\u62c9\u60f3\uff0c\u6210\u5343\u4e0a\u4e07\u7684\u4eba\u90fd\u5931\u8d25\u4e86\uff0c\u8fd9\u6837\u7684\u8def\u7ebf\u4e5f\u8bb8\u6839\u672c\u4e0d\u5b58\u5728\u7684\u3002\u5982\u679c\u6839\u672c\u4e0d\u5b58\u5728\uff0c\u786c\u8981\u53bb\u5bfb\u627e\u5b83\u5c82\u4e0d\u662f\u767d\u8d39\u529b\u6c14\uff01\u4e8e\u662f\uff0c\u6b27\u62c9\u63a5\u4e0b\u6765\u7740\u624b\u5224\u65ad\uff1a\u8fd9\u79cd\u4e0d\u91cd\u590d\u7684\u8def\u7ebf\u7a76\u7adf\u5b58\u5728\u4e0d\u5b58\u5728\uff1f\u7531\u4e8e\u8fd9\u4e48\u6539\u53d8\u4e86\u4e00\u4e0b\u63d0\u95ee\u7684\u89d2\u5ea6\uff0c\u6b27\u62c9\u6293\u4f4f\u4e86\u95ee\u9898\u7684\u5b9e\u8d28\u3002<\/p>\n
\u3000\u3000\u6700\u540e\uff0c\u6b27\u62c9\u8ba4\u771f\u8003\u5bdf\u4e86\u4e00\u7b14\u753b\u56fe\u5f62\u7684\u7ed3\u6784\u7279\u5f81\u3002\u6b27\u62c9\u53d1\u73b0\uff0c\u51e1\u662f\u80fd\u7528\u4e00\u7b14\u753b\u6210\u7684\u56fe\u5f62\uff0c\u90fd\u6709\u8fd9\u6837\u4e00\u4e2a\u7279\u70b9\uff1a\u6bcf\u5f53\u4f60\u7528\u7b14\u753b\u4e00\u6761\u7ebf\u8fdb\u5165\u4e2d\u95f4\u7684\u4e00\u4e2a\u70b9\u65f6\uff0c\u4f60\u8fd8\u5fc5\u987b\u753b\u4e00\u6761\u7ebf\u79bb\u5f00\u8fd9\u4e2a\u70b9\u3002\u5426\u5219\uff0c\u6574\u4e2a\u56fe\u5f62\u5c31\u4e0d\u53ef\u80fd\u7528\u4e00\u7b14\u753b\u51fa\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u5355\u72ec\u8003\u5bdf\u56fe\u4e2d\u7684\u4efb\u4f55\u4e00\u4e2a\u70b9\uff08\u9664\u8d77\u70b9\u548c\u7ec8\u70b9\u5916\uff09\uff0c\u5b83\u90fd\u5e94\u8be5\u4e0e\u5076\u6570\u6761\u7ebf\u76f8\u8fde\uff1b\u5982\u679c\u8d77\u70b9\u4e0e\u7ec8\u70b9\u91cd\u5408\uff0c\u90a3\u4e48\uff0c\u8fde\u8fd9\u4e2a\u70b9\u4e5f\u5e94\u8be5\u4e0e\u5076\u6570\u6761\u7ebf\u76f8\u8fde\u3002\u5728\u4e03\u6865\u95ee\u9898\u7684\u51e0\u4f55\u56fe\u4e2d\uff0cA\u3001B\u3001C\u4e09\u70b9\u5206\u522b\u4e0e3\u6761\u7ebf\u76f8\u8fde\uff0cD\u70b9\u4e0e5\u6761\u7ebf\u76f8\u8fde\u3002\u8fde\u7ebf\u90fd\u662f\u5947\u6570\u6761\u3002\u56e0\u6b64\uff0c\u6b27\u62c9\u65ad\u5b9a\uff1a\u4e00\u7b14\u753b\u51fa\u8fd9\u4e2a\u56fe\u5f62\u662f\u4e0d\u53ef\u80fd\u7684\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u4e0d\u91cd\u590d\u5730\u901a\u8fc77\u5ea7\u6865\u7684\u8def\u7ebf\u662f\u6839\u672c\u4e0d\u5b58\u5728\u7684\uff01\u76f8\u4f20\u6b27\u62c9\u5728\u89e3\u51b3\u4e86\u4e03\u6865\u95ee\u9898\u4e4b\u540e\uff0c\u66fe\u4eff\u7167\u5b83\u7f16\u4e86\u4e00\u4e2a\u201d\u5341\u4e94\u6865\u95ee\u9898\u201d\u3002\u6709\u5174\u8da3\u7684\u8bfb\u8005\u4e0d\u59a8\u505a\u505a\u3002<\/p>\n
\u3000\u3000\u4e03\u6865\u95ee\u9898\u662f\u4e00\u4e2a\u51e0\u4f55\u95ee\u9898\uff0c\u7136\u800c\uff0c\u5b83\u5374\u662f\u4e00\u4e2a\u4ee5\u524d\u7684\u51e0\u4f55\u5b66\u91cc\u6ca1\u6709\u7814\u7a76\u8fc7\u7684\u51e0\u4f55\u95ee\u9898\u3002\u5728\u4ee5\u524d\u7684\u51e0\u4f55\u5b66\u91cc\uff0c\u4e0d\u8bba\u600e\u6837\u79fb\u52a8\u56fe\u5f62\uff0c\u5b83\u7684\u5927\u5c0f\u548c\u5f62\u72b6\u90fd\u662f\u4e0d\u53d8\u7684\uff1b\u800c\u6b27\u62c9\u5728\u89e3\u51b3\u4e03\u6865\u95ee\u9898\u65f6\uff0c\u628a\u9646\u5730\u53d8\u6210\u4e86\u70b9\uff0c\u6865\u6881\u53d8\u6210\u4e86\u7ebf\uff0c\u800c\u4e14\u7ebf\u6bb5\u7684\u957f\u77ed\u66f2\u76f4\uff0c\u4ea4\u70b9\u7684\u51c6\u786e\u65b9\u4f4d\u3002\u9762\u79ef\u3001\u4f53\u79ef\u7b49\u6982\u5ff5\uff0c\u90fd\u53d8\u5f97\u6ca1\u6709\u610f\u4e49\u4e86\u3002\u4e0d\u59a8\u628a\u4e03\u6865\u753b\u6210\u522b\u7684\u4ec0\u4e48\u7c7b\u4f3c\u7684\u5f62\u72b6\uff0c\u7167\u6837\u53ef\u4ee5\u5f97\u51fa\u4e0e\u6b27\u62c9\u4e00\u6837\u7684\u7ed3\u8bba\u3002<\/p>\n
\u3000\u3000\u5f88\u6e05\u695a\uff0c\u56fe\u4e2d\u4ec0\u4e48\u90fd\u53ef\u4ee5\u53d8\uff0c\u552f\u72ec\u70b9\u7ebf\u4e4b\u95f4\u7684\u76f8\u5173\u4f4d\u7f6e\uff0c\u6216\u76f8\u4e92\u8fde\u7ed3\u7684\u60c5\u51b5\u4e0d\u80fd\u53d8\u3002\u6b27\u62c9\u8ba4\u4e3a\u5bf9\u8fd9\u7c7b\u95ee\u9898\u7684\u7814\u7a76\uff0c\u5c5e\u4e8e\u4e00\u95e8\u65b0\u7684\u51e0\u4f55\u5b66\u5206\u652f\uff0c\u4ed6\u79f0\u4e4b\u4e3a\u201d\u4f4d\u7f6e\u51e0\u4f55\u5b66\u201d\u3002\u4f46\u4eba\u4eec\u628a\u5b83\u901a\u4fd7\u5730\u53eb\u505a\u201d\u6a61\u76ae\u51e0\u4f55\u5b66\u201d\u3002\u540e\u6765\uff0c\u8fd9\u95e8\u6570\u5b66\u5206\u652f\u88ab\u6b63\u5f0f\u547d\u540d\u4e3a\u201d\u62d3\u6251\u5b66\u201d\u3002<\/p>\n
\u3000\u3000\u6b27\u62c9\u5bf9\u4e03\u6865\u95ee\u9898\u7684\u7814\u7a76\uff0c\u662f\u62d3\u6251\u5b66\u7814\u7a76\u7684\u5148\u58f0\u3002
\n\u3000\u3000\uff11\uff17\uff15\uff10\u5e74\uff0c\u6b27\u62c9\u53c8\u53d1\u73b0\u4e86\u4e00\u4e2a\u6709\u8da3\u7684\u73b0\u8c61\u3002\u6b63\uff14\u9762\u4f53\u6709\uff14\u4e2a\u9876\u70b9\u3001\uff16\u6761\u68f1\uff0c\u5b83\u7684\u9762\u6570\u52a0\u9876\u70b9\u6570\u51cf\u53bb\u68f1\u6570\u7b49\u4e8e\uff12\uff1b\u6b63\uff16\u9762\u4f53\u6709\uff18\u4e2a\u9876\u70b9\u3001\uff11\uff12\u6761\u68f1\uff0c\u4e8e\u662f\uff0c\u5b83\u7684\u9762\u6570\u52a0\u9876\u70b9\u6570\u51cf\u53bb\u68f1\u6570\u4e5f\u7b49\u4e8e2\u3002\u63a5\u7740\uff0c\u6b27\u62c9\u53c8\u8003\u5bdf\u4e86\u6b63\uff11\uff12\u9762\u4f53\u3001\u6b63\uff12\uff14\u9762\u4f53\uff0c\u53d1\u73b0\u90fd\u6709\u76f8\u540c\u7684\u7ed3\u8bba\u3002\u4e8e\u662f\u7ee7\u7eed\u6df1\u5165\u7814\u7a76\u8fd9\u4e2a\u95ee\u9898\uff0c\u7ec8\u4e8e\u53d1\u73b0\u4e86\u4e00\u4e2a\u8457\u540d\u7684\u5b9a\u7406\uff1a
\n\u3000\u3000\uff26\uff08\u9762\u6570\uff09\uff0b\uff36\uff08\u9876\u70b9\u6570\uff09\uff0d\uff25\uff08\u68f1\u6570\uff09=\uff12
\n\u3000\u3000\u6709\u4eba\u8bf4\uff0c\u8fd9\u662f\u62d3\u6251\u5b66\u7684\u7b2c\u4e00\u4e2a\u5b9a\u7406\u3002
\n\u3000\u3000\u62d3\u6251\u5b66\u4e2d\u6709\u8bb8\u591a\u975e\u5e38\u5947\u5999\u7684\u7ed3\u8bba\u3002\u53d6\u4e00\u5f20\u5c0f\u7eb8\u6761\uff0c\u5c06\u7eb8\u6761\u7684\u4e00\u7aef\u626d\u8f6c180\u00b0\uff0c\u518d\u4e0e\u7eb8\u6761\u7684\u53e6\u4e00\u7aef\u7c98\u5408\u8d77\u6765\uff0c\u5c31\u505a\u6210\u4e86\u4e00\u4e2a\u5c0f\u201d\u6885\u6bd4\u4e4c\u65af\u5e26\u201d\u3002\u522b\u770b\u8fd9\u4e2a\u5c0f\u7eb8\u6761\u5236\u4f5c\u8d77\u6765\u633a\u7b80\u5355\uff0c\u5374\u5947\u7279\u5f97\u53eb\u4eba\u4e0d\u53ef\u601d\u8bae\u3002\u4f8b\u5982\uff0c\u653e\u4e00\u53ea\u8682\u8681\u5230\u7eb8\u5e26\u4e0a\uff0c\u8ba9\u5b83\u6cbf\u7740\u56fe\u4e2d\u7684\u865a\u7ebf\u4e00\u76f4\u5f80\u524d\u722c\uff0c\u90a3\u4e48\uff0c\u8fd9\u53ea\u8682\u8681\u5c31\u53ef\u4ee5\u4e00\u76f4\u722c\u904d\u7eb8\u5e26\u7684\u4e24\u4e2a\u9762\u3002\u5373\u4f7f\u6cbf\u865a\u7ebf\u5c06\u6885\u6bd4\u4e4c\u65af\u5e26\u526a\u5f00\uff0c\u5b83\u4e5f\u4e0d\u4f1a\u65ad\u5f00\uff0c\u4ec5\u4ec5\u53ea\u662f\u957f\u5ea6\u589e\u52a0\u4e86\u4e00\u500d\u800c\u5df2\u3002<\/p>\n
\u3000\u3000\u201d\u8d70\u8ff7\u5bab\u201d\u662f\u4e00\u79cd\u975e\u5e38\u6709\u8da3\u7684\u6570\u5b66\u6e38\u620f\uff0c\u5b9e\u9645\u4e0a\uff0c\u5b83\u662f\u62d3\u6251\u5b66\u91cc\u4e00\u79cd\u5f88\u7b80\u5355\u7684\u5c01\u95ed\u66f2\u7ebf\u3002\u6cd5\u56fd\u6570\u5b66\u5bb6\u7ea6\u5f53\u6307\u51fa\uff1a\u8981\u5224\u65ad\u4e00\u4e2a\u70b9\u5728\u8ff7\u5bab\u7684\u5185\u90e8\u8fd8\u662f\u5916\u90e8\uff0c\u6709\u4e00\u79cd\u5f88\u5de7\u5999\u7684\u65b9\u6cd5\u3002\u8fd9\u5c31\u662f\uff1a\u5148\u5728\u8ff7\u5bab\u7684\u6700\u5916\u9762\u627e\u4e00\u70b9\uff0c\u7528\u76f4\u7ebf\u5c06\u8fd9\u4e24\u4e2a\u70b9\u8fde\u63a5\u8d77\u6765\uff0c\u7136\u540e\u518d\u8003\u5bdf\u76f4\u7ebf\u4e0e\u5c01\u95ed\u66f2\u7ebf\u76f8\u4ea4\u7684\u6b21\u6570\u3002\u5982\u679c\u76f8\u4ea4\u6b21\u6570\u662f\u5947\u6570\uff0c\u5219\u5df2\u77e5\u70b9\u5728\u8ff7\u5bab\u7684\u5185\u90e8\uff0c\u4ece\u8fd9\u91cc\u662f\u8d70\u4e0d\u51fa\u8ff7\u5bab\u7684\uff1b\u53cd\u4e4b\u5219\u4e00\u5b9a\u80fd\u8d70\u51fa\u8ff7\u5bab\u3002<\/p>\n
\u3000\u3000\u5728\u6b27\u62c9\u4e4b\u540e\uff0c\u4eba\u4eec\u53c8\u9646\u7eed\u53d1\u73b0\u4e86\u4e00\u4e9b\u62d3\u6251\u5b66\u5b9a\u7406\u3002\u4f46\u8fd9\u4e9b\u77e5\u8bc6\u90fd\u5f88\u96f6\u788e\uff0c\u76f4\u5230\uff11\uff19\u4e16\u7eaa\u7684\u6700\u540e\u51e0\u5e74\u91cc\uff0c\u6cd5\u56fd\u6570\u5b66\u5bb6\u5e9e\u52a0\u83b1\u5f00\u59cb\u7cfb\u5e95\u5730\u7814\u7a76\u62d3\u6251\u5b66\uff0c\u624d\u5960\u5b9a\u4e86\u8fd9\u95e8\u6570\u5b66\u5206\u652f\u7684\u57fa\u7840\u3002<\/p>\n
\u3000\u3000\u73b0\u5728\uff0c\u62d3\u6251\u5b66\u5df2\u6210\u4e3a20\u4e16\u7eaa\u6700\u4e30\u5bcc\u591a\u5f69\u7684\u4e00\u95e8\u6570\u5b66\u5206\u652f\u3002<\/p>\n
\u516d\u3001 \u8d6b\u5c14\u5df4\u7279\u5728\u54e5\u5c3c\u65af\u5821\u5927\u5b66\u4efb\u655924\u5e74
\n\u8d6b\u5c14\u5df4\u7279\uff1a Johann Friedrich Herbart (1776-1841)
\n\u5fb7\u56fd\u54f2\u5b66\u5bb6\u3001\u6559\u80b2\u5bb6\u548c\u5fc3\u7406\u5bb6\u3002\u751f\u4e8e\u5fb7\u56fd\u5965\u767b\u5821\u3002\u4ed6\u7684\u5e7c\u5e74\u6559\u80b2\u53d7\u76ca\u4e8e\u6bcd\u4eb2\u548c\u5bb6\u5ead\u6559\u5e08\uff0c\u4ee5\u540e\u5165\u62c9\u4e01\u5b66\u6821\uff0c\u4e8e1794\u5e74\u8fdb\u8036\u62ff\u5927\u5b66\u3002\u5728\u5b66\u6821\u5185\u4ed6\u7814\u7a76\u5eb7\u5fb7\u3001\u8d39\u5e0c\u7279\u7b49\u4eba\u7684\u54f2\u5b66\u8457\u4f5c\uff1b\u5f53\u65f6\u521a\u53d1\u8868\u7684\u53e4\u5e0c\u814a\u54f2\u5b66\u5bb6\u5df4\u95e8\u5c3c\u5fb7\uff08Parmenides,\u7ea6\u516c\u5143\u524d\u516d\u4e16\u7eaa\uff09\u5173\u4e8e\u4e00\u5207\u5b58\u5728\u90fd\u662f\u7edf\u4e00\u7684\u548c\u4e0d\u53d8\u7684\u5b66\u8bf4\uff0c\u7ed9\u4ed6\u5f88\u5927\u7684\u5f71\u54cd\u30021797\u5e74\u521d\uff0c\u4ed6\u5728\u4fee\u5b8c\u5927\u5b66\u8bfe\u7a0b\u4e4b\u524d\uff0c\u5373\u53bb\u745e\u58eb\u62c5\u4efb\u4e00\u8d35\u65cf\u7684\u5bb6\u5ead\u6559\u5e08\uff1b\u4ed6\u5bf9\u6559\u80b2\u7684\u5174\u8da3\u5c31\u662f\u7531\u8fd9\u4e2a\u804c\u52a1\u5f15\u8d77\u7684\u3002\u4ed6\u57281799\u5e74\u66fe\u8bbf\u95ee\u8fc7\u67cf\u683c\u591a\u592b\uff0c\u4e0e\u88f4\u65af\u6cf0\u6d1b\u9f50\u76f8\u8bc6\uff0c\u8fd9\u4e00\u8ba4\u8bc6\u7ed9\u4ed6\u7684\u5370\u8c61\u5f88\u6df1\uff0c\u4f46\u662f\u4ed6\u5e76\u672a\u63a5\u53d7\u88f4\u6c0f\u89c2\u70b9\u4e2d\u7684\u6c11\u4e3b\u4e3b\u4e49\u503e\u5411\u30021799\u5e74\u4ee5\u540e\uff0c\u4ed6\u505c\u5c45\u5728\u53cb\u4eba\u5bb6\u4e13\u653b\u54f2\u5b66\uff1b1802\u5e74\u5728\u54e5\u4e01\u6839\u5927\u5b66\u53d6\u5f97\u535a\u58eb\u5b66\u4f4d\uff0c\u968f\u540e\u5373\u5728\u8be5\u6821\u4efb\u6559\u30021809\u5e74\u4ed6\u5e94\u54e5\u5c3c\u65af\u5821\u5927\u5b66\u7684\u8058\u8bf7\uff0c\u7ee7\u5eb7\u5fb7\u4e4b\u540e\uff0c\u8bb2\u6388\u54f2\u5b66\u4e0e\u6559\u80b2\u5b66\uff0c\u5e76\u521b\u7acb\u6559\u80b2\u7814\u7a76\u6240\uff0c\u76ee\u7684\u5728\u4e8e\u8bad\u7ec3\u6559\u5e08\uff0c\u5e94\u7528\u4ed6\u7684\u6559\u80b2\u539f\u7406\u30021833\u5e74\uff0c\u4ed6\u91cd\u56de\u54e5\u4e01\u6839\u5927\u5b66\u4efb\u6559\uff0c\u4e8e1841\u5e74\u901d\u4e16\u3002<\/p>\n
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