{"id":53912,"date":"2024-12-01T18:55:03","date_gmt":"2024-12-01T10:55:03","guid":{"rendered":"https:\/\/swarma.org\/?p=53912"},"modified":"2024-12-01T18:55:03","modified_gmt":"2024-12-01T10:55:03","slug":"ai-%e9%a9%b1%e5%8a%a8%e7%9a%84%e7%ba%af%e6%95%b0%e5%ad%a6%e5%92%8c%e7%90%86%e8%ae%ba%e7%89%a9%e7%90%86%e7%a0%94%e7%a9%b6%ef%bc%9a%e8%87%aa%e4%b8%8a%e8%80%8c%e4%b8%8b%e3%80%81%e8%87%aa%e4%b8%8b","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=53912","title":{"rendered":"AI \u9a71\u52a8\u7684\u7eaf\u6570\u5b66\u548c\u7406\u8bba\u7269\u7406\u7814\u7a76\uff1a\u81ea\u4e0a\u800c\u4e0b\u3001\u81ea\u4e0b\u800c\u4e0a\u548c\u5143\u6570\u5b66"},"content":{"rendered":"
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\u8bba\u6587\u9898\u76ee\uff1aAI-driven research in pure mathematics and theoretical physics<\/span><\/section>\n
\u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/www.nature.com\/articles\/s42254-024-00740-1<\/span><\/section>\n<\/section>\n<\/section>\n<\/blockquote>\n

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2.1 \u81ea\u4e0b\u800c\u4e0a\u7684\u6570\u5b66\uff08Bottom-up mathematics\uff09<\/span><\/p>\n

2.2 \u5143\u6570\u5b66\uff08Meta-mathematics\uff09<\/span><\/p>\n

2.3 \u81ea\u4e0a\u800c\u4e0b\u7684\u6570\u5b66\uff08Top-down mathematics\uff09<\/span><\/span><\/strong><\/p>\n

3. Brich \u6d4b\u8bd5\uff1a\u81ea\u52a8\u6027\u3001\u53ef\u89e3\u91ca\u6027\u3001\u975e\u5e73\u51e1\u6027<\/span><\/strong><\/section>\n
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\u5728\u8fc7\u53bb\u4e94\u5e74\u91cc\uff0c\u4eba\u5de5\u667a\u80fd<\/span>\uff08AI\uff09<\/span>\u5728\u7eaf\u6570\u5b66\u548c\u7406\u8bba\u7269\u7406\u5b66\u7684\u7814\u7a76\u4e2d\u53d6\u5f97\u4e86\u4ee4\u4eba\u77a9\u76ee\u7684\u8fdb\u5c55\u3002\u8fd9\u79cd\u8fdb\u6b65\u7684\u65b9\u5f0f\u4e0e AI \u5728\u8fc7\u53bb\u5341\u5e74\u4e2d\u6539\u53d8\u4eba\u4eec\u65e5\u5e38\u751f\u6d3b\u7684\u65b9\u5f0f\u5927\u76f8\u5f84\u5ead\u3002\u672c\u6587\u5c06\u7528\u201c\u7406\u8bba\u79d1\u5b66\u201d\u4e00\u8bcd\u6765\u6db5\u76d6\u7eaf\u6570\u5b66\u4ee5\u53ca\u5229\u7528\u6570\u5b66\u53d1\u5c55\u548c\u68c0\u9a8c\u7406\u8bba\u548c\u5047\u8bbe\u7684\u8fc7\u7a0b\uff0c\u8fd9\u5305\u62ec\u4e86\u7406\u8bba\u7269\u7406\u5b66\u3002\u6587\u7ae0\u9075\u5faa\u82f1\u56fd\u5b66\u672f\u754c\u7684\u4e60\u60ef\uff0c\u5c06\u7406\u8bba\u7269\u7406\u5b66\u548c\u7406\u8bba\u8ba1\u7b97\u673a\u79d1\u5b66\u89c6\u4f5c\u6570\u5b66\u7684\u5206\u652f\u3002<\/span><\/section>\n

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\u867d\u7136\u5728 1990 \u5e74\u4ee3\uff0cCERN \u7684\u5b9e\u9a8c\u7269\u7406\u5b66\u5bb6\u5728\u5bfb\u627e\u65b0\u7c92\u5b50\u65f6\u5c31\u5f00\u59cb\u4f7f\u7528 AI [1]\uff0c\u4f46\u673a\u5668\u5b66\u4e60\u6280\u672f\u76f4\u5230 2017-2018 \u5e74\u624d\u5728\u7406\u8bba\u7269\u7406\u5b66\u548c\u7eaf\u6570\u5b66\u4e2d\u5d2d\u9732\u5934\u89d2[2-6]\u3002\u5bf9\u53ef\u89e3\u91ca\u6027\u548c\u53ef\u7406\u89e3\u6027<\/span>\uff08interpretability and explicability\uff09<\/span>\u7684\u9700\u6c42\u53ef\u80fd\u662f AI \u5728\u7406\u8bba\u79d1\u5b66\u9886\u57df\u6bd4\u5176\u4ed6\u79d1\u5b66\u9886\u57df\u66f4\u665a\u8d77\u6b65\u7684\u539f\u56e0\u3002\u4e0d\u8fc7\uff0c\u8fd9\u4e2a\u9886\u57df\u6b63\u5728\u8fc5\u901f\u8d76\u4e0a\u3002\u5728\u7406\u8bba\u7269\u7406\u5b66\u4e2d\uff0cAI \u9a71\u52a8\u7684\u7814\u7a76\u5305\u62ec\u4e86\u4ece\u5f26\u7406\u8bba\u4e2d\u7684\u7c92\u5b50\u73b0\u8c61\u5b66\u5230\u5efa\u7acb\u573a\u8bba\u548c\u6df1\u5ea6\u5b66\u4e60\u4e4b\u95f4\u7684\u8054\u7cfb[7]\uff0c\u518d\u5230\u7406\u8bba\u5b87\u5b99\u5b66\u3001\u91cf\u5b50\u573a\u8bba[8]\u4ee5\u53ca\u63ed\u793a\u57fa\u672c\u5bf9\u79f0\u6027[9]\u7684\u7814\u7a76\u3002\u540c\u6837\uff0c\u5728\u7eaf\u6570\u5b66\u9886\u57df\uff0cAI \u7684\u5e94\u7528\u4e5f\u6db5\u76d6\u4e86\u4ee3\u6570\u51e0\u4f55\u3001\u4ee3\u6570\u7ed3\u6784\u4e0e\u8868\u793a\u7406\u8bba\u3001\u7b26\u53f7\u4ee3\u6570\u4e0e\u8ba1\u7b97\u3001\u5fae\u5206\u4e0e\u5ea6\u91cf\u51e0\u4f55\u3001\u6570\u8bba\u3001\u56fe\u8bba\u4e0e\u7ec4\u5408\u6570\u5b66\uff0c\u4ee5\u53ca\u7ebd\u7ed3\u7406\u8bba\u7b49\u3002<\/span><\/section>\n

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\u603b\u7684\u6765\u8bf4\uff0c\u4eba\u4eec\u5bf9\u4e8e AI \u6280\u672f\u5728\u793e\u4f1a\u4e2d\u7684\u89d2\u8272\u6301\u6709\u65e2\u4e50\u89c2\u53c8\u7126\u8651\u7684\u590d\u6742\u6001\u5ea6\u3002\u672c\u6587\u65e8\u5728\u6982\u8ff0\u548c\u8ba8\u8bba\u8fd1\u5e74\u6765\u5728\u7406\u8bba\u79d1\u5b66\u4e2d AI \u5e94\u7528\u7684\u8fdb\u6b65\uff0c\u5e76\u5f3a\u8c03\u5176\u5173\u6ce8\u70b9\u548c\u5c40\u9650\u6027\u3002\u6211\u4eec\u5e0c\u671b\u4eba\u4eec\u80fd\u591f\u7406\u6027\u770b\u5f85 AI\uff0c\u65e2\u4e0d\u8fc7\u5206\u72c2\u70ed\uff0c\u4e5f\u4e0d\u65e0\u7aef\u6050\u60e7\uff0c\u5e76\u76f8\u4fe1\u6570\u5b66\u79d1\u5b66\u672a\u6765\u7684\u53d1\u5c55\u5c06\u662f\u4eba\u7c7b\u4e0e AI \u4e4b\u95f4\u4e0d\u53ef\u907f\u514d\u4e14\u5e0c\u671b\u662f\u548c\u8c10\u7684\u5408\u4f5c\u3002<\/span><\/section>\n

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    \u81ea\u4e0b\u800c\u4e0a\uff08Bottom-up\uff09\u65b9\u6cd5<\/span><\/strong>\uff1a\u8fd9\u79cd\u65b9\u6cd5\u8ba4\u4e3a\u6570\u5b66\u662f\u4ece\u57fa\u7840\u7684\u516c\u7406\u51fa\u53d1\uff0c\u9010\u6b65\u6784\u5efa\u8d77\u6240\u6709\u5b9a\u7406\u548c\u65b9\u7a0b\u7684\u3002\u6211\u4eec\u79f0\u8fd9\u79cd\u65b9\u6cd5\u4e3a\u201c\u81ea\u4e0b\u800c\u4e0a\u201d\uff0c\u4ee5\u4f53\u73b0\u7406\u8bba\u7814\u7a76\u7684\u4e25\u8c28\u6027\u3002\u8fd9\u4e0e\u5e0c\u5c14\u4f2f\u7279<\/span>\uff08Hilbert\uff09<\/span>\u7684\u5f62\u5f0f\u4e3b\u4e49\u8ba1\u5212\u548c\u7f57\u7d20-\u6000\u7279\u6d77\u5fb7<\/span>\uff08Russell\u2013Whitehead\uff09<\/span>\u7684\u903b\u8f91\u4e3b\u4e49\u6709\u76f8\u4f3c\u4e4b\u5904\uff0c\u5373\u6570\u5b66\u662f\u901a\u8fc7\u5728\u660e\u786e\u5b9a\u4e49\u7684\u7b26\u53f7\u4e0a\u5e94\u7528\u7cbe\u786e\u89c4\u5219\u6765\u6784\u5efa\u7684\u3002<\/span><\/section>\n<\/li>\n
  • \n
    \u5143\u6570\u5b66\uff08Meta-mathematics\uff09<\/strong>\uff1a\u5143\u79d1\u5b66\u901a\u5e38\u6307\u7684\u662f\u79d1\u5b66\u7814\u7a76\u7684\u79d1\u5b66\u3002\u5728\u672c\u6587\u7684\u80cc\u666f\u4e0b\uff0c\u5b83\u610f\u5473\u7740\u4ece\u8fdc\u5904\u89c2\u5bdf\u6570\u5b66\uff0c\u5c24\u5176\u662f\u4ece\u5df2\u53d1\u8868\u7684\u8bba\u6587\u8bed\u6599\u5e93\u4e2d\u89c2\u5bdf\uff0c\u800c\u4e0d\u5fc5\u6df1\u5165\u7406\u89e3\u6bcf\u4e00\u4e2a\u7ec6\u8282\u3002<\/span><\/section>\n<\/li>\n
  • \n

    \u81ea\u4e0a\u800c\u4e0b\uff08Top-down\uff09\u65b9\u6cd5<\/strong>\uff1a\u5728\u5b9e\u9645\u7684\u7406\u8bba\u5de5\u4f5c\u4e2d\uff0c\u7814\u7a76\u8005\u5728\u5f00\u59cb\u8bc1\u660e\u6216\u63a8\u5bfc\u4e4b\u524d\uff0c\u5f80\u5f80\u4f1a\u5148\u8fdb\u884c\u201c\u5b9e\u9a8c\u201d\u548c\u63d0\u51fa\u201c\u731c\u60f3\u201d\u3002\u6211\u4eec\u5c06\u8fd9\u79cd\u65b9\u6cd5\u79f0\u4e3a\u201c\u81ea\u4e0a\u800c\u4e0b\u201d\uff0c\u5176\u4e2d\u57fa\u4e8e\u7ecf\u9a8c\u548c\u63a8\u6d4b\u7684\u603b\u4f53\u89c6\u89d2\u5f15\u5bfc\u6211\u4eec\u8d70\u5411\u90a3\u4e9b\u53ea\u80fd\u5728\u4eba\u8111\u4e2d\u627e\u5230\u7b54\u6848\u7684\u95ee\u9898\u3002\u8fd9\u79cd\u65b9\u6cd5\u867d\u7136\u4e0e\u5e03\u52b3\u5a01\u5c14<\/span>\uff08Brouwer\uff09<\/span>\u7684\u76f4\u89c9\u4e3b\u4e49\u6570\u5b66\u6709\u76f8\u4f3c\u4e4b\u5904\uff0c\u4f46\u6211\u4eec\u5e94\u8be5\u533a\u5206\u5f00\u6765\u3002\u6211\u4eec\u5c06\u8fdb\u4e00\u6b65\u8ba8\u8bba\u5373\u4f7f\u79d1\u5b66\u95ee\u9898\u662f\u4e00\u4e2a\u9ed1\u7bb1 \uff0cAI \u5982\u4f55\u5e2e\u52a9\u6211\u4eec\u5728\u5236\u5b9a\u7cbe\u786e\u731c\u60f3\u65b9\u9762\u53d6\u5f97\u5b9e\u8d28\u6027\u8fdb\u5c55\uff0c\u5176\u4e2d\u4e25\u8c28\u6027\u6765\u81ea\u4e8e\u7edf\u8ba1\u63a8\u65ad\u3002<\/span><\/p>\n<\/li>\n<\/ul>\n


    <\/span><\/section>\n
    \u5173\u4e8e\u4e0a\u9762\u4e09\u4e2a\u672f\u8bed\u7684\u4f7f\u7528\uff0c\u6211\u4eec\u501f\u7528\u4e86\u7269\u7406\u5b66\u4e2d\u7684\u81ea\u4e0a\u800c\u4e0b\u548c\u81ea\u4e0b\u800c\u4e0a\u7684\u672f\u8bed\uff0c\u5176\u4e2d\u81ea\u4e0b\u800c\u4e0a\u7684\u6a21\u578b\u6784\u5efa\u8d77\u70b9\u662f\u4f4e\u80fd\u91cf\u5c3a\u5ea6\uff0c\u800c\u81ea\u4e0a\u800c\u4e0b\u7684\u8d77\u70b9\u662f\u9ad8\u80fd\u91cf\u5c3a\u5ea6\u3002\u5728\u540e\u9762\u7684\u5185\u5bb9\u4e2d\uff0c\u6211\u4eec\u5c06\u8be6\u7ec6\u8ba8\u8bba AI \u5982\u4f55\u6210\u4e3a\u8fd9\u4e9b\u65b9\u6cd5\u7684\u5de5\u5177\u3002<\/span><\/section>\n

    <\/span><\/section>\n

    2.1 \u81ea\u4e0b\u800c\u4e0a\u7684\u6570\u5b66\uff08Bottom-up mathematics\uff09<\/span><\/strong><\/span><\/h2>\n

    <\/span><\/section>\n
    \u5728 20 \u4e16\u7eaa 20 \u5e74\u4ee3\u521d\uff0c\u6570\u5b66\u5bb6\u5e0c\u5c14\u4f2f\u7279<\/span>\uff08Hilbert\uff09<\/span>\u63d0\u51fa\u4e86\u4e00\u4e2a\u96c4\u5fc3\u52c3\u52c3\u7684\u8ba1\u5212\uff0c\u65e8\u5728\u4ece\u6700\u57fa\u672c\u7684\u516c\u7406\u51fa\u53d1\uff0c\u6784\u5efa\u8d77\u6574\u4e2a\u6570\u5b66\u4f53\u7cfb\u7684\u771f\u7406\u3002\u7136\u800c\uff0c\u5927\u7ea6\u5341\u5e74\u540e\uff0c\u54e5\u5fb7\u5c14<\/span>\uff08G\u00f6del\uff09<\/span>\u3001\u4e18\u5947<\/span>\uff08Church\uff09<\/span>\u548c\u56fe\u7075<\/span>\uff08Turing\uff09<\/span>\u63d0\u51fa<\/span>\u7684\u4e0d\u53ef\u5224\u5b9a\u6027\u548c\u4e0d\u5b8c\u5907\u6027\u5b9a\u7406\u7ed9\u4e86\u8fd9\u4e2a\u8ba1\u5212\u6c89\u91cd\u7684\u6253\u51fb\u3002\u8fd9\u4e9b\u5b9a\u7406\u63ed\u793a\u4e86\u4e00\u4e2a\u6df1\u523b\u7684\u4e8b\u5b9e\uff1a\u5728\u4efb\u4f55\u6570\u5b66\u4f53\u7cfb\u4e2d\uff0c\u603b\u6709\u4e00\u4e9b\u9648\u8ff0\u662f\u65e0\u6cd5\u88ab\u8bc1\u660e\u5176\u771f\u5047\u7684\u3002\u5c3d\u7ba1\u5982\u6b64\uff0c\u90a3\u4e9b\u53ef\u4ee5\u88ab\u5224\u5b9a\u4e14\u5177\u6709\u7814\u7a76\u4ef7\u503c\u7684\u6570\u5b66\u9648\u8ff0\u662f\u5982\u6b64\u4e4b\u591a\uff0c\u8db3\u4ee5\u8ba9\u6211\u4eec\u5148\u96c6\u4e2d\u7cbe\u529b\u53bb\u63a2\u7d22\u5b83\u4eec\u3002\u56e0\u6b64\uff0c\u5c3d\u7ba1\u7406\u8bba\u4e0a\u6211\u4eec\u65e0\u6cd5\u4ece\u57fa\u7840\u51fa\u53d1\u6784\u5efa\u6240\u6709\u7684\u6570\u5b66\u9648\u8ff0\uff0c\u4f46\u6570\u5b66\u5bb6\u4eec\u4ece\u672a\u653e\u5f03\u8fc7\u5bf9\u5404\u79cd\u547d\u9898\u8bc1\u660e\u7684\u8ffd\u6c42\u3002\u8fd9\u79cd\u52aa\u529b\u6700\u7ec8\u50ac\u751f\u4e86\u73b0\u4ee3\u81ea\u52a8\u5b9a\u7406\u8bc1\u660e\u7a0b\u5e8f<\/span>\uff08Automated Theorem Proving Programme\uff0cATP\uff09<\/span>\u7684\u53d1\u5c55\uff0c\u8fd9\u662f\u5bf9\u6000\u7279\u6d77<\/span>\uff08Alfred North Whitehead\uff09<\/span>\u548c\u7f57\u7d20<\/span>\uff08Bertrand Russell\uff09<\/span>\u5728\u6570\u5b66\u57fa\u7840\u5de5\u4f5c\u7684\u4e00\u79cd\u73b0\u4ee3\u56de\u5e94\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u5230\u4e86 20 \u4e16\u7eaa\u4e0b\u534a\u53f6\uff0c\u4eba\u4eec\u9010\u6e10\u610f\u8bc6\u5230\uff0c\u6ca1\u6709\u8ba1\u7b97\u673a\u7684\u5e2e\u52a9\uff0c\u8bb8\u591a\u6570\u5b66\u7684\u57fa\u672c\u7ed3\u679c\u7684\u8bc1\u660e\u51e0\u4e4e\u662f\u4e0d\u53ef\u80fd\u7684\u3002\u4ece\u7b80\u5316\u4e3a\u5927\u91cf\u66b4\u529b\u8ba1\u7b97\u7684\u95ee\u9898<\/span>\uff08\u6bd4\u5982\u56db\u8272\u5b9a\u7406\uff09<\/span>\u5230\u90a3\u4e9b\u590d\u6742\u5230\u9700\u8981\u8d85\u8fc7\u4eba\u7c7b\u4e00\u751f\u65f6\u95f4\u53bb\u5b8c\u6210\u7684\u95ee\u9898<\/span>\uff08\u6bd4\u5982\u7b80\u5355\u6709\u9650\u7fa4\u7684\u5206\u7c7b\uff09<\/span>\uff0c\u8ba1\u7b97\u673a\u5728\u6570\u5b66\u8bc1\u660e\u4e2d\u7684\u4f5c\u7528\u8d8a\u6765\u8d8a\u91cd\u8981\u3002\u8fd9\u79cd\u5bf9\u673a\u5668\u7684\u4f9d\u8d56\u4fc3\u4f7f\u50cf\u9676\u54f2\u8f69\u8fd9\u6837\u6770\u51fa\u7684\u6570\u5b66\u5bb6\u5728\u56fd\u9645\u6570\u5b66\u5bb6\u5927\u4f1a\u4e0a\u547c\u5401\u601d\u8003\u6570\u5b66\u7684\u672a\u6765\u3002\u867d\u7136\u7b2c\u4e00\u4e2a\u57fa\u4e8e\u673a\u5668\u7684\u8bc1\u660e\u5e2e\u52a9\u8f6f\u4ef6[11]\u5728 20 \u4e16\u7eaa 70 \u5e74\u4ee3\u5c31\u51fa\u73b0\u4e86\uff0c\u4f46\u50cf Isabelle\/HOL[12]\u3001Coq[13]\u3001Agda[14] \u548c Lean[15] \u8fd9\u6837\u7684\u8f6f\u4ef6\u5728\u8fd9\u4e2a\u4e16\u7eaa\u63a8\u52a8\u4e86\u81ea\u52a8\u5b9a\u7406\u8bc1\u660e\u7684\u53d1\u5c55\u3002\u5176\u4e2d\u4e00\u4e2a\u5f15\u4eba\u6ce8\u76ee\u7684\u9879\u76ee\u662f Xena \u9879\u76ee\uff0c\u5b83\u7684\u76ee\u6807\u662f\u5c06\u672c\u79d1\u751f\u6c34\u5e73\u7684\u6240\u6709\u6570\u5b66\u77e5\u8bc6<\/span>\uff08\u5305\u62ec\u6bcf\u4e00\u4e2a\u9648\u8ff0\u548c\u8bc1\u660e\u7684\u6bcf\u4e00\u6b65\uff09<\/span>\u90fd\u5f62\u5f0f\u5316\u5230 Lean \u8fd9\u4e2a\u7cfb\u7edf\u4e2d\u3002\u53bb\u5e74\uff0cLean \u7684 MathLib \u5e93\u8fd8\u88ab\u7528\u6765\u8bc1\u660e\u4e86\u591a\u9879\u5f0f Freiman-Ruzsa \u731c\u60f3\u3002\u5c3d\u7ba1\u5c06\u6240\u6709\u5f53\u4ee3\u6570\u5b66\u77e5\u8bc6\u4ee5 Coq \u6216 Lean \u7684\u683c\u5f0f\u5b58\u50a8\u7684\u6570\u636e\u5e93\u6784\u5efa\u5de5\u4f5c\u8fd8\u8fdc\u672a\u5b8c\u6210\uff0c\u4f46\u8fd9\u6837\u7684\u6570\u5b66\u6570\u636e\u5e93\u4e00\u65e6\u5efa\u6210\uff0c\u5c06\u80fd\u591f\u901a\u8fc7\u6570\u636e\u6316\u6398\u53d1\u73b0\u65b0\u7684\u7406\u8bba\uff0c\u8fd9\u5c06\u662f\u6211\u4eec\u672a\u6765\u53d1\u5c55\u81ea\u52a8\u5b9a\u7406\u8bc1\u660e\u7684\u601d\u8003\u65b9\u5411\u3002<\/span><\/section>\n

    <\/span><\/section>\n

    2.2 \u5143\u6570\u5b66\uff08Meta-mathematics\uff09<\/span><\/strong><\/span><\/h2>\n

    <\/span><\/section>\n
    \u6570\u5b66\u88ab\u89c6\u4e3a\u4e00\u79cd\u8bed\u8a00\uff0c\u8fd9\u4e00\u89c2\u70b9\u4ece\u300a\u6570\u5b66\u539f\u7406\u300b\u5ef6\u7eed\u5230\u73b0\u4ee3\u8ba1\u7b97\u673a\u79d1\u5b66\u3002\u54f2\u5b66\u5bb6\u7ef4\u7279\u6839\u65af\u5766<\/span>\uff08Ludwig Wittgenstein\uff09<\/span>\u542f\u53d1\u6211\u4eec\u5c06\u6570\u5b66\u516c\u5f0f\u548c\u8bc1\u660e\u770b\u4f5c\u7b26\u53f7\u5e8f\u5217\u3002\u81ea\u7136\u8bed\u8a00\u5904\u7406<\/span>\uff08Natural Language Processing\uff0cNLP\uff09<\/span>\u57fa\u4e8e\u56fe\u7075\u6d4b\u8bd5\u7684\u7406\u5ff5\uff0c\u5df2\u7ecf\u53d1\u5c55\u5230 LLMs \u65f6\u4ee3\uff0c\u8fd9\u4e9b\u6a21\u578b\u80fd\u591f\u6a21\u4eff\u4eba\u7c7b\u4ea4\u6d41\uff0c\u4f46\u5e76\u4e0d\u771f\u6b63\u7406\u89e3\u5185\u5bb9\u3002\u4e5f\u5c31\u662f\u8bf4\uff0cLLMs \u5e76\u6ca1\u6709\u5bf9\u5e95\u5c42\u6750\u6599\u7684\u201c\u7406\u89e3\u201d\u3002\u8fd9\u4e9b\u6a21\u578b\u4ec5\u4ec5\u57fa\u4e8e\u5927\u91cf\u7684\u7edf\u8ba1\u6837\u672c\u8bed\u6599\u5e93\uff0c\u5c06\u5355\u8bcd\u4ee5\u6b63\u786e\u7684\u987a\u5e8f\u7ec4\u5408\u5728\u4e00\u8d77\u3002\u629b\u5f00\u201c\u7406\u89e3\u201d\u7684\u54f2\u5b66\u542b\u4e49<\/span>\uff08\u8fd9\u4e5f\u662f\u6211\u4eec\u9009\u62e9\u5c06\u8fd9\u4e2a\u65b9\u5411\u79f0\u4e3a\u201c\u5143\u6570\u5b66\u201d\u7684\u539f\u56e0\uff09<\/span>\uff0c\u5f88\u660e\u663e LLMs \u5728\u6a21\u4eff\u4eba\u7c7b\u6c9f\u901a\u65b9\u9762\u5177\u6709\u53d8\u9769\u6027\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u5728\u6570\u5b66\u548c\u7406\u8bba\u7269\u7406\u7814\u7a76\u4e2d\uff0cLLMs \u7684\u5e94\u7528\u5c55\u793a\u4e86\u5b83\u4eec\u80fd\u591f\u8bc6\u522b\u79d1\u5b66\u9886\u57df\u5185\u4e0d\u540c\u5b50\u9886\u57df\u4e4b\u95f4\u7684\u5dee\u5f02\u6027\u3002Word2Vec \u795e\u7ecf\u7f51\u7edc\u53ef\u80fd\u662f\u6700\u57fa\u672c\u7684 LLMs \u6280\u672f\uff0c\u5728\u5e94\u7528\u4e8e arXiv \u548c viXra \u4e24\u79cd\u9884\u5370\u672c\u670d\u52a1\u5668\u7684\u7814\u7a76\u4e2d\uff0cWord2Vec \u5c55\u793a\u4e86\u5176\u5728\u7406\u89e3\u79d1\u5b66\u6587\u732e\u9886\u57df\u548c\u533a\u5206\u4e3b\u6d41\u4e0e\u975e\u4e3b\u6d41\u79d1\u5b66\u601d\u60f3\u65b9\u9762\u7684\u6f5c\u529b\u3002\u901a\u8fc7\u5206\u6790 arXiv \u9884\u5370\u672c\u670d\u52a1\u5668\u7684\u6807\u9898\uff0cWord2Vec \u53ef\u4ee5\u533a\u5206\u51fa\u7406\u8bba\u7269\u7406\u7684\u4e0d\u540c\u65b9\u5411\u3002\u7531\u4e8e viXra \u5305\u542b\u4e86\u4e00\u4e9b\u672a\u88ab\u4e3b\u6d41\u79d1\u5b66\u63a5\u53d7\u7684\u89c2\u70b9\u548c\u7406\u8bba\uff0cWord2Vec \u5728 viXra \u4e2d\u7684\u4f5c\u7528\u4e0d\u90a3\u4e48\u663e\u8457\u3002\u8fd9\u8868\u660e\u4e3b\u6d41\u79d1\u5b66\u7684\u8bed\u6cd5\u6bd4\u8fb9\u7f18\u79d1\u5b66\u7684\u8bed\u6cd5\u5728\u6807\u9898\u5c42\u9762\u4e0a\u66f4\u4e3a\u81ea\u6d3d\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u5982\u4eca\uff0cWord2Vec \u5df2\u7ecf\u88ab\u5176\u4ed6\u6df1\u5ea6\u5b66\u4e60\u67b6\u6784<\/span>\uff08\u5982 transformers\uff09<\/span>\u6240\u53d6\u4ee3\uff0cLLMs \u5728\u6570\u5b66\u9886\u57df\u7684\u5e94\u7528\u6b63\u5728\u84ec\u52c3\u53d1\u5c55\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0cDeepMind \u7684 AlphaGeo \u6700\u8fd1\u80fd\u591f\u4e3a\u6b27\u51e0\u91cc\u5f97\u51e0\u4f55\u4e2d\u7684\u5965\u6797\u5339\u514b\u7ea7\u522b\u95ee\u9898\u751f\u6210\u6b63\u786e\u7684\u3001\u4eba\u7c7b\u53ef\u7406\u89e3\u7684\u8bc1\u660e\uff0c\u5c3d\u7ba1\u8fd9\u4e00\u8fc7\u7a0b\u4e2d\u4ecd\u90e8\u5206\u4f9d\u8d56\u4e8e\u4f20\u7edf\u641c\u7d22\u65b9\u6cd5\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u8fd9\u4e9b\u8fdb\u6b65\u8868\u660e\uff0c\u5982\u679c\u5b58\u5728\u4e00\u4e2a\u5b8c\u6574\u7684\u3001\u7cbe\u786e\u683c\u5f0f\u7684\u8bed\u8a00\u6570\u636e\u5e93\uff0c\u6bd4\u5982\u201cLean\u201d\uff0c\u7528\u4e8e\u6240\u6709\u5f53\u4ee3\u6570\u5b66\uff0c\u90a3\u4e48LLMs \u5bf9\u8fd9\u4e00\u5e9e\u5927\u6570\u636e\u96c6\u7684\u65b9\u6cd5\u5e94\u8be5\u80fd\u591f\u4ea7\u751f\u65b0\u7684\u6570\u5b66\u3002<\/span><\/section>\n


    <\/span><\/h2>\n

    2.3 \u81ea\u4e0a\u800c\u4e0b\u7684\u6570\u5b66\uff08Top-down mathematics\uff09<\/span><\/strong><\/span><\/h2>\n


    <\/strong><\/span><\/p>\n

    \u6211\u4eec\u8ba8\u8bba\u7684\u5f88\u591a\u5185\u5bb9\u90fd\u6d89\u53ca\u5230\u6784\u5efa\u6b63\u786e\u7684\u6570\u5b66\u9648\u8ff0\u3002\u4f46\u5b9e\u9645\u4e0a\uff0c\u5f88\u591a\u65f6\u5019\u6211\u4eec\u5e76\u4e0d\u6e05\u695a\u5e94\u8be5\u8bc1\u660e\u4ec0\u4e48\u3002\u5b9e\u9645\u4e0a\uff0c\u6570\u5b66\u5bb6\u662f\u5982\u4f55\u5de5\u4f5c\u7684\u5462\uff1f\u6570\u5b66\u8bba\u6587\u5f80\u5f80\u662f\u5012\u7740\u5199\u7684\u3002\u65e5\u590d\u4e00\u65e5\uff0c\u6570\u5b66\u5bb6\u5728\u7eb8\u4e0a\u6d82\u9e26\uff0c\u5c1d\u8bd5\u5404\u79cd\u60f3\u6cd5\u3001\u9519\u8bef\u548c\u8868\u8fbe\uff0c\u76f4\u5230\u627e\u5230\u4e00\u4e9b\u6709\u610f\u4e49\u7684\u7ed3\u679c\uff0c\u7136\u540e\u518d\u56de\u8fc7\u5934\u6765\uff0c\u7528\u5b9a\u4e49\u3001\u5b9a\u7406\u548c\u63a8\u5bfc\u6765\u6b63\u5f0f\u5316\u8fd9\u4e9b\u7ed3\u679c\uff0c\u4ece\u800c\u5f97\u51fa\u903b\u8f91\u4e0a\u7684\u7ed3\u8bba\u3002\u56e0\u6b64\uff0c\u5c3d\u7ba1\u6570\u5b66\u548c\u7406\u8bba\u7269\u7406\u7684\u671f\u520a\u8bba\u6587\u770b\u8d77\u6765\u662f\u81ea\u4e0b\u800c\u4e0a\u7684\uff0c\u4f46\u53d1\u73b0\u8fc7\u7a0b\u6070\u6070\u76f8\u53cd\uff0c\u8fd9\u79cd\u53cc\u91cd\u6027\u88ab\u79f0\u4e3a\u201c\u7efc\u5408\u4e0e\u5206\u6790\u201d\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u5386\u53f2\u4e0a\uff0c\u4e00\u4e9b\u6700\u4f1f\u5927\u7684\u7406\u8bba\u53d1\u73b0\u5c31\u662f\u8fd9\u6837\u4ea7\u751f\u7684\u3002\u725b\u987f<\/span>\uff08Isaac Newton\uff09<\/span>\u548c\u6b27\u62c9<\/span>\uff08Leonhard Euler\uff09<\/span>\u5728\u6570\u5b66\u89e3\u6790\u548c\u6536\u655b\u7684\u9002\u5f53\u6982\u5ff5\u51fa\u73b0\u524d\u7684\u51e0\u4e2a\u4e16\u7eaa\uff0c\u5c31\u81ea\u7531\u5730\u64cd\u7eb5\u7740\u5404\u79cd\u5fae\u79ef\u5206\u8868\u8fbe\u5f0f\uff1b\u4f3d\u7f57\u74e6<\/span>\uff08Evariste Galois \uff09<\/span>\u5728\u7fa4<\/span>\uff08groups\uff09<\/span>\u548c\u57df<\/span>\uff08fields\uff09<\/span>\u7684\u5b9a\u4e49\u51fa\u73b0\u4e4b\u524d\uff0c\u901a\u8fc7\u89c2\u5bdf\u7f6e\u6362\u7fa4<\/span>\uff08permutation groups\uff09<\/span> \u7684\u7ed3\u6784\u5c55\u793a\u4e86\u4e94\u6b21\u65b9\u7a0b\u65e0\u89e3\u7684\u95ee\u9898\u3002\u5728\u7269\u7406\u5b66\u4e2d\uff0c\u7406\u8bba\u5bb6\u4eec\u81ea\u7531\u5730\u64cd\u7eb5\u8d39\u66fc\u79ef\u5206\uff0c\u4ee5\u83b7\u5f97\u4e0e\u5b9e\u9a8c\u60ca\u4eba\u4e00\u81f4\u7684\u7ed3\u679c\uff0c\u5c3d\u7ba1\u91cf\u5b50\u573a\u8bba\u7684\u6570\u5b66\u4e25\u683c\u8868\u8ff0\u5c1a\u4e0d\u5b8c\u5584\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u8fd1\u5e74\u6765\uff0c\u4eba\u4eec\u8d8a\u6765\u8d8a\u62c5\u5fc3 AI \u53ef\u80fd\u4f1a\u53d6\u4ee3\u4eba\u7c7b\u6570\u5b66\u5bb6\u3002\u6709\u4e9b\u4eba\u5c06\u4eba\u7c7b\u6570\u5b66\u5bb6\u89c6\u4e3a\u81ea\u4e0b\u800c\u4e0a\u7684\u903b\u8f91\u7406\u8bba\u673a\u5668\uff0c\u4ece\u5b9a\u4e49\u51fa\u53d1\u6784\u5efa\u8bc1\u660e\u548c\u63a8\u5bfc\u3002\u4f46\u5b9e\u9645\u4e0a\uff0c\u771f\u6b63\u7684\u6570\u5b66\u7814\u7a76\u662f\u57fa\u4e8e\u7075\u611f\u3001\u76f4\u89c9\u548c\u7ecf\u9a8c\u7684\u7ed3\u5408\u3002\u4e0e\u5b66\u9662\u6d3e\u4e25\u683c\u7684\u81ea\u4e0b\u800c\u4e0a\u53d9\u8ff0\u76f8\u6bd4\uff0c\u6211\u4eec\u79f0\u8fd9\u79cd\u65b9\u6cd5\u4e3a\u57fa\u4e8e\u6a21\u7cca\u7f8e\u5b66\u7684\u81ea\u4e0a\u800c\u4e0b\u3002\u5f53\u7136\uff0c\u6700\u7ec8\u6240\u6709\u7684\u9648\u8ff0\u90fd\u5fc5\u987b\u662f\u4e25\u683c\u7684\uff0c\u4efb\u4f55\u6a21\u7cca\u548c\u4e0d\u51c6\u786e\u90fd\u5fc5\u987b\u88ab\u63d0\u70bc\u51fa\u6765\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u4e5f\u8bb8\u4e0e\u666e\u904d\u89c2\u5ff5\u76f8\u53cd\uff0c\u5373\u4f7f\u662f\u6700\u7eaf\u7cb9\u7684\u6570\u5b66\u53d1\u73b0\u4e5f\u79bb\u4e0d\u5f00\u6570\u636e\u3002\u8fd9\u4e9b\u6570\u636e\u4e0d\u662f\u5e26\u6709\u8bef\u5dee\u548c\u65b9\u5dee\u7684\u5b9e\u9a8c\u6570\u636e\uff0c\u800c\u662f\u5206\u7c7b\u548c\u8ba1\u7b97\u7684\u7ed3\u679c\uff0c\u4f8b\u5982\u6709\u9650\u7fa4<\/span>\uff08finite groups\uff09<\/span>\u7684\u7279\u5f81\u8868\u3002\u8fd9\u4e9b\u201c\u7eaf\u6570\u636e\u201d\u662f\u7cbe\u786e\u7684\uff0c\u6ca1\u6709\u7edf\u8ba1\u8bef\u5dee\uff0c\u5e76\u4e14\u80fd\u591f\u63ed\u793a\u5e95\u5c42\u7406\u8bba\u3002\u6b63\u5982\u6570\u5b66\u5bb6\u963f\u8bfa\u5fb7<\/span>\uff08Vladimir Arnold\uff09<\/span>\u6240\u8bf4\uff0c\u201c\u6570\u5b66\u662f\u7269\u7406\u5b66\u4e2d\u5b9e\u9a8c\u6210\u672c\u8f83\u4f4e\u7684\u90e8\u5206\u201d\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u9762\u5bf9\u5bfb\u627e\u8d28\u6570\u6a21\u5f0f\u7684\u53e4\u8001\u95ee\u9898\uff0c16 \u5c81\u7684\u9ad8\u65af<\/span>\uff08Carl Friedrich Gauss\uff09<\/span>\u5b9a\u4e49\u4e86\u8d28\u6570\u8ba1\u6570\u51fd\u6570<\/span>\uff08prime counting function\uff09<\/span>\uff0c\u8be5\u51fd\u6570\u7ed9\u51fa\u4e86\u4e0d\u8d85\u8fc7\u6b63\u5b9e\u6570 x \u7684\u8d28\u6570\u6570\u91cf\u3002\u4ed6\u53c2\u8003\u4e86\u5f53\u65f6\u7684\u8868\u683c\uff0c\u5e76\u624b\u5de5\u8ba1\u7b97\u4e86\u6570\u4e07\u4e2a\u66f4\u591a\u7684\u6570\u5b57\uff0c\u7b80\u5355\u5730\u7ed8\u5236\u4e86 \u03c0(x)\u3002\u9ad8\u65af\u731c\u60f3 \u03c0(x) \u4e0e x\/ln(x) \u5927\u81f4\u6210\u6bd4\u4f8b\u3002\u8fd9\u4e00\u6df1\u523b\u7684\u89c2\u5bdf\u76f4\u5230\u67ef\u897f<\/span>\uff08Augustin-Louis Cauchy\uff09<\/span>\u548c\u9ece\u66fc<\/span>\uff08Bernhard Riemann\uff09<\/span>\u5efa\u7acb\u590d\u5206\u6790\u4e4b\u540e\uff0c\u624d\u7531\u963f\u8fbe\u739b<\/span>\uff08Jacques Hadamard\uff09<\/span>\u548c\u666e\u6851<\/span>\uff08Charles Jean de la Vall\u00e9e Poussin\uff09<\/span>\u5728 1896 \u5e74\u8bc1\u660e\uff0c\u73b0\u5728\u88ab\u79f0\u4e3a\u8d28\u6570\u5b9a\u7406\uff0c\u662f\u6570\u5b66\u4e2d\u6700\u91cd\u8981\u7684\u7ed3\u679c\u4e4b\u4e00\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u5728 20 \u4e16\u7eaa\uff0c\u6570\u5b66\u5bb6\u4f2f\u5947<\/span>\uff08Bryan John Birch\uff09<\/span>\u548c\u65af\u6e29\u7eb3\u987f-\u6234\u5c14<\/span>\uff08Peter Swinnerton-Dyerplotted\uff09<\/span>\u4f7f\u7528 1960 \u5e74\u4ee3\u7684\u65e9\u671f\u8ba1\u7b97\u673a\uff0c\u7ed8\u5236\u4e86\u692d\u5706\u66f2\u7ebf\u7684\u79e9\u548c\u5176\u4ed6\u6570\u91cf\uff0c\u5e76\u731c\u60f3\u66f2\u7ebf\u7684 L \u51fd\u6570 L(s\uff09\u5728 s \u8d8b\u5411 1 \u65f6\u6d88\u5931\u7684\u9636\u6570\u7b49\u4e8e\u79e9\u3002\u8fd9\u4e00\u89c2\u5bdf\u88ab\u79f0\u4e3a\u4f2f\u5947-\u65af\u6e29\u7eb3\u987f-\u6234\u5c14\u731c\u60f3\uff0c\u662f\u4e00\u4e2a\u5343\u5e74\u5956\u95ee\u9898\uff0c\u5bf9\u73b0\u4ee3\u6570\u5b66\u81f3\u5173\u91cd\u8981\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u4ee5\u4e0a\u53ea\u662f\u65e0\u6570\u4f8b\u5b50\u4e2d\u7684\u4e24\u4e2a\uff0c\u8bf4\u660e\u901a\u8fc7\u5b9e\u9a8c\u7eaf\u6570\u636e\u53ef\u4ee5\u5f97\u51fa\u6df1\u523b\u7684\u7ed3\u679c\u3002\u5b83\u4eec\u5f3a\u8c03\u4e86\u731c\u60f3\u7684\u91cd\u8981\u6027\u3002\u5728\u7406\u8bba\u7814\u7a76\u4e2d\uff0c\u627e\u5230\u6709\u8da3\u7684\u95ee\u9898\u81f3\u5173\u91cd\u8981\uff0c\u800c\u8fd9\u4e2a\u8fc7\u7a0b\u5f80\u5f80\u7531\u51e0\u4e4e\u65e0\u6cd5\u5b9a\u4e49\u7684\u76f4\u89c9\u8fc7\u7a0b\u5f15\u5bfc\u3002\u54c8\u4ee3<\/span>\uff08Godfrey Harold Hardy\uff09<\/span>\u5bf9\u6570\u5b66\u7684\u5b9a\u4e49\u662f\u7b80\u6d01\u7684\uff1a\u201c\u6570\u5b66\u5bb6\u3001\u753b\u5bb6\u6216\u8bd7\u4eba\uff0c\u90fd\u662f\u6a21\u5f0f\u7684\u521b\u9020\u8005\u201d\u3002\u5927\u591a\u6570\u7814\u7a76\u73b0\u5b9e\u4e16\u754c\u6570\u636e\u7684\u79d1\u5b66\u5bb6\u4f1a\u9996\u5148\u5c06\u95ee\u9898\u63d0\u70bc\u6210\u6570\u5b66\u8868\u793a\u3002\u7136\u540e\uff0c\u5b83\u518d\u6b21\u6210\u4e3a\u4ece\u56fe\u8868\u548c\u56fe\u5f62\u5230\u6b63\u5f0f\u7b26\u53f7\u7684\u6570\u5b66\u6a21\u5f0f\u8bc6\u522b\u6e38\u620f\u3002\u4f46\u6709\u4e00\u4ef6\u4e8b\u662f AI \u7cfb\u7edf\u6bd4\u4eba\u7c7b\u505a\u5f97\u66f4\u597d\u7684\uff0c\u90a3\u5c31\u662f\u6a21\u5f0f\u8bc6\u522b\uff0c\u7279\u522b\u662f\u5728\u6570\u636e\u7ef4\u5ea6\u5f88\u9ad8\u7684\u60c5\u51b5\u4e0b\u3002\u8fd9\u4e00\u70b9\u5728\u4e0b\u9762\u7684\u7b80\u5355\u5b9e\u9a8c\u4e2d\u5f97\u5230\u4e86\u4f53\u73b0\u3002<\/span><\/section>\n

    <\/span><\/section>\n
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    <\/span><\/section>\n

    <\/p>\n


    <\/span><\/section>\n
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    <\/span><\/section>\n
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    <\/span><\/section>\n
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    3. Brich \u6d4b\u8bd5\uff1a<\/strong><\/span><\/strong><\/strong><\/p>\n

    \u81ea\u52a8\u6027\u3001\u53ef\u89e3\u91ca\u6027\u3001\u975e\u5e73\u51e1\u6027<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

    \n

    <\/section>\n

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


    <\/p>\n

    \u5728\u81ea\u4e0a\u800c\u4e0b\u7684\u6570\u5b66\u7814\u7a76\u4e2d\uff0c\u6211\u4eec\u9996\u5148\u9700\u8981\u8bc6\u522b\u51fa\u95ee\u9898\u6240\u5728\uff0c\u7136\u540e\u786e\u5b9a\u4e00\u4e2a\u7b56\u7565\u6765\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u3002\u8fd9\u4e24\u4e2a\u6b65\u9aa4\u90fd\u4f9d\u8d56\u4e8e\u4e30\u5bcc\u7684\u7ecf\u9a8c\u548c\u76f4\u89c9\u3002\u867d\u7136\u5927\u578b\u8bed\u8a00\u6a21\u578b\uff0c\u6bd4\u5982\u5e94\u7528\u4e8e\u6570\u636e\u5e93\u7684 Lean \u7684 MathLib\uff0c\u5728\u8fd9\u65b9\u9762\u5df2\u7ecf\u53d6\u5f97\u4e86\u4e00\u4e9b\u521d\u6b65\u7684\u8fdb\u5c55\uff0c\u4f46\u5728\u63d0\u51fa\u731c\u60f3\u8fd9\u4e00\u73af\u8282\uff0c\u6211\u4eec\u8fd8\u6709\u5f88\u957f\u7684\u8def\u8981\u8d70\u3002\u5386\u53f2\u4e0a\uff0c\u50cf\u9ad8\u65af\u548c Birch-Swinnerton-Dyer \u8fd9\u6837\u7684\u6570\u5b66\u5bb6\u4eec\u4ee5\u5176\u5353\u8d8a\u7684\u76f4\u89c9\u63d0\u51fa\u4e86\u91cd\u8981\u7684\u731c\u60f3\u3002\u73b0\u5728\u7684\u95ee\u9898\u662f\uff0cAI<\/strong> <\/strong>\u662f\u5426\u80fd\u591f\u5e2e\u52a9\u6211\u4eec\u533a\u5206\u54ea\u4e9b\u731c\u60f3\u662f\u6709\u4ef7\u503c\u7684\uff0c\u54ea\u4e9b\u662f\u65e0\u7528\u7684\uff1f\u6211\u4eec\u80fd\u5426\u4ece\u6570\u5b66\u6570\u636e\u4e2d\u53d1\u73b0\u4e00\u4e9b\u6a21\u5f0f\uff0c\u5f15\u5bfc\u6211\u4eec\u8d70\u5411\u6709\u8da3\u800c\u975e\u5e73\u51e1\u7684\u6570\u5b66\u53d1\u73b0\uff1f<\/strong>\u8fd9\u4e9b\u95ee\u9898\u5df2\u7ecf\u5f15\u8d77\u4e86\u4eba\u5de5\u667a\u80fd\u9886\u57df\u5185\u4e00\u4e9b\u7cfb\u7edf\u7684\u601d\u8003\u3002<\/span><\/section>\n

    <\/span><\/section>\n

    2023 \u5e74\uff0c\u6587\u7ae0\u4f5c\u8005\u53c2\u4e0e\u534f\u52a9\u7ec4\u7ec7\u4e86\u4e00\u4e2a\u5728\u5251\u6865\u4e3e\u884c\u7684\u4e3a\u671f\u516d\u4e2a\u6708\u7684\u5de5\u4f5c\u4f1a\u8bae<\/span>\uff08https:\/\/www.newton.ac.uk\/event\/blh\/\uff09<\/span>\uff0c\u671f\u95f4\u53c2\u4e0e\u8005\u4eec\u5c1d\u8bd5\u4e3a\u4eba\u5de5\u667a\u80fd\u9a71\u52a8\u7684\u7406\u8bba\u53d1\u73b0\uff0c\u5c24\u5176\u662f\u4eba\u5de5\u667a\u80fd\u8f85\u52a9\u7684\u731c\u60f3\u63d0\u51fa\u3001\u5236\u5b9a\u4e00\u4e9b\u6807\u51c6\u3002\u8fd9\u4e9b\u6807\u51c6\u5305\u62ec\uff1a<\/span><\/p>\n

      \n
    • \n

      \u81ea\u52a8\u6027\uff1a<\/span><\/strong>\u53d1\u73b0\u5b8c\u5168\u7531\u4eba\u5de5\u667a\u80fd\u901a\u8fc7\u6a21\u5f0f\u8bc6\u522b\u81ea\u52a8\u5b8c\u6210\uff0c\u4e0d\u9700\u8981\u4eba\u4e3a\u5e72\u9884\u3002<\/span><\/p>\n<\/li>\n

    • \n

      \u53ef\u89e3\u91ca\u6027\uff1a<\/span><\/strong>\u4efb\u4f55\u731c\u60f3\u6216\u7ed3\u8bba\u90fd\u5fc5\u987b\u5bf9\u4eba\u7c7b\u6570\u5b66\u5bb6\u6765\u8bf4\u662f\u6e05\u6670\u660e\u786e\u7684\uff0c\u4ee5\u81f3\u4e8e\u4ed6\u4eec\u65e0\u6cd5\u5c06\u5176\u4e0e\u4eba\u7c7b\u540c\u4e8b\u63d0\u51fa\u7684\u533a\u522b\u5f00\u6765\u3002<\/span><\/p>\n<\/li>\n

    • \n
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      <\/span><\/section>\n
      \u8fd9\u4e9b\u6807\u51c6\u662f\u7531 Birch \u7684\u4e00\u6b21\u6f14\u8bb2\u542f\u53d1\u7684\uff0c\u56e0\u6b64\u88ab\u79f0\u4e3a Birch \u6d4b\u8bd5\u3002\u8fd9\u4e9b\u6807\u51c6\u975e\u5e38\u4e25\u683c\uff0c\u5230\u76ee\u524d\u4e3a\u6b62\uff0c\u8fd8\u6ca1\u6709\u4efb\u4f55\u4e00\u4e2a\u4eba\u5de5\u667a\u80fd\u8f85\u52a9\u7684\u7406\u8bba\u53d1\u73b0\u80fd\u591f\u5b8c\u5168\u6ee1\u8db3\u8fd9\u4e09\u4e2a\u6761\u4ef6\u3002\u4e0b\u9762\u6211\u4eec\u901a\u8fc7\u4e00\u4e9b\u4f8b\u5b50\u6765\u770b\u770b\u5728\u8fd9\u4e9b\u6807\u51c6\u4e0b\uff0c\u4eba\u5de5\u667a\u80fd\u5728\u54ea\u4e9b\u65b9\u9762\u505a\u5f97\u597d\uff0c\u54ea\u4e9b\u65b9\u9762\u8fd8\u6709\u5f85\u63d0\u9ad8\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u4f8b\u5982\uff0c\u65e9\u671f\u901a\u8fc7\u6df1\u5ea6\u5b66\u4e60\u6765\u83b7\u53d6\u62d3\u6251\u4e0d\u53d8\u91cf\u7684\u5b9e\u9a8c[16]\uff0c\u8fd9\u4e9b\u5b9e\u9a8c\u7684\u51c6\u786e\u7387\u5df2\u7ecf\u63d0\u9ad8\u5230\u4e86 99.9%\u4ee5\u4e0a\uff0c\u8fd9\u6697\u793a\u4e86\u5728\u4ee3\u6570\u51e0\u4f55\u4e2d\u53ef\u80fd\u5b58\u5728\u4e00\u4e9b\u6211\u4eec\u5c1a\u672a\u77e5\u6653\u7684\u7ed3\u6784\uff0c\u8fd9\u4e9b\u7ed3\u6784\u80fd\u591f\u5e2e\u52a9\u6211\u4eec\u8fdb\u884c\u8ba1\u7b97\uff0c\u800c\u4e0d\u5fc5\u4f9d\u8d56\u4e8e\u90a3\u4e9b\u6807\u51c6\u4e14\u8ba1\u7b97\u6210\u672c\u9ad8\u6602\u7684\u65b9\u6cd5\u3002\u4f46\u8fd9\u4e9b\u7ed3\u679c\u4e5f\u66b4\u9732\u4e86\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u65b9\u6cd5\u7684\u4e00\u4e2a\u5178\u578b\u95ee\u9898\uff1a\u6211\u4eec\u65e0\u6cd5\u4ece\u4e2d\u63d0\u53d6\u51fa\u4e00\u4e2a\u53ef\u89e3\u91ca\u7684\u516c\u5f0f\u3002\u56e0\u6b64\uff0c\u5b83\u4eec\u6ca1\u6709\u901a\u8fc7 Birch \u6d4b\u8bd5\u7684\u53ef\u89e3\u91ca\u6027\u6761\u4ef6\u3002\u53e6\u4e00\u4e2a\u4f8b\u5b50\u662f\uff0c\u652f\u6301\u5411\u91cf\u673a\u901a\u8fc7\u7ed8\u5236 Cayley \u4e58\u6cd5\u8868\u627e\u5230\u4e86\u7b80\u5355\u548c\u975e\u7b80\u5355\u6709\u9650\u7fa4\u4e4b\u95f4\u7684\u5206\u79bb[17]\uff0c\u4f46\u5206\u79bb\u7684\u8d85\u66f2\u9762\u975e\u5e38\u590d\u6742\uff0c\u5e76\u4e14\u968f\u7740\u66f4\u591a\u7fa4\u6837\u672c\u7684\u6dfb\u52a0\u800c\u8fdb\u4e00\u6b65\u53d8\u5f62\uff0c\u56e0\u6b64\u53ef\u89e3\u91ca\u6027\u6761\u4ef6\u4ecd\u672a\u6ee1\u8db3\u3002\u901a\u8fc7\u663e\u8457\u6027\u5206\u6790\u53d1\u73b0\u7684\u7ed3\u4e0d\u53d8\u91cf\u5173\u7cfb\u548c\u89e3\u5f00\u6781\u5176\u590d\u6742\u7684\u7ed3\u6240\u9700\u7684 Reidemeister \u79fb\u52a8\uff0c\u867d\u7136\u65b0\u9896\u3001\u6709\u8da3\u4e14\u7cbe\u786e\uff0c\u4f46\u8981\u4e48\u5df2\u7ecf\u88ab\u8bc1\u660e\uff0c\u8981\u4e48\u5728\u8be5\u9886\u57df\u6ca1\u6709\u8db3\u591f\u7684\u5f71\u54cd\u529b\uff0c\u56e0\u6b64\u5b83\u4eec\u6ca1\u6709\u901a\u8fc7\u975e\u5e73\u51e1\u6027\u6761\u4ef6\u3002\u7c7b\u4f3c\u5730\uff0c\u62c9\u9a6c\u52aa\u91d1\u673a\u5668<\/span>\uff08Ramanujan machine\uff09<\/span>\u53d1\u73b0\u7684\u8fde\u5206\u6570\u6052\u7b49\u5f0f\u6216 AI Feynman \u53d1\u73b0\u7684\u7269\u7406\u5b88\u6052\u5b9a\u5f8b\u4e5f\u5c5e\u4e8e\u8fd9\u4e00\u7c7b\u3002\u5373\u4f7f\u5728\u5b9e\u9645\u4efb\u52a1\u4e2d\uff0c\u6bd4\u5982 DeepMind \u53d1\u73b0\u7684\u66f4\u5feb\u7684\u77e9\u9635\u4e58\u6cd5\u7b97\u6cd5\uff0c\u4e5f\u5f88\u5feb\u88ab\u4eba\u7c7b\u7814\u7a76\u4eba\u5458\u8bbe\u8ba1\u7684\u7b97\u6cd5\u8d85\u8d8a\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u5728\u6240\u6709 AI \u5f15\u5bfc\u7684\u7406\u8bba\u53d1\u73b0\u4e2d\uff0c\u6700\u63a5\u8fd1\u6ee1\u8db3\u8fd9\u4e09\u4e2a\u6807\u51c6\u7684\u662f\u6570\u8bba\u4e2d\u7684 murmuration \u731c\u60f3\u3002\u8fd9\u79cd\u65b9\u6cd5\u6ee1\u8db3\u4e86\u53ef\u89e3\u91ca\u6027\u548c\u975e\u5e73\u51e1\u6027\uff0c\u4f46\u6ca1\u6709\u6ee1\u8db3\u81ea\u52a8\u6027\uff0c\u56e0\u4e3a\u4eba\u7c7b\u7814\u7a76\u4eba\u5458\u5728\u8fc7\u7a0b\u4e2d\u8fdb\u884c\u4e86\u5e72\u9884\u3002\u4ed6\u4eec\u5bf9 AI \u5728 Birch-Swinnerton-Dyer \u731c\u60f3\u80cc\u666f\u4e0b\u533a\u5206\u692d\u5706\u66f2\u7ebf\u7684\u7b49\u7ea7\u505a\u5f97\u5982\u6b64\u4e4b\u597d\u611f\u5230\u975e\u5e38\u60ca\u8bb6\u3002<\/span><\/section>\n


      <\/span><\/p>\n


      <\/span><\/p>\n

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      <\/section>\n

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      <\/svg><\/section>\n<\/section>\n<\/section>\n
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      4. \u5c55\u671b<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

      \n

      <\/section>\n

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

      <\/span><\/section>\n
      \u4ece\u4e8b\u7406\u8bba\u7814\u7a76\u7684\u4eba\u4eec\u53ef\u4ee5\u653e\u5fc3\uff0c\u81f3\u5c11\u5728\u53ef\u9884\u89c1\u7684\u672a\u6765\uff0c\u4ed6\u4eec\u7684\u5de5\u4f5c\u4e0d\u4f1a\u88ab\u53d6\u4ee3\u3002\u4eba\u7c7b\u8fd8\u6ca1\u6709\u5efa\u7acb\u8d77\u4e00\u4e2a\u5168\u9762\u7684\u3001\u81ea\u4e0b\u800c\u4e0a\u7684\u6570\u5b66\u6570\u636e\u5e93\uff0c\u8986\u76d6\u6240\u6709\u7684\u6570\u5b66\u9886\u57df\u3002\u5373\u4f7f\u6709\u4e86\u8fd9\u6837\u7684\u6570\u636e\u5e93\uff0c\u5927\u578b\u8bed\u8a00\u6a21\u578b\u5728\u9762\u5bf9\u8bc1\u660e\u7b56\u7565\u7684\u5de8\u5927\u641c\u7d22\u7a7a\u95f4\u65f6\u4e5f\u4f1a\u9047\u5230\u6311\u6218\u3002\u518d\u52a0\u4e0a\u81ea\u4e0a\u800c\u4e0b\u6570\u5b66\u4e2d Birch \u6d4b\u8bd5\u7684\u4e25\u683c\u6807\u51c6\uff0c\u6211\u4eec\u79bb\u5b8c\u5168\u81ea\u52a8\u5316\u7684\u7406\u8bba\u53d1\u73b0\u8fd8\u5f88\u8fdc\u3002\u4e0d\u8fc7\uff0c\u4eba\u5de5\u667a\u80fd\u5df2\u7ecf\u5f00\u59cb\uff0c\u5e76\u4e14\u5c06\u7ee7\u7eed\u5728\u4e0e\u4eba\u7c7b\u6570\u5b66\u5bb6\u548c\u7406\u8bba\u79d1\u5b66\u5bb6\u7684\u5408\u4f5c\u4e2d\u626e\u6f14\u5173\u952e\u89d2\u8272\u3002\u5728\u6211\u4eec\u8ba8\u8bba\u7684\u4e09\u4e2a\u65b9\u5411\u4e0a\uff0c\u6211\u4eec\u65e2\u6709\u7d27\u8feb\u7684\u4efb\u52a1\uff0c\u4e5f\u6709\u957f\u8fdc\u7684\u76ee\u6807\u3002<\/span><\/section>\n

      <\/span><\/section>\n