隨手寫 September 21, 2025 隱含目標

陶哲軒本人隨後也在 Mastodon 上發表對形式化與 AI 工具的看法。他認為，AI 的工作方式與人類不同：AI 可能會成功完成「明確目標」（如完成某定理的形式化證明），卻跳過了「隱含目標」——像是幫助建立合作機制、訓練新手、整理更好理解的證明結構、補充可納入 Mathlib 的子命題等。
https://www.techbang.com/posts/125460-ai-gauss-solves-math-problem-terence-tao-explains
About the author

喜愛用文字說明自己眼中所見的一切
張貼留言
<script type="text/javascript" src="https://www.blogger.com/static/v1/widgets/432983155-widgets.js"></script>
<script type='text/javascript'>
window['__wavt'] = 'AOuZoY6l_rYb9xMHT4A7-zlz2NJgiijXBg:1773526025558';_WidgetManager._Init('//www.blogger.com/rearrange?blogID\x3d19530189','//www.ckizumi.com/2025/09/september-21-2025-at-0651am.html','19530189');
_WidgetManager._SetDataContext([{'name': 'blog', 'data': {'blogId': '19530189', 'title': '\u7cca\u5857\u5c0f\u6cc9\u6307\u5357', 'url': 'https://www.ckizumi.com/2025/09/september-21-2025-at-0651am.html', 'canonicalUrl': 'https://www.ckizumi.com/2025/09/september-21-2025-at-0651am.html', 'homepageUrl': 'https://www.ckizumi.com/', 'searchUrl': 'https://www.ckizumi.com/search', 'canonicalHomepageUrl': 'https://www.ckizumi.com/', 'blogspotFaviconUrl': 'https://www.ckizumi.com/favicon.ico', 'bloggerUrl': 'https://www.blogger.com', 'hasCustomDomain': true, 'httpsEnabled': true, 'enabledCommentProfileImages': true, 'gPlusViewType': 'FILTERED_POSTMOD', 'adultContent': false, 'analyticsAccountNumber': 'UA-3305637-9', 'encoding': 'UTF-8', 'locale': 'zh-TW', 'localeUnderscoreDelimited': 'zh_tw', 'languageDirection': 'ltr', 'isPrivate': false, 'isMobile': false, 'isMobileRequest': false, 'mobileClass': '', 'isPrivateBlog': false, 'isDynamicViewsAvailable': true, 'feedLinks': '\x3clink rel\x3d\x22alternate\x22 type\x3d\x22application/atom+xml\x22 title\x3d\x22\u7cca\u5857\u5c0f\u6cc9\u6307\u5357 - Atom\x22 href\x3d\x22https://www.ckizumi.com/feeds/posts/default\x22 /\x3e\n\x3clink rel\x3d\x22alternate\x22 type\x3d\x22application/rss+xml\x22 title\x3d\x22\u7cca\u5857\u5c0f\u6cc9\u6307\u5357 - RSS\x22 href\x3d\x22https://www.ckizumi.com/feeds/posts/default?alt\x3drss\x22 /\x3e\n\x3clink rel\x3d\x22service.post\x22 type\x3d\x22application/atom+xml\x22 title\x3d\x22\u7cca\u5857\u5c0f\u6cc9\u6307\u5357 - Atom\x22 href\x3d\x22https://www.blogger.com/feeds/19530189/posts/default\x22 /\x3e\n\n\x3clink rel\x3d\x22alternate\x22 type\x3d\x22application/atom+xml\x22 title\x3d\x22\u7cca\u5857\u5c0f\u6cc9\u6307\u5357 - Atom\x22 href\x3d\x22https://www.ckizumi.com/feeds/5223888818386567233/comments/default\x22 /\x3e\n', 'meTag': '', 'adsenseHostId': 'ca-host-pub-1556223355139109', 'adsenseHasAds': false, 'adsenseAutoAds': false, 'boqCommentIframeForm': true, 'loginRedirectParam': '', 'view': '', 'dynamicViewsCommentsSrc': '//www.blogblog.com/dynamicviews/4224c15c4e7c9321/js/comments.js', 'dynamicViewsScriptSrc': '//www.blogblog.com/dynamicviews/5ac9c0fa1f330b04', 'plusOneApiSrc': 'https://apis.google.com/js/platform.js', 'disableGComments': true, 'interstitialAccepted': false, 'sharing': {'platforms': [{'name': '\u53d6\u5f97\u9023\u7d50', 'key': 'link', 'shareMessage': '\u53d6\u5f97\u9023\u7d50', 'target': ''}, {'name': 'Facebook', 'key': 'facebook', 'shareMessage': '\u5206\u4eab\u5230 Facebook', 'target': 'facebook'}, {'name': 'BlogThis\uff01', 'key': 'blogThis', 'shareMessage': 'BlogThis\uff01', 'target': 'blog'}, {'name': 'X', 'key': 'twitter', 'shareMessage': '\u5206\u4eab\u5230 X', 'target': 'twitter'}, {'name': 'Pinterest', 'key': 'pinterest', 'shareMessage': '\u5206\u4eab\u5230 Pinterest', 'target': 'pinterest'}, {'name': '\u4ee5\u96fb\u5b50\u90f5\u4ef6\u50b3\u9001', 'key': 'email', 'shareMessage': '\u4ee5\u96fb\u5b50\u90f5\u4ef6\u50b3\u9001', 'target': 'email'}], 'disableGooglePlus': true, 'googlePlusShareButtonWidth': 0, 'googlePlusBootstrap': '\x3cscript type\x3d\x22text/javascript\x22\x3ewindow.___gcfg \x3d {\x27lang\x27: \x27zh_TW\x27};\x3c/script\x3e'}, 'hasCustomJumpLinkMessage': true, 'jumpLinkMessage': '\u7e7c\u7e8c\u95b1\u8b80 \xbb', 'pageType': 'item', 'postId': '5223888818386567233', 'postImageThumbnailUrl': 'https://lh3.googleusercontent.com/-_R-pp0yPACo/aM8w3LT5_oI/AAAAAAABmFQ/0LeBxk_oPdMvj66T5tv0wWfW2p8lEKSiACNcBGAsYHQ/s72-c/IMG_20250921_065405.jpg', 'postImageUrl': 'https://lh3.googleusercontent.com/-_R-pp0yPACo/aM8w3LT5_oI/AAAAAAABmFQ/0LeBxk_oPdMvj66T5tv0wWfW2p8lEKSiACNcBGAsYHQ/s1600/IMG_20250921_065405.jpg', 'pageName': '\u96a8\u624b\u5beb September 21, 2025 \u96b1\u542b\u76ee\u6a19', 'pageTitle': '\u7cca\u5857\u5c0f\u6cc9\u6307\u5357: \u96a8\u624b\u5beb September 21, 2025 \u96b1\u542b\u76ee\u6a19'}}, {'name': 'features', 'data': {}}, {'name': 'messages', 'data': {'edit': '\u7de8\u8f2f', 'linkCopiedToClipboard': '\u5df2\u5c07\u9023\u7d50\u8907\u88fd\u5230\u526a\u8cbc\u7c3f\uff01', 'ok': '\u78ba\u5b9a', 'postLink': '\u6587\u7ae0\u9023\u7d50'}}, {'name': 'template', 'data': {'name': 'custom', 'localizedName': '\u81ea\u8a02', 'isResponsive': true, 'isAlternateRendering': false, 'isCustom': true}}, {'name': 'view', 'data': {'classic': {'name': 'classic', 'url': '?view\x3dclassic'}, 'flipcard': {'name': 'flipcard', 'url': '?view\x3dflipcard'}, 'magazine': {'name': 'magazine', 'url': '?view\x3dmagazine'}, 'mosaic': {'name': 'mosaic', 'url': '?view\x3dmosaic'}, 'sidebar': {'name': 'sidebar', 'url': '?view\x3dsidebar'}, 'snapshot': {'name': 'snapshot', 'url': '?view\x3dsnapshot'}, 'timeslide': {'name': 'timeslide', 'url': '?view\x3dtimeslide'}, 'isMobile': false, 'title': '\u96a8\u624b\u5beb September 21, 2025 \u96b1\u542b\u76ee\u6a19', 'description': '\u9676\u54f2\u8ed2\u672c\u4eba\u96a8\u5f8c\u4e5f\u5728 Mastodon \u4e0a\u767c\u8868\u5c0d\u5f62\u5f0f\u5316\u8207 AI \u5de5\u5177\u7684\u770b\u6cd5\u3002\u4ed6\u8a8d\u70ba\uff0cAI \u7684\u5de5\u4f5c\u65b9\u5f0f\u8207\u4eba\u985e\u4e0d\u540c\uff1aAI \u53ef\u80fd\u6703\u6210\u529f\u5b8c\u6210\u300c\u660e\u78ba\u76ee\u6a19\u300d\uff08\u5982\u5b8c\u6210\u67d0\u5b9a\u7406\u7684\u5f62\u5f0f\u5316\u8b49\u660e\uff09\uff0c\u537b\u8df3\u904e\u4e86\u300c\u96b1\u542b\u76ee\u6a19\u300d\u2014\u2014\u50cf\u662f\u5e6b\u52a9\u5efa\u7acb\u5408\u4f5c\u6a5f\u5236\u3001\u8a13\u7df4\u65b0\u624b\u3001\u6574\u7406\u66f4\u597d\u7406\u89e3\u7684\u8b49\u660e\u7d50\u69cb\u3001\u88dc\u5145\u53ef\u7d0d\u5165 Mathlib ...', 'featuredImage': 'https://lh3.googleusercontent.com/-_R-pp0yPACo/aM8w3LT5_oI/AAAAAAABmFQ/0LeBxk_oPdMvj66T5tv0wWfW2p8lEKSiACNcBGAsYHQ/s1600/IMG_20250921_065405.jpg', 'url': 'https://www.ckizumi.com/2025/09/september-21-2025-at-0651am.html', 'type': 'item', 'isSingleItem': true, 'isMultipleItems': false, 'isError': false, 'isPage': false, 'isPost': true, 'isHomepage': false, 'isArchive': false, 'isLabelSearch': false, 'postId': 5223888818386567233}}, {'name': 'widgets', 'data': [{'title': '\u7cca\u5857\u5c0f\u6cc9\u6307\u5357 (\u6a19\u982d)', 'type': 'Header', 'sectionId': 'sec_Header_Title', 'id': 'Header01'}, {'title': '\u4eca\u5929\u60f3\u627e\u4e9b\u4ec0\u9ebc\u5462?', 'type': 'BlogSearch', 'sectionId': 'sec_Header_Search', 'id': 'BlogSearch01'}, {'title': 'Header Icon', 'type': 'TextList', 'sectionId': 'sec_Header_Icon', 'id': 'TextList01'}, {'title': 'Bookmark Posts', 'type': 'LinkList', 'sectionId': 'sec_Header_Icon', 'id': 'LinkList02'}, {'title': 'Navigation Menu (Simple)', 'type': 'PageList', 'sectionId': 'sec_Nav_Widgets_1', 'id': 'PageList01'}, {'title': 'Tabbed Menu', 'type': 'LinkList', 'sectionId': 'sec_Under_Header', 'id': 'LinkList05'}, {'title': 'Pinned Post', 'type': 'FeaturedPost', 'sectionId': 'sec_Top_Widgets', 'id': 'FeaturedPost01', 'postId': '2982460811464593169'}, {'title': '\u7db2\u8a8c\u6587\u7ae0', 'type': 'Blog', 'sectionId': 'sec_Main_Widgets', 'id': 'Blog01', 'posts': [{'id': '5223888818386567233', 'title': '\u96a8\u624b\u5beb September 21, 2025 \u96b1\u542b\u76ee\u6a19', 'featuredImage': 'https://lh3.googleusercontent.com/-_R-pp0yPACo/aM8w3LT5_oI/AAAAAAABmFQ/0LeBxk_oPdMvj66T5tv0wWfW2p8lEKSiACNcBGAsYHQ/s1600/IMG_20250921_065405.jpg', 'showInlineAds': false}], 'headerByline': {'regionName': 'header1', 'items': [{'name': 'timestamp', 'label': 'On'}]}, 'footerBylines': [{'regionName': 'footer1', 'items': [{'name': 'comments', 'label': 'Comment'}, {'name': 'icons', 'label': ''}]}, {'regionName': 'footer2', 'items': [{'name': 'labels', 'label': 'in'}]}, {'regionName': 'footer3', 'items': [{'name': 'location', 'label': 'Location:'}]}], 'allBylineItems': [{'name': 'timestamp', 'label': 'On'}, {'name': 'comments', 'label': 'Comment'}, {'name': 'icons', 'label': ''}, {'name': 'labels', 'label': 'in'}, {'name': 'location', 'label': 'Location:'}]}, {'title': 'Table of contents', 'type': 'HTML', 'sectionId': 'sec_Main_Widgets', 'id': 'HTML11'}, {'title': 'Popular Posts', 'type': 'PopularPosts', 'sectionId': 'sec_Side_Widgets', 'id': 'PopularPosts01', 'posts': [{'title': '\u300a\u5275\u300b\uff1a\u8de8\u8d8a\u56db\u5341\u5e74\u7684\u96fb\u5b50\u4e16\u754c\u722d\u9738\u6230', 'id': 5819427695913826662}, {'title': 'Excel \u7522\u751f\u56fa\u5b9a\u4f4d\u6578\u7684\u6578\u503c', 'id': 4663386662764009497}, {'title': '\u767e\u5e74\u66f8\u9999\uff1a\u570b\u5716\u8207\u570b\u81fa\u5716\u7684\u4ea4\u7e54\u53f2\u6f14\u9032', 'id': 2982460811464593169}]}, {'title': 'Labels', 'type': 'Label', 'sectionId': 'sec_Side_Widgets', 'id': 'Label01'}, {'title': 'Take me back', 'type': 'HTML', 'sectionId': 'sec_Error_404', 'id': 'HTML404'}, {'title': 'Organization [BlogTitle]', 'type': 'Image', 'sectionId': 'sec_Footer_Organization', 'id': 'Image21'}, {'title': 'Social Media Links', 'type': 'LinkList', 'sectionId': 'sec_Footer_Organization', 'id': 'LinkList21'}, {'title': 'Credit', 'type': 'HTML', 'sectionId': 'sec_Footer_Bottom', 'id': 'HTML21'}, {'title': 'Mobile Menu', 'type': 'TextList', 'sectionId': 'sec_Mobile_Menu', 'id': 'TextList99'}, {'title': 'Labels', 'type': 'Label', 'sectionId': 'sec_Theme_Hidden', 'id': 'Label41'}, {'title': '\u806f\u7d61\u8868\u55ae', 'type': 'ContactForm', 'sectionId': 'sec_Theme_Hidden', 'id': 'ContactForm41'}, {'title': 'Pageviews last month', 'type': 'Stats', 'sectionId': 'sec_Theme_Hidden', 'id': 'Stats41'}, {'title': 'Firebase Configurations', 'type': 'LinkList', 'sectionId': 'sec_Addon_Widgets', 'id': 'LinkList61'}]}]);
_WidgetManager._RegisterWidget('_HeaderView', new _WidgetInfo('Header01', 'sec_Header_Title', document.getElementById('Header01'), {}, 'displayModeFull'));
_WidgetManager._RegisterWidget('_BlogSearchView', new _WidgetInfo('BlogSearch01', 'sec_Header_Search', document.getElementById('BlogSearch01'), {}, 'displayModeFull'));
_WidgetManager._RegisterWidget('_TextListView', new _WidgetInfo('TextList01', 'sec_Header_Icon', document.getElementById('TextList01'), {}, 'displayModeFull'));
_WidgetManager._RegisterWidget('_LinkListView', new _WidgetInfo('LinkList02', 'sec_Header_Icon', document.getElementById('LinkList02'), {}, 'displayModeFull'));
_WidgetManager._RegisterWidget('_PageListView', new _WidgetInfo('PageList01', 'sec_Nav_Widgets_1', document.getElementById('PageList01'), {'title': 'Navigation Menu (Simple)', 'links': [{'isCurrentPage': false, 'href': 'https://www.ckizumi.com/', 'id': '0', 'title': '\u56de\u5230\u9996\u9801'}, {'isCurrentPage': false, 'href': 'https://www.ckizumi.com/search/label/%40%E9%9A%BB%E8%A8%80%E7%89%87%E8%AA%9E', 'title': '[\u5c08\u6b04] \u96bb\u5b57\u7247\u8a9e'}, {'isCurrentPage': false, 'href': 'https://www.ckizumi.com/search/label/%40%E7%BE%8E%E5%91%B3%E6%9B%B8%E7%B1%A4', 'title': '[\u5c08\u6b04] \u7f8e\u5473\u66f8\u7c64'}, {'isCurrentPage': false, 'href': 'https://www.ckizumi.com/search/label/%40%E9%9B%BB%E8%85%A6%E7%9B%92%E5%AD%90', 'title': '[\u5c08\u6b04] \u96fb\u8166\u76d2\u5b50'}, {'isCurrentPage': false, 'href': 'https://www.ckizumi.com/search/label/%23%E8%A1%A8%E6%BC%94%F0%9F%8E%AD', 'title': '#\u8868\u6f14\ud83c\udfad'}, {'isCurrentPage': false, 'href': 'https://www.ckizumi.com/search/label/%40%E7%99%BC%E5%B1%95%E8%A9%B1%E9%A1%8C', 'title': '[\u8ffd\u8e64] \u767c\u5c55\u8a71\u984c'}], 'mobile': false, 'showPlaceholder': true, 'hasCurrentPage': false}, 'displayModeFull'));
_WidgetManager._RegisterWidget('_LinkListView', new _WidgetInfo('LinkList05', 'sec_Under_Header', document.getElementById('LinkList05'), {}, 'displayModeFull'));
_WidgetManager._RegisterWidget('_FeaturedPostView', new _WidgetInfo('FeaturedPost01', 'sec_Top_Widgets', document.getElementById('FeaturedPost01'), {}, 'displayModeFull'));
_WidgetManager._RegisterWidget('_BlogView', new _WidgetInfo('Blog01', 'sec_Main_Widgets', document.getElementById('Blog01'), {'cmtInteractionsEnabled': false, 'lightboxEnabled': true, 'lightboxModuleUrl': 'https://www.blogger.com/static/v1/jsbin/2645113145-lbx__zh_tw.js', 'lightboxCssUrl': 'https://www.blogger.com/static/v1/v-css/828616780-lightbox_bundle.css'}, 'displayModeFull'));
_WidgetManager._RegisterWidget('_HTMLView', new _WidgetInfo('HTML11', 'sec_Main_Widgets', document.getElementById('HTML11'), {}, 'displayModeFull'));
_WidgetManager._RegisterWidget('_PopularPostsView', new _WidgetInfo('PopularPosts01', 'sec_Side_Widgets', document.getElementById('PopularPosts01'), {}, 'displayModeFull'));
_WidgetManager._RegisterWidget('_LabelView', new _WidgetInfo('Label01', 'sec_Side_Widgets', document.getElementById('Label01'), {}, 'displayModeFull'));
_WidgetManager._RegisterWidget('_HTMLView', new _WidgetInfo('HTML404', 'sec_Error_404', document.getElementById('HTML404'), {}, 'displayModeFull'));
_WidgetManager._RegisterWidget('_ImageView', new _WidgetInfo('Image21', 'sec_Footer_Organization', document.getElementById('Image21'), {'resize': true}, 'displayModeFull'));
_WidgetManager._RegisterWidget('_LinkListView', new _WidgetInfo('LinkList21', 'sec_Footer_Organization', document.getElementById('LinkList21'), {}, 'displayModeFull'));
_WidgetManager._RegisterWidget('_HTMLView', new _WidgetInfo('HTML21', 'sec_Footer_Bottom', document.getElementById('HTML21'), {}, 'displayModeFull'));
_WidgetManager._RegisterWidget('_TextListView', new _WidgetInfo('TextList99', 'sec_Mobile_Menu', document.getElementById('TextList99'), {}, 'displayModeFull'));
_WidgetManager._RegisterWidget('_LabelView', new _WidgetInfo('Label41', 'sec_Theme_Hidden', document.getElementById('Label41'), {}, 'displayModeFull'));
_WidgetManager._RegisterWidget('_ContactFormView', new _WidgetInfo('ContactForm41', 'sec_Theme_Hidden', document.getElementById('ContactForm41'), {'contactFormMessageSendingMsg': '\u50b3\u9001\u4e2d...', 'contactFormMessageSentMsg': '\u60a8\u7684\u90f5\u4ef6\u5df2\u5bc4\u51fa\u3002', 'contactFormMessageNotSentMsg': '\u7121\u6cd5\u50b3\u9001\u90f5\u4ef6\uff0c\u8acb\u7a0d\u5f8c\u518d\u8a66\u3002', 'contactFormInvalidEmailMsg': '\u8acb\u8f38\u5165\u6709\u6548\u7684\u96fb\u5b50\u90f5\u4ef6\u5730\u5740\u3002', 'contactFormEmptyMessageMsg': '\u90f5\u4ef6\u6b04\u4f4d\u4e0d\u53ef\u7a7a\u767d\u3002', 'title': '\u806f\u7d61\u8868\u55ae', 'blogId': '19530189', 'contactFormNameMsg': '\u540d\u7a31', 'contactFormEmailMsg': '\u4ee5\u96fb\u5b50\u90f5\u4ef6\u50b3\u9001', 'contactFormMessageMsg': '\u8a0a\u606f', 'contactFormSendMsg': '\u50b3\u9001', 'contactFormToken': 'AOuZoY4bjOB00pssppdSEmAqKORrn9ckSA:1773526025558', 'submitUrl': 'https://www.blogger.com/contact-form.do'}, 'displayModeFull'));
_WidgetManager._RegisterWidget('_StatsView', new _WidgetInfo('Stats41', 'sec_Theme_Hidden', document.getElementById('Stats41'), {'title': 'Pageviews last month', 'showGraphicalCounter': false, 'showAnimatedCounter': false, 'showSparkline': true, 'statsUrl': '//www.ckizumi.com/b/stats?style\x3dBLACK_TRANSPARENT\x26timeRange\x3dLAST_WEEK\x26token\x3dAPq4FmA54q7ywzZ0iIwoT0YEYhz5r_t6SPEcaOsn4chjB5zFv-UnYS_8p6RiRYNtxRkUuhq_mZltDN_D5lYRSLeQ1GPVkpe9ng'}, 'displayModeFull'));
_WidgetManager._RegisterWidget('_LinkListView', new _WidgetInfo('LinkList61', 'sec_Addon_Widgets', document.getElementById('LinkList61'), {}, 'displayModeFull'));
</script>
</body>
糊塗小泉指南

隨手寫 September 21, 2025 隱含目標

About the author

張貼留言

《創》：跨越四十年的電子世界爭霸戰

Excel 產生固定位數的數值

百年書香：國圖與國臺圖的交織史演進
