{"id":848308,"date":"2023-10-25T11:13:18","date_gmt":"2023-10-25T11:13:18","guid":{"rendered":"https:\/\/www.capgemini.com\/dk-en\/?p=848308&#038;preview=true&#038;preview_id=848308"},"modified":"2025-03-19T04:12:36","modified_gmt":"2025-03-19T04:12:36","slug":"exploring-probabilistic-modeling-and-the-future-of-math","status":"publish","type":"post","link":"https:\/\/www.capgemini.com\/dk-en\/insights\/expert-perspectives\/exploring-probabilistic-modeling-and-the-future-of-math\/","title":{"rendered":"Exploring probabilistic modeling and the future of math"},"content":{"rendered":"\n<header class=\"wp-block-cg-blocks-hero-blogs header-hero-blogs\"><div class=\"container\"><div class=\"hero-blogs\"><div class=\"hero-blogs-content-wrapper\"><div class=\"row\"><div class=\"col-12\"><div class=\"header-title\"><h1>Exploring Probabilistic Modeling and the Future of Math<\/h1><\/div><\/div><\/div><\/div><div class=\"hero-blogs-bottom\"><div class=\"header-author\"><div class=\"author-img\"><img decoding=\"async\" src=\"https:\/\/www.capgemini.com\/wp-content\/uploads\/2023\/07\/Robert-H.P.-Engels.jpg?w=200&amp;quality=10\" alt=\"\" loading=\"lazy\"\/><\/div><div class=\"author-name-date\"><h5 class=\"author-name\">Robert H. P. Engels<\/h5><h5 class=\"blog-date\">Oct 23, 2023<\/h5><\/div><\/div><div class=\"brand-image\"> <\/div><\/div><\/div><\/div><\/header>\n\n\n\n<section class=\"wp-block-cg-blocks-group undefined section section--article-content\"><div class=\"article-main-content\"><div class=\"container\"><div class=\"row\"><div class=\"col-12 col-md-1\"><nav class=\"article-social\"><ul class=\"social-nav\"><li class=\"ip-order-fb\"><a href=\"https:\/\/www.facebook.com\/sharer\/sharer.php?u=https:\/\/www.capgemini.com\/?p=965284\" target=\"_blank\" rel=\"noopener noreferrer\" title=\"opens in a new window\"><i aria-hidden=\"true\" class=\"icon-fb\"><\/i><span class=\"sr-only\">Facebook<\/span><\/a><\/li><li class=\"ip-order-tw\"><a href=\"https:\/\/twitter.com\/intent\/tweet?url=https:\/\/www.capgemini.com\/?p=965284&amp;text=\" target=\"_blank\" rel=\"noopener noreferrer\" title=\"opens in a new window\"><i aria-hidden=\"true\" class=\"icon-tw\"><\/i><span class=\"sr-only\">Twitter<\/span><\/a><\/li><li class=\"ip-order-li\"><a href=\"https:\/\/www.linkedin.com\/shareArticle?url=https:\/\/www.capgemini.com\/?p=965284&amp;text=\" target=\"_blank\" rel=\"noopener noreferrer\" title=\"opens in a new window\"><i aria-hidden=\"true\" class=\"icon-li\"><\/i><span class=\"sr-only\">Linkedin<\/span><\/a><\/li><\/ul><\/nav><\/div><div class=\"col-12 col-md-11 col-lg-10\"><div class=\"article-text article-quote-text\">\n<h2 class=\"wp-block-heading\" id=\"h-some-days-you-get-these-chains-of-interesting-events-following-up-on-each-other\">Some days you get these chains of interesting events following up on each other.<\/h2>\n\n\n\n<p>This morning I read the &#8220;GPT can solve math[.. ]&#8221; paper (<a href=\"https:\/\/lnkd.in\/dzd7K3sx\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/lnkd.in\/dzd7K3sx<\/a>), then I read some responses to that (o.a. Gary Marcus, X-tweets etc). During and after the TED AI I had many interesting discussions on the topic of probabilistic modelling vs models of math as we know (knew?) it, and this paper sparked some thoughts (so: mission accomplished).<\/p>\n\n\n\n<p>It occurs to me that we have a generation of PhD students building LLMs that have probably not really got interested model thinking and mathematical proofs. I.e. the thinking behind Einsteins\u00b4 relativity theory, the thinking behind Euler&#8217;s Graph theory, the type of thinking that led (indeed) to a mathematical model that you can implement in a calculator (low footprint), calculates correctly (100% trustworthy) and in addition can calculate things 100% correct on input unseen before.<\/p>\n\n\n\n<p>The question really condenses down to the fact whether you believe in the abstraction capability in current algorithms used for training todays LLMs. Are attention layers at all able to build abstractions on their own (and not regurgitating from abstractions it got ready-served by humans)? Optimism in the Valley is big, just add more data and the problem will go away.<\/p>\n\n\n\n<p>But without changing the underlying attention layer design this seems to be a fallacy. Learning to abstract really means to build metalevels on your information, condense signals and their relations. That is something different as predicting chains of tokens. Such an abstraction layer can be seen as building a 3D puzzle, whereas current attention mechanisms seem single-layered. With a single layer, the most you can build is a 2D puzzle.<\/p>\n\n\n\n<p>With that picture in mind, you can observe that current solutions by LLM suppliers is to extend the 2D puzzle, making it larger (adding more data from all over), or giving it higher resolution for a specific task (like the math paper mentioned above). But no sincere attempts seem to have been made yet to build a 3D picture, which would mean to rock the foundation of the foundation models and rebuild the attention layer mechanism to cover for this deficit.<\/p>\n\n\n\n<p>Until then, let&#8217;s focus on getting functions to work reliable and off-load model-based tasks (math, engineering, logic, reasoning) to external capability agents and stop pretending that 2D can become 3D without changing the foundation.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/www.capgemini.com\/wp-content\/uploads\/2023\/10\/1697838702308.jpg?w=960\" alt=\"\" class=\"wp-image-965297\"\/><\/figure>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button is-style-outline is-style-outline--1\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/www.linkedin.com\/posts\/robertengels_gpt4mathpaper-probabilisticvsmathematicalmodeling-activity-7121251674739871744-w5NK\/?utm_source=share&amp;utm_medium=member_ios\" target=\"_blank\" rel=\"noreferrer noopener\">Add your voices on LinkedIn<\/a><\/div>\n<\/div>\n<\/div><\/div><\/div><\/div><\/div><\/section>\n\n\n\n<section class=\"wp-block-cg-blocks-wrapper-people-slider section section--expert-slider wrapper-people-slider undefined\"><div class=\"container\"><div class=\"content-title\"><h2 data-maxlength=\"34\" class=\"people-heading-title\">Meet the author<\/h2><\/div><\/div><div class=\"slider slider-boxed\"><div class=\"container\"><div class=\"slider-window\"><div class=\"slider-list\">\t\t<div class=\"slide\">\n\t\t\t<div class=\"box\">\n\t\t\t\t<div class=\"row\">\n\t\t\t\t\t<div class=\"col-md-6 col-lg-4 box-img-wrapper\">\n\t\t\t\t\t\t<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/www.capgemini.com\/dk-en\/wp-content\/uploads\/sites\/7\/2021\/05\/Robert-Engels.jpg\" alt=\"Robert Engels\"\/>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div class=\"col-md-6 col-lg-8 box-inner\">\n\t\t\t\t\t\t<div class=\"row title-social-media-header\">\n\t\t\t\t\t\t\t<div class=\"col-md-12 col-lg-6 mbl-social-icon\">\n\t\t\t\t\t\t\t\t<ul class=\"social-nav\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<li><a aria-label=\"Email\" href=\"mailto:robert.engels@capgemini.com\"><i aria-hidden=\"true\" class=\"mail-ico\"><\/i><\/a><\/li>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<li><a aria-label=\"Linkedin\" target=\"_blank\" title=\"Opens in a new window\" href=\"https:\/\/www.linkedin.com\/in\/esisnorge\/\"><i aria-hidden=\"true\" class=\"icon-li\"><\/i><\/a><\/li>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/ul>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"col-md-12 col-lg-6 box-container\">\n\t\t\t\t\t\t\t\t<div class=\"box-title\">\n\t\t\t\t\t\t\t\t\t<h3 class=\"people-profile-title\">Robert Engels<\/h3>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span>Global CTIO and Head of Lab for AI Futures and Insights &amp; Data<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"col-md-12 col-lg-6 social-box-container dkt-social-icon\">\n\t\t\t\t\t\t\t\t<ul class=\"social-nav\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<li><a aria-label=\"Email\" href=\"mailto:robert.engels@capgemini.com\"><i aria-hidden=\"true\" class=\"mail-ico\"><\/i><\/a><\/li>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<li><a aria-label=\"Linkedin\" target=\"_blank\" title=\"Opens in a new window\" href=\"https:\/\/www.linkedin.com\/in\/esisnorge\/\"><i aria-hidden=\"true\" class=\"icon-li\"><\/i><\/a><\/li>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/ul>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"people-info\">Robert is an innovation lead and a thought leader in several sectors and regions, with a basis in his role of Chief Technology Officer for Northern and Central Europe in our Insights &#038; Data Global Business Line. Based in Norway, he is a known lecturer, public speaker, and panel moderator. Robert holds a PhD in artificial intelligence from the Technical University in Karlsruhe, Germany.<\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div><\/div><\/div><div class=\"slider-nav\"><button class=\"slider-prev inactive\" aria-label=\"Slider-previous\" tabindex=\"-1\"><\/button><ul class=\"slider-paginator\"><\/ul><button class=\"slider-next\" aria-label=\"Slider-next\"><\/button><\/div><\/div><\/section>\n\n\n\n<section class=\"wp-block-cg-blocks-group undefined section section--article-content\"><div class=\"article-main-content\"><div class=\"container\"><div class=\"row\"><div class=\"col-12 col-md-11 col-lg-10 offset-md-1 offset-lg-1\"><div class=\"article-text article-quote-text\"><\/div><\/div><\/div><\/div><\/div><\/section>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":263,"featured_media":848309,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"cg_dt_proposed_to":[],"cg_seo_hreflang_relations":"[]","cg_seo_canonical_relation":"","cg_seo_hreflang_x_default_relation":"{\"uuid\":\"e2152e2f-c20b-436d-9706-b560e48b2e9a\",\"blogId\":\"\",\"domain\":\"\",\"sitePath\":\"\",\"postLink\":\"\",\"postId\":null,\"isSaved\":true,\"isCrossLink\":false,\"hasCrossLink\":false}","cg_dt_approved_content":true,"cg_dt_mandatory_content":false,"cg_dt_notes":"","cg_dg_source_changed":true,"cg_dt_link_disabled":false,"_yoast_wpseo_primary_brand":"","_jetpack_memberships_contains_paid_content":false,"footnotes":"","featured_focal_points":""},"categories":[1],"tags":[],"brand":[],"service":[],"industry":[],"partners":[],"blog-topic":[127],"content-group":[621],"class_list":["post-848308","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized","blog-topic-innovation","content-group-technovision"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.8 (Yoast SEO v22.8) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Exploring probabilistic modeling and the future of math - Capgemini Denmark<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.capgemini.com\/dk-en\/insights\/expert-perspectives\/exploring-probabilistic-modeling-and-the-future-of-math\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Exploring probabilistic modeling and the future of math\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.capgemini.com\/dk-en\/insights\/expert-perspectives\/exploring-probabilistic-modeling-and-the-future-of-math\/\" \/>\n<meta property=\"og:site_name\" content=\"Capgemini Denmark\" \/>\n<meta property=\"article:published_time\" content=\"2023-10-25T11:13:18+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-03-19T04:12:36+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.capgemini.com\/dk-en\/wp-content\/uploads\/sites\/7\/2025\/10\/New-Web-preview-global.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1200\" \/>\n\t<meta property=\"og:image:height\" content=\"627\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"Robert H. 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