[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-121837-en":3,"doc-seo-121837-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},121837,3848291630094,"Emma Wilson","https://eur-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45",8,"Research & Report","From the String Landscape to the Mathematical Landscape - A Machine-Learning Outlook","The paper reviews a research program that uses machine learning to investigate the landscape of mathematical problems, treating AI as a bridge to human intuition beyond automated theorem proving. It emphasizes how learning-based methods can support conjecture formulation, pattern recognition, and computational tasks. The discussion connects these ideas to string theory’s vacuum degeneracy challenge and highlights the combinatorial and statistical nature of the underlying geometry and topology.","City Research Online  \nCity, University of London Institutional Repository  \nCitation: He, Y-H. (2023) . From the String Landscape to the Mathematical Landscape: A Machine-Learning Outlook. Paper presented at the International Workshop on Lie Theory and Its Applications in Physics, 20-26 Jun 2021, Sofia, Bulgaria. doi: 10. 1007/978-981-19- 4751-3_2  \nThis is the accepted version of the paper.  \nThis version of the publication may differ from the final published version.  \nPermanent repository link: [https://openaccess.city.ac.uk/id/eprint/32852/](https://openaccess.city.ac.uk/id/eprint/32852/)  \nLink to published version: [https://doi.org/10.1007/978-981-19-4751-3_2](https://doi.org/10.1007/978-981-19-4751-3_2)  \n[Copyright:](Copyright: City Research Online aims to make research outputs of City)[ City Research Online aims to make research outputs of City](Copyright: City Research Online aims to make research outputs of City), University of London available to a wider audience. Copyright and Moral Rights remain with the author(s) and/or copyright holders. URLs from City Research Online may be freely distributed and linked to.  \nReuse: Copies of full items can be used for personal research or study, educational, or not-for-profit purposes without prior permission or charge. Provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content isnot changed in any way.  \n\n| City Research Online: | [http://openaccess.city.ac.uk/](http://openaccess.city.ac.uk/) | [publications@city.ac.uk](publications@city.ac.uk) |\n| --- | --- | --- |\n|  |  |  |\n\nFrom the String Landscape to the Mathematical Landscape: a Machine-Learning Outlook  \narXiv :2202 .06086v1 [hep-th] 12 Feb 2022  \nYang-Hui He  \nAbstract We review the recent programme of using machine-learning to explore the landscape of mathematical problems. With this paradigm as a model for human intuition-complementary to and in contrast with the more formalistic approach of automated theorem proving-we highlight some experiments on how AI helps with conjecture formulation, pattern recognition and computation.  \n1 The String Landscape  \nPerhaps the greatest theoretical challenge to string theory as a theory of everything is the vast proliferation of possible vacuum solutions, each of which is a possible 4-dimensional \\universe\" that descends from the 10 spacetime dimensions of the superstring. This is the so-called \\vacuum degeneracy problem\", or the \\string landscape problem\". The reason for this multitude is the vast number of possible geometries for the missing 6 dimensions. Whether we consider compacti􀀌cation, where the a Calabi-Yau manifold constitutes the missing dimensions, or con􀀌gurations of branes whose world-volumes complement these dimensions, we are inevitably confronted with the heart of the problem: geometrical structures, often due to an underlying combinatorial problem, tend to grow exponentially with dimension.  \nWe can see this from estimates of possible vacua, which engender such astronomical numbers as 10500 to 10 105 [1{3] . These estimates come from  \nYang-Hui He  \nLondon Institute for Mathematical Sciences, Royal Institution of Great Britain, 21 Albemarle St. , London, W1S 4BS; Merton College, University of Oxford, OX1 4JD, UK; Department of Mathematics, City, University of London, EC1V0HB, UK; School of Physics, NanKai University, Tianjin, 300071, P.R. China.  \ne-mail: [hey@maths.ox.ac.uk](hey@maths.ox.ac.uk)  \n2 Yang-Hui He  \ntallying \\typical\" number of topologies of \\typical\" manifolds, as governed by the number of holes (or more strictly, algebraic cycles) of various dimensions within the manifolds. Such topological quantities are immanently combinatorial in nature.  \nLacking a fundamental \\selection principle\" [4] - which would 􀀌nd our universe among the myriad-the traditional approaches have been statistical valuations [5], or brute-force searching for the Standard Mode","cbCaioxoAXewvb3E","https://ap.wps.com/l/cbCaioxoAXewvb3E","pdf",909990,1,12,"English","en",105,"# Abstract\n# The String Landscape\n## Calabi-Yau Manifolds: from Geometry to Physics","[{\"question\":\"How does the paper position machine learning relative to automated theorem proving?\",\"answer\":\"It frames machine learning as complementary to automated theorem proving: more aligned with human intuition while still in contrast to purely formal approaches.\"},{\"question\":\"What is the core difficulty of the string landscape discussed in the paper?\",\"answer\":\"The string landscape problem arises from the enormous proliferation of vacuum solutions, driven by the vast number of possible geometrical structures for the compactified dimensions.\"},{\"question\":\"In what ways does AI help with mathematical work according to the abstract?\",\"answer\":\"AI is highlighted for supporting conjecture formulation, pattern recognition, and computation within mathematical exploration.\"}]","From the String Landscape to the Mathematical Landscape - A Machine-Learning Outlook | PDF",1785807152,30,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"from-the-string-landscape-to-the-mathematical-landscape-a-machine-learning-outlook","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/from-the-string-landscape-to-the-mathematical-landscape-a-machine-learning-outlook/121837/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-04",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"How does the paper position machine learning relative to automated theorem proving?","Question",{"text":75,"@type":76},"It frames machine learning as complementary to automated theorem proving: more aligned with human intuition while still in contrast to purely formal approaches.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What is the core difficulty of the string landscape discussed in the paper?",{"text":80,"@type":76},"The string landscape problem arises from the enormous proliferation of vacuum solutions, driven by the vast number of possible geometrical structures for the compactified dimensions.",{"name":82,"@type":73,"acceptedAnswer":83},"In what ways does AI help with mathematical work according to the abstract?",{"text":84,"@type":76},"AI is highlighted for supporting conjecture formulation, pattern recognition, and computation within mathematical exploration.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,122,127,130,134],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":29,"slug":121},"research-report",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]