{"id":"https://openalex.org/W7117259628","doi":"https://doi.org/10.1145/3786333","title":"A Survey on Large Language Models for Mathematical Reasoning","display_name":"A Survey on Large Language Models for Mathematical Reasoning","publication_year":2025,"publication_date":"2025-12-25","ids":{"openalex":"https://openalex.org/W7117259628","doi":"https://doi.org/10.1145/3786333"},"language":"en","primary_location":{"id":"doi:10.1145/3786333","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3786333","pdf_url":null,"source":{"id":"https://openalex.org/S157921468","display_name":"ACM Computing Surveys","issn_l":"0360-0300","issn":["0360-0300","1557-7341"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Computing Surveys","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5121286524","display_name":"Peng-Yuan Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I4210164862","display_name":"Artificial Intelligence in Medicine (Canada)","ror":"https://ror.org/05p590m36","country_code":"CA","type":"company","lineage":["https://openalex.org/I4210164862"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Peng-Yuan Wang","raw_affiliation_strings":["National Key Laboratory for Novel Software Technology, School of Artificial Intelligence, Nanjing University"],"raw_orcid":"https://orcid.org/0009-0006-1545-9457","affiliations":[{"raw_affiliation_string":"National Key Laboratory for Novel Software Technology, School of Artificial Intelligence, Nanjing University","institution_ids":["https://openalex.org/I4210164862"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5121282171","display_name":"Tian-Shuo Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I4210164862","display_name":"Artificial Intelligence in Medicine (Canada)","ror":"https://ror.org/05p590m36","country_code":"CA","type":"company","lineage":["https://openalex.org/I4210164862"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Tian-Shuo Liu","raw_affiliation_strings":["National Key Laboratory for Novel Software Technology, School of Artificial Intelligence, Nanjing University"],"raw_orcid":"https://orcid.org/0009-0005-2515-3200","affiliations":[{"raw_affiliation_string":"National Key Laboratory for Novel Software Technology, School of Artificial Intelligence, Nanjing University","institution_ids":["https://openalex.org/I4210164862"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5121267011","display_name":"Chenyang Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I881766915","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760","country_code":"CN","type":"education","lineage":["https://openalex.org/I881766915"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chenyang Wang","raw_affiliation_strings":["School of Artificial Intelligence, Nanjing University"],"raw_orcid":"https://orcid.org/0009-0007-0526-1321","affiliations":[{"raw_affiliation_string":"School of Artificial Intelligence, Nanjing University","institution_ids":["https://openalex.org/I881766915"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5121278726","display_name":"Ziniu Li","orcid":null},"institutions":[{"id":"https://openalex.org/I4210116924","display_name":"Chinese University of Hong Kong, Shenzhen","ror":"https://ror.org/02d5ks197","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633","https://openalex.org/I180726961","https://openalex.org/I4210116924"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ziniu Li","raw_affiliation_strings":["The Chinese University of Hong Kong - Shenzhen"],"raw_orcid":"https://orcid.org/0000-0003-0449-002X","affiliations":[{"raw_affiliation_string":"The Chinese University of Hong Kong - Shenzhen","institution_ids":["https://openalex.org/I4210116924"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Yidi Wang","orcid":"https://orcid.org/0009-0009-0494-9292"},"institutions":[{"id":"https://openalex.org/I4210164862","display_name":"Artificial Intelligence in Medicine (Canada)","ror":"https://ror.org/05p590m36","country_code":"CA","type":"company","lineage":["https://openalex.org/I4210164862"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Yidi Wang","raw_affiliation_strings":["National Key Laboratory for Novel Software Technology, School of Artificial Intelligence, Nanjing University"],"raw_orcid":"https://orcid.org/0009-0009-0494-9292","affiliations":[{"raw_affiliation_string":"National Key Laboratory for Novel Software Technology, School of Artificial Intelligence, Nanjing University","institution_ids":["https://openalex.org/I4210164862"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5121290051","display_name":"Shu Yan","orcid":null},"institutions":[{"id":"https://openalex.org/I881766915","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760","country_code":"CN","type":"education","lineage":["https://openalex.org/I881766915"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shu Yan","raw_affiliation_strings":["School of Computer Science, Nanjing University"],"raw_orcid":"https://orcid.org/0009-0009-5491-5779","affiliations":[{"raw_affiliation_string":"School of Computer Science, Nanjing University","institution_ids":["https://openalex.org/I881766915"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037623663","display_name":"Chengxing Jia","orcid":null},"institutions":[{"id":"https://openalex.org/I4210164862","display_name":"Artificial Intelligence in Medicine (Canada)","ror":"https://ror.org/05p590m36","country_code":"CA","type":"company","lineage":["https://openalex.org/I4210164862"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Chengxing Jia","raw_affiliation_strings":["National Key Laboratory for Novel Software Technology, School of Artificial Intelligence, Nanjing University"],"raw_orcid":"https://orcid.org/0009-0000-3421-606X","affiliations":[{"raw_affiliation_string":"National Key Laboratory for Novel Software Technology, School of Artificial Intelligence, Nanjing University","institution_ids":["https://openalex.org/I4210164862"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5121300088","display_name":"Xu-Hui Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I4210164862","display_name":"Artificial Intelligence in Medicine (Canada)","ror":"https://ror.org/05p590m36","country_code":"CA","type":"company","lineage":["https://openalex.org/I4210164862"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Xu-Hui Liu","raw_affiliation_strings":["National Key Laboratory for Novel Software Technology, School of Artificial Intelligence, Nanjing University"],"raw_orcid":"https://orcid.org/0000-0003-2663-7600","affiliations":[{"raw_affiliation_string":"National Key Laboratory for Novel Software Technology, School of Artificial Intelligence, Nanjing University","institution_ids":["https://openalex.org/I4210164862"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5121288633","display_name":"Xinwei Chen","orcid":null},"institutions":[{"id":"https://openalex.org/I4210128188","display_name":"Polgenix (United States)","ror":"https://ror.org/039rc8x03","country_code":"US","type":"company","lineage":["https://openalex.org/I4210128188"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xinwei Chen","raw_affiliation_strings":["polixir"],"raw_orcid":"https://orcid.org/0009-0008-6453-8535","affiliations":[{"raw_affiliation_string":"polixir","institution_ids":["https://openalex.org/I4210128188"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084009769","display_name":"J. Xu","orcid":null},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Jiacheng Xu","raw_affiliation_strings":["Nanyang Technological University"],"raw_orcid":"https://orcid.org/0009-0008-4315-6976","affiliations":[{"raw_affiliation_string":"Nanyang Technological University","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5121286556","display_name":"Yang Yu","orcid":null},"institutions":[{"id":"https://openalex.org/I4210164862","display_name":"Artificial Intelligence in Medicine (Canada)","ror":"https://ror.org/05p590m36","country_code":"CA","type":"company","lineage":["https://openalex.org/I4210164862"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Yang Yu","raw_affiliation_strings":["National Key Laboratory for Novel Software Technology, School of Artificial Intelligence, Nanjing University"],"raw_orcid":"https://orcid.org/0000-0002-1052-5447","affiliations":[{"raw_affiliation_string":"National Key Laboratory for Novel Software Technology, School of Artificial Intelligence, Nanjing University","institution_ids":["https://openalex.org/I4210164862"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":11,"corresponding_author_ids":["https://openalex.org/A5121286524"],"corresponding_institution_ids":["https://openalex.org/I4210164862"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.7964616,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"58","issue":"8","first_page":"1","last_page":"35"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10028","display_name":"Topic Modeling","score":0.19939999282360077,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10028","display_name":"Topic Modeling","score":0.19939999282360077,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11714","display_name":"Multimodal Machine Learning Applications","score":0.13300000131130219,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13629","display_name":"Text Readability and Simplification","score":0.08030000329017639,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cognition","display_name":"Cognition","score":0.46140000224113464},{"id":"https://openalex.org/keywords/verbal-reasoning","display_name":"Verbal reasoning","score":0.446399986743927},{"id":"https://openalex.org/keywords/automated-reasoning","display_name":"Automated reasoning","score":0.44620001316070557},{"id":"https://openalex.org/keywords/psychology-of-reasoning","display_name":"Psychology of reasoning","score":0.4431000053882599},{"id":"https://openalex.org/keywords/reinforcement-learning","display_name":"Reinforcement learning","score":0.31700000166893005},{"id":"https://openalex.org/keywords/case-based-reasoning","display_name":"Case-based reasoning","score":0.30469998717308044},{"id":"https://openalex.org/keywords/language-model","display_name":"Language model","score":0.2976999878883362},{"id":"https://openalex.org/keywords/qualitative-reasoning","display_name":"Qualitative reasoning","score":0.29750001430511475}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7452999949455261},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4973999857902527},{"id":"https://openalex.org/C169900460","wikidata":"https://www.wikidata.org/wiki/Q2200417","display_name":"Cognition","level":2,"score":0.46140000224113464},{"id":"https://openalex.org/C188147891","wikidata":"https://www.wikidata.org/wiki/Q147638","display_name":"Cognitive science","level":1,"score":0.44679999351501465},{"id":"https://openalex.org/C36964233","wikidata":"https://www.wikidata.org/wiki/Q7920942","display_name":"Verbal reasoning","level":3,"score":0.446399986743927},{"id":"https://openalex.org/C195344581","wikidata":"https://www.wikidata.org/wiki/Q2555318","display_name":"Automated reasoning","level":2,"score":0.44620001316070557},{"id":"https://openalex.org/C183521366","wikidata":"https://www.wikidata.org/wiki/Q7256422","display_name":"Psychology of reasoning","level":4,"score":0.4431000053882599},{"id":"https://openalex.org/C539667460","wikidata":"https://www.wikidata.org/wiki/Q2414942","display_name":"Management science","level":1,"score":0.34450000524520874},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.31700000166893005},{"id":"https://openalex.org/C20162079","wikidata":"https://www.wikidata.org/wiki/Q1151406","display_name":"Case-based reasoning","level":2,"score":0.30469998717308044},{"id":"https://openalex.org/C137293760","wikidata":"https://www.wikidata.org/wiki/Q3621696","display_name":"Language model","level":2,"score":0.2976999878883362},{"id":"https://openalex.org/C83725634","wikidata":"https://www.wikidata.org/wiki/Q7268699","display_name":"Qualitative reasoning","level":2,"score":0.29750001430511475},{"id":"https://openalex.org/C2777508537","wikidata":"https://www.wikidata.org/wiki/Q7936620","display_name":"Visual reasoning","level":2,"score":0.2874999940395355},{"id":"https://openalex.org/C76969082","wikidata":"https://www.wikidata.org/wiki/Q486902","display_name":"Mathematical model","level":2,"score":0.28049999475479126},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.27309998869895935},{"id":"https://openalex.org/C37335422","wikidata":"https://www.wikidata.org/wiki/Q6888134","display_name":"Model-based reasoning","level":3,"score":0.2705000042915344},{"id":"https://openalex.org/C146072743","wikidata":"https://www.wikidata.org/wiki/Q192161","display_name":"Formal language","level":2,"score":0.2678000032901764},{"id":"https://openalex.org/C105409693","wikidata":"https://www.wikidata.org/wiki/Q5937824","display_name":"Human intelligence","level":2,"score":0.26489999890327454},{"id":"https://openalex.org/C195324797","wikidata":"https://www.wikidata.org/wiki/Q33742","display_name":"Natural language","level":2,"score":0.2615000009536743},{"id":"https://openalex.org/C2522767166","wikidata":"https://www.wikidata.org/wiki/Q2374463","display_name":"Data science","level":1,"score":0.25839999318122864},{"id":"https://openalex.org/C172347087","wikidata":"https://www.wikidata.org/wiki/Q3217196","display_name":"Language of mathematics","level":2,"score":0.25040000677108765}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3786333","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3786333","pdf_url":null,"source":{"id":"https://openalex.org/S157921468","display_name":"ACM Computing Surveys","issn_l":"0360-0300","issn":["0360-0300","1557-7341"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Computing Surveys","raw_type":"journal-article"},{"id":"pmh:oai:dr.ntu.edu.sg:10356/211093","is_oa":false,"landing_page_url":"https://hdl.handle.net/10356/211093","pdf_url":null,"source":{"id":"https://openalex.org/S4306402609","display_name":"DR-NTU (Nanyang Technological University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I172675005","host_organization_name":"Nanyang Technological University","host_organization_lineage":["https://openalex.org/I172675005"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5862880122","display_name":null,"funder_award_id":"62495093","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W2001771035","https://openalex.org/W2048229624","https://openalex.org/W2072950331","https://openalex.org/W2126316555","https://openalex.org/W3170403598","https://openalex.org/W4304195441","https://openalex.org/W4385571045","https://openalex.org/W4389524159","https://openalex.org/W4394606408","https://openalex.org/W4402683967","https://openalex.org/W4407254806","https://openalex.org/W4415237471","https://openalex.org/W4415798274","https://openalex.org/W4416036482","https://openalex.org/W4416649973"],"related_works":[],"abstract_inverted_index":{"Mathematical":[0],"reasoning":[1,38,132,152],"has":[2,61],"long":[3],"represented":[4],"one":[5],"of":[6,36,110,154],"the":[7,34],"most":[8],"fundamental":[9,105],"and":[10,57,89,92,99,113,127,134,156],"challenging":[11],"frontiers":[12],"in":[13,28,40,108,150],"artificial":[14],"intelligence":[15],"research.":[16],"In":[17],"recent":[18,94],"years,":[19],"large":[20],"language":[21],"models":[22,49],"(LLMs)":[23],"have":[24],"achieved":[25],"significant":[26],"advances":[27],"this":[29],"area.":[30],"This":[31,140],"survey":[32,141],"examines":[33],"development":[35],"mathematical":[37,51,76],"abilities":[39],"LLMs":[41,155],"through":[42,136],"two":[43],"high-level":[44],"cognitive":[45],"phases:":[46],"comprehension,":[47],"where":[48],"gain":[50],"understanding":[52],"via":[53],"diverse":[54],"pretraining":[55,126],"strategies,":[56],"answer":[58],"generation,":[59],"which":[60],"progressed":[62],"from":[63,79],"direct":[64],"prediction":[65],"to":[66,82,143,160,164],"step-by-step":[67],"Chain-of-Thought":[68],"(CoT)":[69],"reasoning.":[70],"We":[71],"review":[72],"methods":[73],"for":[74,147,157],"enhancing":[75,151],"reasoning,":[77],"ranging":[78],"training-free":[80],"prompting":[81],"fine-tuning":[83,88],"approaches":[84],"such":[85],"as":[86],"supervised":[87],"reinforcement":[90],"learning,":[91],"discuss":[93],"work":[95],"on":[96],"extended":[97],"CoT":[98],"\u201ctest-time":[100],"scaling\u201d.":[101],"Despite":[102],"notable":[103],"progress,":[104],"challenges":[106],"remain":[107],"terms":[109],"capacity,":[111],"efficiency,":[112],"generalization.":[114],"To":[115],"address":[116],"these":[117,162],"issues,":[118],"we":[119],"highlight":[120],"promising":[121],"research":[122],"directions,":[123],"including":[124],"advanced":[125],"knowledge":[128],"augmentation":[129],"techniques,":[130],"formal":[131],"frameworks,":[133],"meta-generalization":[135],"principled":[137],"learning":[138],"paradigms.":[139],"tries":[142],"provide":[144],"some":[145],"insights":[146],"researchers":[148],"interested":[149],"capabilities":[153],"those":[158],"seeking":[159],"apply":[161],"techniques":[163],"other":[165],"domains.":[166]},"counts_by_year":[],"updated_date":"2026-05-05T08:41:31.759640","created_date":"2025-12-25T00:00:00"}
