{"id":"https://openalex.org/W7155565605","doi":"https://doi.org/10.48550/arxiv.2604.21916","title":"MathDuels: Evaluating LLMs as Problem Posers and Solvers","display_name":"MathDuels: Evaluating LLMs as Problem Posers and Solvers","publication_year":2026,"publication_date":"2026-04-23","ids":{"openalex":"https://openalex.org/W7155565605","doi":"https://doi.org/10.48550/arxiv.2604.21916"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.21916","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.21916","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.21916","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044711737","display_name":"Zhiqiu Xu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xu, Zhiqiu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008090688","display_name":"Shibo Jin","orcid":"https://orcid.org/0000-0003-3514-4605"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jin, Shibo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134473190","display_name":"Shreya Arya","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Arya, Shreya","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5075879790","display_name":"Mayur Naik","orcid":"https://orcid.org/0000-0003-1348-8618"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Naik, Mayur","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10028","display_name":"Topic Modeling","score":0.30959999561309814,"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":0.30959999561309814,"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/T11902","display_name":"Intelligent Tutoring Systems and Adaptive Learning","score":0.10369999706745148,"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.054099999368190765,"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/benchmark","display_name":"Benchmark (surveying)","score":0.6211000084877014},{"id":"https://openalex.org/keywords/pipeline","display_name":"Pipeline (software)","score":0.57669997215271},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.5720000267028809},{"id":"https://openalex.org/keywords/problem-solver","display_name":"Problem solver","score":0.511900007724762},{"id":"https://openalex.org/keywords/rasch-model","display_name":"Rasch model","score":0.5110999941825867},{"id":"https://openalex.org/keywords/frontier","display_name":"Frontier","score":0.5011000037193298}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6406999826431274},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.6211000084877014},{"id":"https://openalex.org/C43521106","wikidata":"https://www.wikidata.org/wiki/Q2165493","display_name":"Pipeline (software)","level":2,"score":0.57669997215271},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.5720000267028809},{"id":"https://openalex.org/C3019612716","wikidata":"https://www.wikidata.org/wiki/Q730920","display_name":"Problem solver","level":2,"score":0.511900007724762},{"id":"https://openalex.org/C101266164","wikidata":"https://www.wikidata.org/wiki/Q2131821","display_name":"Rasch model","level":2,"score":0.5110999941825867},{"id":"https://openalex.org/C2778571376","wikidata":"https://www.wikidata.org/wiki/Q1355821","display_name":"Frontier","level":2,"score":0.5011000037193298},{"id":"https://openalex.org/C37736160","wikidata":"https://www.wikidata.org/wiki/Q1801315","display_name":"Adversarial system","level":2,"score":0.4973999857902527},{"id":"https://openalex.org/C2779530757","wikidata":"https://www.wikidata.org/wiki/Q1207505","display_name":"Quality (philosophy)","level":2,"score":0.4302999973297119},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.391400009393692},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3476000130176544},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.3009999990463257},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2985999882221222},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2962000072002411},{"id":"https://openalex.org/C76969082","wikidata":"https://www.wikidata.org/wiki/Q486902","display_name":"Mathematical model","level":2,"score":0.29269999265670776},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.29190000891685486},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.26739999651908875},{"id":"https://openalex.org/C539667460","wikidata":"https://www.wikidata.org/wiki/Q2414942","display_name":"Management science","level":1,"score":0.2614000141620636},{"id":"https://openalex.org/C42475967","wikidata":"https://www.wikidata.org/wiki/Q194292","display_name":"Operations research","level":1,"score":0.2529999911785126}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.21916","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.21916","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.21916","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.21916","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"As":[0,132],"frontier":[1,110],"language":[2],"models":[3,24,40,111,134,170],"attain":[4],"near-ceiling":[5],"performance":[6],"on":[7],"static":[8],"mathematical":[9],"benchmarks,":[10],"existing":[11],"evaluations":[12],"are":[13,60,118,171],"increasingly":[14],"unable":[15],"to":[16],"differentiate":[17],"model":[18,85],"capabilities,":[19],"largely":[20],"because":[21],"they":[22,138],"cast":[23],"solely":[25],"as":[26,168],"solvers":[27],"of":[28,102],"fixed":[29,159],"problem":[30,68,93],"sets.":[31],"We":[32,161],"introduce":[33],"MathDuels,":[34],"a":[35,63,158,163],"self-play":[36],"benchmark":[37],"in":[38,129],"which":[39],"occupy":[41],"dual":[42],"roles:":[43],"each":[44,103],"authors":[45],"math":[46],"problems":[47,53,140],"under":[48],"adversarial":[49],"prompting":[50],"and":[51,70,73,92,115,121],"solves":[52],"authored":[54,105],"by":[55,75],"every":[56],"other":[57],"participant.":[58],"Problems":[59],"produced":[61],"through":[62],"three-stage":[64],"generation":[65],"pipeline":[66],"(meta-prompting,":[67],"generation,":[69],"difficulty":[71,149],"amplification),":[72],"validated":[74],"an":[76],"independent":[77],"verifier":[78],"that":[79,113,122,141,166],"excludes":[80],"ill-posed":[81],"questions.":[82],"A":[83],"Rasch":[84],"(Rasch,":[86],"1993)":[87],"jointly":[88],"estimates":[89],"solver":[90],"abilities":[91],"difficulties;":[94],"author":[95],"quality":[96],"is":[97],"derived":[98],"from":[99],"the":[100,136,147],"difficulties":[101],"model's":[104],"problems.":[106],"Experiments":[107],"across":[108],"19":[109],"reveal":[112],"authoring":[114],"solving":[116],"capabilities":[117],"partially":[119],"decoupled,":[120],"dual-role":[123],"evaluation":[124],"reveals":[125],"capability":[126],"separations":[127],"invisible":[128],"single-role":[130],"benchmarks.":[131],"newer":[133],"enter":[135],"arena,":[137],"produce":[139],"defeat":[142],"previously":[143],"dominant":[144],"solvers,":[145],"so":[146],"benchmark's":[148],"co-evolves":[150],"with":[151],"participant":[152],"strength":[153],"rather":[154],"than":[155],"saturating":[156],"at":[157],"ceiling.":[160],"host":[162],"public":[164],"leaderboard":[165],"updates":[167],"new":[169],"released.":[172]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-04-25T00:00:00"}