{"id":"https://openalex.org/W7213890442","doi":"https://doi.org/10.48550/arxiv.2609.21132","title":"Mathematics Graduate Training in the Age of AI","display_name":"Mathematics Graduate Training in the Age of AI","publication_year":2026,"publication_date":"2026-09-17","ids":{"openalex":"https://openalex.org/W7213890442","doi":"https://doi.org/10.48550/arxiv.2609.21132"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.21132","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.21132","pdf_url":"https://arxiv.org/pdf/2609.21132","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.21132","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039063170","display_name":"David A. Glickenstein","orcid":"https://orcid.org/0000-0002-9238-0973","observed_orcids":["https://orcid.org/0000-0002-9238-0973"]},"institutions":[{"id":"https://openalex.org/I138006243","display_name":"University of Arizona","ror":"https://ror.org/03m2x1q45","country_code":"US","type":"education","lineage":["https://openalex.org/I138006243"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Glickenstein, David","raw_affiliation_strings":["University of Arizona"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Arizona","institution_ids":["https://openalex.org/I138006243"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5039063170"],"corresponding_institution_ids":["https://openalex.org/I138006243"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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/T10130","display_name":"Mathematics Education and Teaching Techniques","score":0.6220999956130981,"subfield":{"id":"https://openalex.org/subfields/3304","display_name":"Education"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10130","display_name":"Mathematics Education and Teaching Techniques","score":0.6220999956130981,"subfield":{"id":"https://openalex.org/subfields/3304","display_name":"Education"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11832","display_name":"Doctoral Education Challenges and Solutions","score":0.13570000231266022,"subfield":{"id":"https://openalex.org/subfields/3304","display_name":"Education"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.09610000252723694,"subfield":{"id":"https://openalex.org/subfields/1207","display_name":"History and Philosophy of Science"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/generative-ai","display_name":"generative AI","score":0.9129999876022339},{"id":"https://openalex.org/keywords/mathematical-judgment","display_name":"mathematical judgment","score":0.9750000238418579},{"id":"https://openalex.org/keywords/thesis-defense","display_name":"thesis defense","score":0.5059999823570251},{"id":"https://openalex.org/keywords/curriculum-policy","display_name":"curriculum policy","score":0.4180000126361847}],"concepts":[{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.6046000123023987},{"id":"https://openalex.org/C2777211547","wikidata":"https://www.wikidata.org/wiki/Q17141490","display_name":"Training (meteorology)","level":2,"score":0.5770999789237976},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.4625999927520752},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46239998936653137},{"id":"https://openalex.org/C3020528894","wikidata":"https://www.wikidata.org/wiki/Q20820271","display_name":"Graduate students","level":2,"score":0.45010000467300415},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4066999852657318},{"id":"https://openalex.org/C118840557","wikidata":"https://www.wikidata.org/wiki/Q5161405","display_name":"Connected Mathematics","level":2,"score":0.391400009393692},{"id":"https://openalex.org/C119754765","wikidata":"https://www.wikidata.org/wiki/Q7307430","display_name":"Reform mathematics","level":3,"score":0.3529999852180481},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.3434999883174896},{"id":"https://openalex.org/C2985790989","wikidata":"https://www.wikidata.org/wiki/Q141212","display_name":"Graduate education","level":2,"score":0.34119999408721924},{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.3172999918460846},{"id":"https://openalex.org/C98318862","wikidata":"https://www.wikidata.org/wiki/Q5170130","display_name":"Core-Plus Mathematics Project","level":3,"score":0.3165000081062317},{"id":"https://openalex.org/C39758115","wikidata":"https://www.wikidata.org/wiki/Q6786779","display_name":"Math wars","level":3,"score":0.27619999647140503},{"id":"https://openalex.org/C2779463800","wikidata":"https://www.wikidata.org/wiki/Q5062222","display_name":"Center (category theory)","level":2,"score":0.272599995136261}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.21132","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.21132","pdf_url":"https://arxiv.org/pdf/2609.21132","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.21132","doi":"https://doi.org/10.48550/arxiv.2609.21132","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.21132","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.21132","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.21132","pdf_url":"https://arxiv.org/pdf/2609.21132","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"score":0.9235000014305115,"id":"https://metadata.un.org/sdg/4","display_name":"Quality education"}],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320332414","display_name":"Department of Mechanical Engineering, University of Texas at Austin","ror":"https://ror.org/00hj54h04"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213890442.pdf","grobid_xml":"https://content.openalex.org/works/W7213890442.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7214177392","https://openalex.org/W7213999915","https://openalex.org/W7204109008","https://openalex.org/W7220660715","https://openalex.org/W7204228896","https://openalex.org/W7160927281","https://openalex.org/W7220817304","https://openalex.org/W7129635837","https://openalex.org/W7134148411","https://openalex.org/W6885010948"],"abstract_inverted_index":{"Generative":[0],"AI":[1],"changes":[2],"the":[3,29,46,68,75,82],"conditions":[4],"under":[5],"which":[6],"graduate":[7,24,34,122],"mathematics":[8,23,35,49,86],"is":[9,21,37,109],"learned,":[10],"assessed,":[11],"written,":[12],"and":[13,41,104,116],"defended.":[14],"The":[15,107],"central":[16],"claim":[17],"of":[18,48,70,95],"this":[19,127],"paper":[20],"that":[22],"programs":[25,123],"should":[26],"respond":[27],"to":[28,39,65,79,81,84,110,126],"moment":[30],"by":[31],"clarifying":[32],"what":[33],"education":[36,50],"trying":[38],"teach":[40],"assess.":[42],"In":[43],"most":[44],"ways,":[45],"goals":[47,69],"have":[51],"not":[52],"changed.":[53],"Rather,":[54],"with":[55],"changing":[56],"tools":[57],"it":[58],"has":[59],"become":[60],"more":[61],"essential":[62],"than":[63],"ever":[64],"make":[66],"clear":[67],"mathematical":[71,77,114],"training.":[72],"We":[73],"use":[74],"term":[76],"judgment":[78],"refer":[80],"capacity":[83],"evaluate":[85],"(e.g.,":[87],"claims,":[88],"definitions,":[89],"examples,":[90],"proofs,":[91],"analogies,":[92],"computations,":[93],"uses":[94],"tools,":[96],"research":[97],"directions)":[98],"as":[99],"mathematically":[100],"sound,":[101],"useful,":[102],"well-posed,":[103],"appropriately":[105],"justified.":[106],"recommendation":[108],"center":[111],"training":[112],"on":[113],"judgment,":[115],"we":[117],"examine":[118],"possible":[119],"policies":[120],"for":[121],"in":[124],"Mathematics":[125],"end.":[128]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-22T00:00:00"}
