{"id":"https://openalex.org/W2014078972","doi":"https://doi.org/10.2307/2686292","title":"The History of Mathematics: An Introduction","display_name":"The History of Mathematics: An Introduction","publication_year":1986,"publication_date":"1986-09-01","ids":{"openalex":"https://openalex.org/W2014078972","doi":"https://doi.org/10.2307/2686292","mag":"2014078972"},"language":"en","primary_location":{"id":"doi:10.2307/2686292","doi":"https://doi.org/10.2307/2686292","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2686292","pdf_url":null,"source":{"id":"https://openalex.org/S193011845","display_name":"College Mathematics Journal","issn_l":"0746-8342","issn":["0746-8342","1931-1346"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["jufo-1","norway-1","poland-20","russia-white-list-4"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The College Mathematics Journal","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"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/A5031589048","display_name":"David Wheeler","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"David Wheeler","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"David M. Burton","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"David M. Burton","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":2.2457,"has_fulltext":false,"cited_by_count":235,"citation_normalized_percentile":{"value":0.88435269,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"17","issue":"4","first_page":"373","last_page":"373"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.9994999766349792,"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"}},{"id":"https://openalex.org/T13175","display_name":"Historical Astronomy and Related Studies","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T14475","display_name":"History of Science and Medicine","score":9.999999747378752e-05,"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/history-of-mathematics","display_name":"history of mathematics","score":0.9900000095367432},{"id":"https://openalex.org/keywords/number-systems","display_name":"number systems","score":0.8169999718666077},{"id":"https://openalex.org/keywords/ancient-egyptian-mathematics","display_name":"ancient Egyptian mathematics","score":0.6570000052452087},{"id":"https://openalex.org/keywords/babylonian-mathematics","display_name":"Babylonian mathematics","score":0.8899999856948853},{"id":"https://openalex.org/keywords/greek-mathematics","display_name":"ancient Greek mathematics","score":0.8809999823570251},{"id":"https://openalex.org/keywords/pythagorean-theorem","display_name":"Pythagorean theorem","score":0.8050000071525574},{"id":"https://openalex.org/keywords/euclid-s-elements","display_name":"Euclid's Elements","score":0.7170000076293945},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.6060000061988831},{"id":"https://openalex.org/keywords/number-theory","display_name":"number theory","score":0.43700000643730164},{"id":"https://openalex.org/keywords/diophantine-equations","display_name":"Diophantine equations","score":0.6150000095367432},{"id":"https://openalex.org/keywords/irrational-numbers","display_name":"irrational numbers","score":0.4350000023841858},{"id":"https://openalex.org/keywords/ancient-chinese-mathematics","display_name":"ancient Chinese mathematics","score":0.39100000262260437},{"id":"https://openalex.org/keywords/indian-mathematics","display_name":"Indian mathematics","score":0.5210000276565552},{"id":"https://openalex.org/keywords/islamic-mathematics","display_name":"Islamic mathematics","score":0.578000009059906},{"id":"https://openalex.org/keywords/fibonacci","display_name":"Fibonacci","score":0.36500000953674316},{"id":"https://openalex.org/keywords/calculus","display_name":"calculus","score":0.30300000309944153},{"id":"https://openalex.org/keywords/history-of-mathematics-education","display_name":"history of mathematics education","score":0.453000009059906},{"id":"https://openalex.org/keywords/mathematics-curriculum-reform","display_name":"mathematics curriculum reform","score":0.41200000047683716},{"id":"https://openalex.org/keywords/mathematics-teaching-methods","display_name":"mathematics teaching methods","score":0.32600000500679016},{"id":"https://openalex.org/keywords/mathematics-assessment","display_name":"mathematics assessment","score":0.3240000009536743}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7621644735336304},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.6427907943725586},{"id":"https://openalex.org/C72074766","wikidata":"https://www.wikidata.org/wiki/Q185264","display_name":"History of mathematics","level":2,"score":0.4774946868419647},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3478269577026367},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2307/2686292","doi":"https://doi.org/10.2307/2686292","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2686292","pdf_url":null,"source":{"id":"https://openalex.org/S193011845","display_name":"College Mathematics Journal","issn_l":"0746-8342","issn":["0746-8342","1931-1346"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["jufo-1","norway-1","poland-20","russia-white-list-4"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The College Mathematics Journal","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W17432017","https://openalex.org/W173757569","https://openalex.org/W560177802","https://openalex.org/W2495190426","https://openalex.org/W6968625606","https://openalex.org/W2955422529","https://openalex.org/W2790960234","https://openalex.org/W2115038101","https://openalex.org/W2961162767","https://openalex.org/W633429200"],"abstract_inverted_index":{"The":[0,29,43,54,73,88,98,107,121,143,161,184,189,195,205,226,234,249,275,280,286,297,304,317,358,362,378,386,396,405,415,418,425,430,436,447,464,473,479,482,505,517,522,532,537,543,553,560,566,572,579,582,605,620,625,640,651,687,690,701,708,713,722,729,739,748,753,760,776,779,788,797,810,813,826,837,847,862,881,894,903,914,934,972,978,990,997,1010,1032,1041,1050,1061,1084,1095,1103,1121,1149,1164,1172,1192,1196,1201,1210,1234,1237,1252,1260,1296],"History":[1,44],"of":[2,23,38,45,49,62,123,140,145,159,164,180,191,198,207,211,228,239,245,251,260,266,272,277,282,288,291,295,299,315,332,337,347,360,365,369,376,380,383,388,403,408,413,420,427,432,438,467,485,507,541,547,574,589,607,627,630,642,669,677,683,692,710,717,724,732,737,742,755,763,781,799,816,820,839,849,854,857,864,875,891,912,916,936,976,992,999,1012,1034,1043,1052,1063,1067,1072,1086,1097,1123,1128,1137,1151,1155,1178,1183,1198,1208,1239,1254,1263,1277],"Mathematics:":[3,422,493,608],"An":[4,367],"Introduction,":[5],"7e":[6],"by":[7],"David":[8],"M.":[9],"Burton":[10],"Preface":[11],"1":[12],"Early":[13,85,104,243,469,814,1202],"Number":[14,24,36,60,76,176,353,450,599,937],"Systems":[15],"and":[16,41,71,201,220,256,269,310,321,462,495,502,511,520,539,557,563,594,610,617,657,674,698,705,744,772,783,792,832,844,860,869,896,907,931,941,946,961,987,1005,1017,1037,1078,1089,1107,1113,1133,1146,1187,1205,1215,1224,1228,1232,1246,1266,1281],"Symbols":[17],"1.1":[18],"Primitive":[19],"Counting":[20,1169],"A":[21,94,126,157,173,313,441,634,660,1242,1288],"Sense":[22],"Notches":[25],"as":[26,33,131],"Tally":[27],"Marks":[28],"Peruvian":[30],"Quipus:":[31],"Knots":[32],"Numbers":[34,50,113,230,258,591,951,1125,1191],"1.2":[35],"Recording":[37,61],"the":[39,63,118,138,151,181,202,240,246,270,273,278,292,311,333,338,348,373,384,401,433,454,488,500,551,595,615,631,643,646,670,678,684,693,805,821,865,870,947,1000,1029,1073,1114,1142,1156,1170,1206,1282],"Egyptians":[40],"Greeks":[42],"Herodotus":[46],"Hieroglyphic":[47],"Representation":[48],"Egyptian":[51,91,102,105,129,135],"Hieratic":[52],"Numeration":[53],"Greek":[55,192,421,444,1297],"Alphabetic":[56],"Numeral":[57],"System":[58,77],"1.3":[59],"Babylonians":[64],"Babylonian":[65,74,155,162,169,178],"Cuneiform":[66],"Script":[67],"Deciphering":[68],"Cuneiform:":[69],"Grotefend":[70],"Rawlinson":[72],"Positional":[75],"Writing":[78],"in":[79,84,459,471,499,614,1285],"Ancient":[80,397,523],"China":[81,463],"2":[82],"Mathematics":[83,130,156,193,218,429,470,498,712,915,1153,1160,1241,1287],"Civilizations":[86],"2.1":[87],"Rhind":[89,119],"Papyrus":[90,120,187],"Mathematical":[92,186,483,529,886,956],"Papyri":[93],"Key":[95],"to":[96,550,804,968,1023,1027,1141,1300],"Deciphering:":[97],"Rosetta":[99],"Stone":[100],"2.2":[101],"Arithmetic":[103,133,366,879,1110],"Multiplication":[106],"Unit":[108],"Fraction":[109],"Table":[110],"Representing":[111],"Rational":[112],"2.3":[114],"Four":[115],"Problems":[116,170,265,452,1302],"from":[117,453],"Method":[122,752],"False":[124],"Position":[125],"Curious":[127],"Problem":[128,236,466,477,586,597,603,874],"Applied":[132],"2.4":[134],"Geometry":[136,215,325,329,759,1054,1060],"Approximating":[137],"Area":[139,204],"a":[141,146,409,1058],"Circle":[142,274],"Volume":[144],"Truncated":[147],"Pyramid":[148,153],"Speculations":[149],"About":[150],"Great":[152,632],"2.5":[154],"Tablet":[158,174],"Reciprocals":[160],"Treatment":[163],"Quadratic":[165],"Equations":[166,458],"Two":[167],"Characteristic":[168],"2.6":[171],"Plimpton":[172],"Concerning":[175],"Triples":[177,600],"Use":[179,890],"Pythagorean":[182,217,235,241,247,339,596,598],"Theorem":[183,242,340,364,975],"Cairo":[185],"3":[188],"Beginnings":[190,1253],"3.1":[194],"Geometric":[196,237,344],"Discoveries":[197,741],"Thales":[199,210],"Greece":[200],"Aegean":[203],"Dawn":[206,709],"Demonstrative":[208],"Geometry:":[209,770,1069,1075],"Miletos":[212],"Measurements":[213],"Using":[214],"3.2":[216],"Pythagoras":[219],"His":[221],"Followers":[222],"Nichomachus'":[223],"Introductio":[224],"Arithmeticae":[225,1009],"Theory":[227,354,451,851,927,1015,1177,1185,1200,1276],"Figurative":[229],"Zeno's":[231],"Paradox":[232],"3.3":[233],"Proofs":[238],"Solutions":[244,1299],"Equation":[248,672,686],"Crisis":[250],"Incommensurable":[252],"Quantities":[253],"Theon's":[254],"Side":[255],"Diagonal":[257],"Eudoxus":[259],"Cnidos":[261],"3.4":[262],"Three":[263],"Construction":[264,346],"Antiquity":[267],"Hippocrates":[268],"Quadrature":[271,407],"Duplication":[276],"Cube":[279],"Trisection":[281],"an":[283],"Angle":[284],"3.5":[285],"Quadratrix":[287],"Hippias":[289,294],"Rise":[290],"Sophists":[293],"Elis":[296],"Grove":[298],"Academia:":[300],"Plato's":[301],"Academy":[302],"4":[303],"Alexandrian":[305,428],"School:":[306,1212],"Euclid":[307,309,361],"4.1":[308],"Elements":[312,334,1046],"Center":[314],"Learning:":[316],"Museum":[318],"Euclid's":[319,326,335,352],"Life":[320,986],"Writings":[322,754],"4.2":[323],"Euclidean":[324,355],"Foundation":[327],"for":[328,443,636,949],"Book":[330,341],"I":[331],"Proof":[336],"II":[342],"on":[343,901,925,983,1091,1119],"Algebra":[345,506,1120,1136],"Regular":[349],"Pentagon":[350],"4.3":[351],"Divisibility":[356],"Properties":[357,588],"Algorithm":[359],"Fundamental":[363],"Infinity":[368],"Primes":[370],"4.4":[371],"Eratosthenes,":[372],"Wise":[374],"Man":[375],"Alexandria":[377],"Sieve":[379],"Eratosthenes":[381],"Measurement":[382],"Earth":[385],"Almagest":[387],"Claudius":[389],"Ptolemy":[390],"Ptolemy's":[391],"Geographical":[392],"Dictionary":[393],"4.5":[394],"Archimedes":[395,468],"World's":[398],"Genius":[399],"Estimating":[400],"Value":[402],"pi":[404],"Sand-Reckoner":[406],"Parabolic":[410],"Segment":[411],"Apollonius":[412],"Perga:":[414],"Conics":[416],"5":[417],"Twilight":[419],"Diophantus":[423],"5.1":[424],"Decline":[426,538],"Waning":[431],"Golden":[434,795],"Age":[435,1085],"Spread":[437,716],"Christianity":[439],"Constantinople,":[440],"Refuge":[442],"Learning":[445,542,549,638],"5.2":[446],"Arithmetica":[448,455,786,971],"Diophantus's":[449],"5.3":[456],"Diophantine":[457],"Greece,":[460],"India,":[461],"Cattle":[465],"India":[472],"Chinese":[474,524,528],"Hundred":[475],"Fowls":[476],"5.4":[478],"Later":[480,527,801],"Commentators":[481],"Collection":[484],"Pappus":[486],"Hypatia,":[487],"First":[489,533],"Woman":[490],"Mathematician":[491,662],"Roman":[492],"Boethius":[494],"Cassiodorus":[496],"5.5":[497],"Near":[501],"Far":[503],"East":[504],"al-Khowarizmi":[508],"Abu":[509],"Kamil":[510],"Thabit":[512],"ibn":[513],"Qurra":[514],"Omar":[515],"Khayyam":[516],"Astronomers":[518],"al-Tusi":[519],"al-Karashi":[521],"Nine":[525],"Chapters":[526],"Works":[530,573],"6":[531],"Awakening:":[534],"Fibonacci":[535,580,590,593],"6.1":[536],"Revival":[540,935],"Carolingian":[544],"Pre-Renaissance":[545],"Transmission":[546],"Arabic":[548],"West":[552],"Pioneer":[554],"Translators:":[555],"Gerard":[556],"Adelard":[558],"6.2":[559],"Liber":[561,564,583],"Abaci":[562],"Quadratorum":[565,571],"Hindu-Arabic":[567],"Numerals":[568],"Fibonacci's":[569,601],"Liver":[570],"Jordanus":[575],"de":[576,750,1047],"Nemore":[577],"6.3":[578],"Sequence":[581],"Abaci's":[584],"Rabbit":[585],"Some":[587,1271],"6.4":[592],"Tournament":[602],"7":[604],"Renaissance":[606,622],"Cardan":[609],"Tartaglia":[611,658],"7.1":[612],"Europe":[613],"Fourteenth":[616],"Fifteenth":[618],"Centuries":[619],"Italian":[621,652],"Artificial":[623],"Writing:":[624],"Invention":[626,736],"Printing":[628],"Founding":[629],"Universities":[633,1158],"Thirst":[635],"Classical":[637],"7.2":[639],"Battle":[641],"Scholars":[644],"Restoring":[645],"Algebraic":[647,761],"Tradition:":[648],"Robert":[649],"Recorde":[650],"Algebraists:":[653],"Pacioli,":[654],"del":[655],"Ferro":[656],"Cardan,":[659],"Scoundrel":[661],"7.3":[663],"Cardan's":[664,667],"Ars":[665],"Magna":[666],"Solution":[668,682],"Cubic":[671,679,689],"Bombelli":[673],"Imaginary":[675],"Roots":[676],"7.4":[680],"Ferrari's":[681],"Quartic":[685],"Resolvant":[688],"Story":[691],"Quintic":[694],"Equation:":[695],"Ruffini,":[696],"Abel":[697],"Galois":[699],"8":[700],"Mechanical":[702],"World:":[703],"Descartes":[704,756],"Newton":[706,793],"8.1":[707],"Modern":[711,725,1098,1286],"Seventeenth":[714],"Century":[715,1166],"Knowledge":[718],"Galileo's":[719],"Telescopic":[720],"Observations":[721],"Beginning":[723],"Notation:":[726],"Francois":[727],"Vieta":[728],"Decimal":[730],"Fractions":[731],"Simon":[733],"Steven":[734],"Napier's":[735],"Logarithms":[738],"Astronomical":[740],"Brahe":[743],"Kepler":[745],"8.2":[746],"Descartes:":[747],"Discours":[749],"la":[751],"Inventing":[757],"Cartesian":[758],"Aspect":[762],"La":[764],"Geometrie":[765],"Descartes'":[766],"Principia":[767,777],"Philosophia":[768],"Perspective":[769],"Desargues":[771],"Poncelet":[773],"8.3":[774],"Newton:":[775],"Mathematica":[778],"Textbooks":[780],"Oughtred":[782],"Harriot":[784],"Wallis'":[785],"Infinitorum":[787],"Lucasian":[789],"Professorship:":[790],"Barrow":[791],"Newton's":[794,823],"Years":[796],"Laws":[798],"Motion":[800],"Years:":[802],"Appointment":[803],"Mint":[806],"8.4":[807],"Gottfried":[808],"Leibniz:":[809],"Calculus":[811,822,825],"Controversy":[812],"Work":[815],"Leibniz":[817],"Leibniz's":[818],"Creation":[819,1066],"Fluxional":[824],"Dispute":[827],"over":[828],"Priority":[829],"Maria":[830],"Agnesi":[831],"Emilie":[833],"du":[834,883],"Chatelet":[835],"9":[836],"Development":[838],"Probability":[840,850,902,926],"Theory:":[841,938],"Pascal,":[842],"Bernoulli,":[843,929],"Laplace":[845,897,919],"9.1":[846],"Origins":[848],"Graunt's":[852],"Bills":[853],"Mortality":[855],"Games":[856],"Chance:":[858],"Dice":[859],"Cards":[861],"Precocity":[863],"Young":[866,1082],"Pascal":[867,868],"Cycloid":[871],"De":[872,909],"Mere's":[873],"Points":[876],"9.2":[877],"Pascal's":[878],"Triangle":[880,884],"Traite":[882],"Arithmetique":[885],"Induction":[887,892],"Francesco":[888],"Maurolico's":[889],"9.3":[893],"Bernoullis":[895],"Christiaan":[898],"Huygens's":[899],"Pamphlet":[900],"Bernoulli":[904],"Brothers:":[905],"John":[906,1064],"James":[908],"Moivre's":[910],"Doctrine":[911],"Chances":[913],"Celestial":[917],"Phenomena:":[918],"Mary":[920],"Fairfax":[921],"Somerville":[922],"Laplace's":[923],"Research":[924],"Daniel":[928],"Poisson,":[930],"Chebyshev":[932],"10":[933],"Fermat,":[939],"Euler,":[940],"Gauss":[942,996],"10.1":[943],"Martin":[944],"Mersenne":[945],"Search":[948],"Perfect":[950,964],"Scientific":[952],"Societies":[953],"Marin":[954],"Mersenne's":[955],"Gathering":[957],"Numbers,":[958],"Pe":[959],"rfect":[960],"Not":[962],"So":[963],"10.2":[965],"From":[966],"Fermat":[967,977],"Euler":[969],"Fermat's":[970],"Famous":[973],"Last":[974,1173],"Eighteenth-Century":[979],"Enlightenment":[980],"Maclaurin's":[981],"Treatise":[982,1118],"Fluxions":[984],"Euler's":[985],"Contributions":[988],"10.3":[989],"Prince":[991],"Mathematicians:":[993],"Carl":[994],"Friedrich":[995],"Period":[998],"French":[1001],"Revolution:":[1002],"Lagrange,":[1003],"Monge,":[1004],"Carnot":[1006],"Gauss's":[1007,1055],"Disquisitiones":[1008],"Legacy":[1011],"Gauss:":[1013],"Congruence":[1014],"Dirichlet":[1016],"Jacobi":[1018],"11":[1019],"Nineteenth-Century":[1020],"Contributions:":[1021],"Lobachevsky":[1022,1070],"Hilbert":[1024,1108],"11.1":[1025],"Attempts":[1026],"Prove":[1028],"Parallel":[1030],"Postulate":[1031],"Efforts":[1033],"Proclus,":[1035],"Playfair,":[1036],"Wallis":[1038],"Saccheri":[1039],"Quadrilaterals":[1040],"Accomplishments":[1042],"Legendre":[1044],"Legendre's":[1045],"geometrie":[1048],"11.2":[1049],"Founders":[1051],"Non-Euclidean":[1053,1068],"Attempt":[1056],"at":[1057],"New":[1059,1074],"Struggle":[1062],"Bolyai":[1065],"Models":[1071],"Riemann,":[1076],"Beltrami,":[1077],"Klein":[1079],"Grace":[1080],"Chisholm":[1081],"11.3":[1083],"Rigor":[1087],"D'Alembert":[1088],"Cauchy":[1090],"Limits":[1092],"Fourier's":[1093],"Series":[1094],"Father":[1096],"Analysis,":[1099],"Weierstrass":[1100],"Sonya":[1101],"Kovalevsky":[1102],"Axiomatic":[1104],"Movement:":[1105],"Pasch":[1106],"11.4":[1109],"Generalized":[1111],"Babbage":[1112],"Analytical":[1115],"Engine":[1116],"Peacock's":[1117],"Representations":[1122],"Complex":[1124],"Hamilton's":[1126],"Discovery":[1127],"Quaternions":[1129],"Matrix":[1130],"Algebra:":[1131],"Cayley":[1132],"Sylvester":[1134],"Boole's":[1135],"Logic":[1138],"12":[1139],"Transition":[1140],"Twenthieth":[1143],"Century:":[1144],"Cantor":[1145],"Kronecker":[1147],"12.1":[1148],"Emergence":[1150],"American":[1152,1159],"Ascendency":[1154],"German":[1157],"Takes":[1161],"Root:":[1162],"1800-1900":[1163],"Twentieth":[1165],"Consolidation":[1167],"12.2":[1168],"Infinite":[1171,1179],"Universalist:":[1174],"Poincare":[1175],"Cantor's":[1176],"Sets":[1180,1189],"Kronecker's":[1181],"View":[1182],"Set":[1184,1199],"Countable":[1186],"Uncountable":[1188],"Transcendental":[1190],"Continuum":[1193],"Hypothesis":[1194],"12.3":[1195],"Paradoxes":[1197,1203],"Zermelo":[1204],"Axiom":[1207],"Choice":[1209],"Logistic":[1211],"Frege,":[1213],"Peano":[1214],"Russell":[1216],"Hilbert's":[1217],"Formalistic":[1218],"Approach":[1219],"Brouwer's":[1220],"Intuitionism":[1221],"13":[1222],"Extensions":[1223],"Generalizations:":[1225],"Hardy,":[1226],"Hausdorff,":[1227],"Noether":[1229],"13.1":[1230],"Hardy":[1231,1245],"Ramanujan":[1233,1250],"Tripos":[1235],"Examination":[1236],"Rejuvenation":[1238],"English":[1240],"Unique":[1243],"Collaboration:":[1244],"Littlewood":[1247],"India's":[1248],"Prodigy,":[1249],"13.2":[1251],"Point-Set":[1255],"Topology":[1256],"Frechet's":[1257],"Metric":[1258],"Spaces":[1259,1262,1269],"Neighborhood":[1261],"Hausdorff":[1264],"Banach":[1265],"Normed":[1267],"Linear":[1268],"13.3":[1270],"Twentieth-Century":[1272],"Developments":[1273],"Emmy":[1274],"Noether's":[1275],"Rings":[1278],"Von":[1279],"Neumann":[1280],"Computer":[1283],"Women":[1284],"Few":[1289],"Recent":[1290],"Advances":[1291],"General":[1292],"Bibliography":[1293],"Additional":[1294],"Reading":[1295],"Alphabet":[1298],"Selected":[1301],"Index":[1303]},"counts_by_year":[{"year":2024,"cited_by_count":22},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":12},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":32},{"year":2014,"cited_by_count":16},{"year":2013,"cited_by_count":11},{"year":2012,"cited_by_count":10}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}