EUGENE GARFIELD” lvSTITU TEFC)HSClk NTIF ICI NF(IUMATION 3501 MA HKETST PHILADELPHIA PA 19104
‘l%e Mmt-Chl Physkd+eiences Publications in the 1945-1954 Science Cifaiim Index. Part 2. Twenty Citation Ckssics in Matlmnatics
Number 42 October 15, 1990
When I fust reported to Current Gmterrts@ “impact.” That is, citations simply indicate readers that ISI@had compiled the Science that the cited work has been used in some Cifatkm hdexm (SCF’ ) cumulation for way by the author referring to it. It would 1945-1954, I indicated that it would serve be simplistic, if not absurd, to argue that the well the growing community of science importance of research can be measured historians. 1 Indeed, the cumulation has solely on the basis of citation frequencies enabled us for the first time to identi@ the and ranks thereof. most-cited publications in the postwar Brush attempts to answer this question by decade, a crucial time of rapid growth and comparing the lists of most-cited articles development in science and technology. with subjectivejudgments, such as the award Last year Bernard Dixon, contributing of prestigious prizes, or the opinions of editor to Biotechnology and former editor historians of science. As he noted in the first of New Scientist, discussed the 102 life- part of his essay, 48 percent of the most- sciences papers that were highly cited dur- cited physics publications included an author ing this petiod.2.3 More recently, the 52 who had won the Nobel Prize. For the high most-cited physical-sciences publications in impact chemistry publications, this figure the 1945-1954 SCI were examined by was 40 percent.’4However, he alsQobserves Stephen G. Brush, Department of History that these were not necessarily the works for and Institute for Physical Science and Tech- which the authors were honored by the nology, University of Maryland, College prize, a point I have stated previously.s Park.q Since virtually all of these Citation For the 20 most-cited mathematics articles Classicsm were in chemistry and physics, presented here, Brush uses the Fields Medal he requested additional lists of high impact as an independent measure of’ ‘influence. ” works in mathematics, astronomy, and the The Fields Medal is awarded qmdrermially earth sciences. In the essay that follows, by the International Congress of Mathemati- Brush continues his discussion by examining cians and is widely regarded as equivalent the 20 most-cited mathematics papas. Next in prestige to the Nobel Prizes. Brush found week, he will conclude with a look at 42 that no Fields Medal winners were among Cifation Cfassics in astronomy and the the authors of these 20 high impact mathe- earth sciences. matics articles. On this basis, he concludes Brush raises a question that often comes that “the most-cited publications in mathe- up whenever we publish undifferentiated matics do not contain the most important lists of papers ranked by citations: Are these research, ” and that “the most important most-cited articles the most “influential”? research in mathematics, as judged by We have consistently and repeatedly stated awards of the Fields Medal, is not highly that citations alone do not necessarily in- cited. ” dicate importance, quality, or influence. We This conclusion is perhaps premature instead prefer to use the more neutral term since it is based on a rather small sample
376 Tabk 1: Tbe top 100 mathematics mcm$cited la 1978 and 1979. Asterisks (*) indicae Fields Medsl winners. A=cifations from themab axe jcw-nsls in 1978 and 1979. B-fold cimtiom fmm SCF jcwds in 1978 and 1979.
AB AB AB I 64 202 Adams. John Frank 103 6.50 Coumnt, Rkbotd 284 461 Hardy, Godfrey Harold [ )njvers(fy o[ Manchester New York Umvcrsa!y IJnwersify of Cambridge Manchester. UK New York, NY Cambridge, UK 164 265 Agmon, Sbmucd 128 159 Curlfs, Cbmfes Wbltffesey Ihl 217 Hmfsh-CJmndm Hebrew L:n,verstty llmverstry of Oregon Jns:i!ute for Advanced Study Jerusalem, Israel Eugene, OR Princeton, NJ Ii” 1-1 . Abffc.rs. Lam Valerfcm 145 l~o “Delfgae. Pleme 138 235 Harfraam,PFOIF Harvard University lmfltut des Hautcs Eludes Johns Hopkins University C’ambndgc, MA Scmntifiques BaJllmorc, MD 108 127 Allsen, %& Mag.nu! B“res-wr-Yvette France 141 lt12 Huuhorne, Robsrt Cope [Intverwly of 0s10 148 263 Dfeudomne. lean Akxandre [Iniversify of CafiicmnM Oslo, Norwa} Umvermy of N,cc Berkeley, CA 140 157 Anfn, Mkhae! Nice, France Hasse, Helmut Masw.chuscus Insu!ute of 346 435 Dkmkr. Jacques tlmvcrswy of Hamburg Technology (ln,vcrs,ly of PBrls VI Hamburg, FRG Cambridge, MA Pans, France He fgason. Sfgurdur IMI !Ml Aschbeder, Michael Ill 1.3- Dougfns. Ronald Georqe Mr.ssacbuselis Insmute of Califomla lnsmute 0! Stale llm,. mslw of Technology Technology New York Cambridge, MA Pasadena, CA Smny Brook NY Hemtefu, ftmef N. 252 444 “ Affyah, Mkbsel Fmncfa -Q4 5,4 Dunford, Nefsoa L!”,ver,,ty 01 Chicago Oxford Unwerslty Yale (In,. crslty Cbtcago, [L Oxford UK New Haven. CT Hewitt. Edwfn 12h 136 Am fander, hfmwfce 101 824 Erdelyf, Arthur [Imvcrwty of Wmhmgton Brande)s University [Inwerstty of Edmhurgh %altfe. WA Wrdthmm. MA Edinburgh, L;K Hffle, Efnar 222 2s5 Bass, J-Lyman 295 485 Erdo$. Pauf [ Ini.erslly of Calif orma Columbia Um, erstty Hunganan Academy of La Jolla, CA New York NY Sciences Hfkon. Pefer John 110 “In JJellmsn, Rkbrd EmesI Budapes[ Hungary Case Western Reserve [:nwcrwy of Scwtbern 119 125 Fek, Waker tlmverwy Califom,a Yak Umvcrst[) Cleveland, OH Los Angeles, CA New Ha\en CT Jifrzeb?uch. Frkdrfcb 1.31 333 Berg,, Claude Jacques [61 3Ml Frkdman. Avaer 1lntverwy of Bon” CNRS Norihwes(mn [:n,, ers,ty Bonn, FRG Pans, France E.ansto” IL 334 4’4I r,..“Ormlumer..——-,– L.”.—. 129 338 Bkkholf, Gwrett l“- 22(I Fuchs. Lnszlo Vofter Harvard Unrwrsily Tufanc [Jntversn[v [rnwersify of Lund Cambridge. MA New Orleans LA Lund, Sweden 29” 38” Borel. Armmd 20- “4H Geff.nd, fzraff l-n lfw Hupperf, Be?mam Jnsl]lule for Advanced Mofseevkb IImverswy of Mainz Study Mathe”a!tcs fnmtute Mamz, FRG llf SR Academy of Sc,mces Pn”cemn, NJ Ill 123 JWMW1,Kemkfcbf 51” ’23 Bourbaki, Nkofm Moscow, USSR Princeton (Ire>, France 109 112 Gfauherman. George faanc Pri”cc ton, NJ 13- lh” Brmwr, Rkfmrd Dagoberf ~lnwers,ty of Chjcago 26 I 343 Jacobso=, Natbae Harvard llmversity Chicago, [L Yale University Cambndgc. MA 103 2W Go~h6erg. fsrael New Haven, CT 115 120 Bredon, Gf.m E. TSudfkovkb 225 285 KsPkmky, Irvfmg Rutgers University Tel A,i. Umvcrmty University of Chicago New Bmmwick, NJ Tel Avi,. Israel Chicago, IL 1“3 .342 Brezfs, HaJm 293 321 Gormutefn, Dankl 131 638 Karffn, %nue~ [Inwerslfy of Pans VI Rutgers [ Iniverslty Stanford University Paris, France New Bmmswick, NJ Stanford, CA 190 250 Browder, Feffx s8rf 126 lJI Gmuerf, ffrnm .343 646 Kate. Toste [Jnwerwty of Chicago onwerslty of Gomngen LJniversify of California Cbtcago, JL Gottingen, FRG Berkeley, CA 101 140 Calderon, Afbwto Pedro 4W WI ‘Grothendkck, Akxandre 144 201 KobayashL S&m.&Ld [ I“)versify of Chicago Universmy of Mompcffier 11 Unwersity of California Chmago, IL Mcmtpellier, France Berkeley, CA l-w 20- CmflIz, Leonard I06 W J4afe, Jack KenneIh 131 2f13 Kraanosdsfiff,Mark Duke LJniverstcy Brown University Afeksamdrovfcb Durham, NC Prowcfencc, RI Moscow Control Problems 167 236 Catfr.n, Hemf Paul 147 199 Haff, Mmsfufl Institute Univm-sify of Parts x] California Ins fitute of Moscow, USSR Paris, France Techdogy 136 212 Karstawnkf, Kazfmlem 131 1“8 Cfffford. Al[red Pasadcoa, CA Warcaw University Hoblftzeffe 20’ 492 Hafraos, Patd kiCfUd Warsaw,Poland Tukne University Jndiana LJniversily )24 285 Ladyzbenskak, Ofgs New Orleans, LA Blmmingmn, IN Afekssmtrovm 112 14” Cohn,Paul Morkl 101 48.3 H.wmy. Frunk Leningrad Umversity University of Lcmdo” [Inaversity of Michigan Leningrad, USSR London, LJK Ann Arbor, Ml
377 Spanler, Edwla Hemry [!m~crs, ty of Cal!fomm Berkck) CA 108 4(!4 La,, Peter Dsvfd 13- I +1 . QufJleLI, Dankl G 2<3 394 Stefn, Elks M. ?+CWYork \jm\m,l) Massachusetts Inw,tuw of ?nnccton tlnwersny YW York. NY Technology Prmce!on, NJ I $() Ih- Llmdens[r.ms, lomm Cambridge MA I(M 112 Swan, Rkhard Gordoz Hebrew [’n, \ers,ty 1(N 1“0 Rockakkfar. Ralmb,. Tvrreff [>”i.ers, fy of Chtcago Jerusakm. Israel I ntvcrsth of W’ashmgton Chtcago IL 2 ! () 5$? LIOIU, Jacques. Louh Seattle WA I 1“ 339 Titchmarsb, Edward Charles College de France 224 .349 RIMJJII,Walter Oxford L!nlbers)tv Pans. France ,l”,,=M,,Y *, W,,c<,n,tn Oxford [’K I 12 IW LoreII[z. George G. %dmon W] [(14 IW Tutae, WUJJXUIThomas l’”,, em, t> of Te, a, !10 I.M %kal. ShokbJro Cnt+erstty of Waterloo Aus!m T-x N:hon [Intbcrmy WawrIoo [?nada 13“ 249 M,ckcy. George Tokyo Japan 145 IN w ●fJ. ChmLes TererIc* Wbltefaw 111 li.1 S810, MLk10 CkB Har, ard (ln,~crs!ty Kyoto (In]\ crstitv Uni. crwt) of Lt, erpool Cambridge MA K,,)!,,. JaPa” LI\crp
Table 2: Tbe nexJ 103 mathematician mosJ cited in 1978 and 1979. Asterisks (*) indicafe Fields MedsJ win- ners. A= citations from the msfb core iowmds in 1978 snd 1979. B =totzd cifations from SCP journals in 1978 and 1979 &B AE AB . . -() 9(1 AmI.rm. Herbert 91 Bousfkld. AldIJt@ Kafght ‘4 lh2 CmmLeU. Mkbael G. [:nmcrslq ~f Zurich l’nlberstty of Ilh.oM L’nl\emt~ of WIsconstn Zurich, Sw!tzcrla”d Chicago IL SJadlson, Wf M -h Amksur, SMmsho. A. Bowen. Rohzrf E n- 9 I Day, MdJJo. M, Hebrew ( Im.ersny L!ll,, er,>tyof Cal, frmlla (~”,. ers,ty of Ilfi”m Jerusalem. lsracl Berkeley, CA ll,ba”a. fL “1 no Anckeold, Aldo Browder. W Ufkm M F# Demnzwe. MkLwe! [“n, vcrsi~ of Strashour~ Pnnccton llniverslly Ecok Polylcchmquc $trasbourg. France Pnncemn. NJ PIafiscau France ~1 XC Amokd, Vktor Igore.lch Cndeson, Lennan Ad 91 I(M Dkksom Lecmrmd E. Ln!+crsq of MOWWA Edvsrd [’n,, ers, h of C’h,cz.g,, !.%OSCO.J, (1SSR M,{\ag-Leflkt lnm,, utc Ch,caRo, ”fL “ w 123 Ardn. EmJJ D]ursholm S*cdcn -() W Dfewel. Joseph [)nt+crstfy of Hamburg I(K1 I II Cmsefa. John WLUkm SCC.11 Kc”! Smw llnt, eml) Hamburg, FRG [Jn,wrs,ry of [-am b“dgc Kent, OH ‘4 98 Aweson. Wffffam fkrnes Cambridge (>K t19 w Dok4. Albmchl l)n,, ms,ty Of Callf orma n“ I 4? Chem, [email protected]= [In,vers,fy of He,dc)b,rg Berkeley, CA ( ln,.cm,~ of Cal, fom,a He,dclbcrg, FRG 83 90 Ausfaad=r, Lou& Berkeley. CA 1(!0 l-l E!fed)erg, SS!RU,I Cny (Inwersdy of Ncw k ork 93 I33 Cbevafky, Cfmde Ccdumb,a [’m,ers, t> New York, NY Cnlvers, ty of Pans VfJJ New York, NY 99 !54 Be=, L@nm Pans, France 81 93 Everkt. Wkffkm Norrk Columbia (:ntverwty “b 194 Coddf@on, Emf A. [rnt\CrSI@ of Dundm New York. NY Un,ven,ly of Cailfom,a Dunder, U K 93 I04 Sfng, sJ.H. Los Angeles. CA “4 F’tderer, Her+Je” unwermfy of Texas “8 8“ Comm. Pkrre EucUde Brow” Un,ws,[y Aumn, TX LOulslana State [I”werwty Providence. Rf -2 I05 Boas, Ralph P. Baton Rouge, LA I(Kl 121 “FdfemIaB, Cfumfes Lcaub Norlhwestem {Inwemty n3 113 COIIQ2G AhfR Pnncelcm [lmvmsn> Evanston, fL fmmut des Htmtts Eludes Pmcetcm NJ 93 fco Bonzdf, Frmik Feathem. #one Sc,emifiques 91 885 Fcfb, Wfffhm UntversiIy of Edinburgh Bures-sur-Yvetfc, France Prmcetcm O“i.ers)ly Edinburgh. UK 78 119 Coxeter, Harold SCou Princeton, NJ 79 118 Boff. Ramd MacDodd ‘0 % Fox, Ralph H. Harvard Onivers#ty Unrvermfy of Toronto Princeton L1.!+ersnty Cambridge. MA Toronto, Canada Princeton, NJ
378 AB AB AB 86 9“ Frobfkb. Albrecht 93 118 Kothe, Gottfrfed 97 271 Seaal. Irvfnn Ezra ( lmversity of London (University of Frankfurt Mlsachmeyls Imtitute of London, UK Frankfmt, FRG Technology -3 91 Gabrfel, Pferre 92 !M Kretn, Mark G. Cambndgc. MA ( Inwer$ity of Zurich Institute of PhysicaJ 81 98 Skrpfmkl, Wscfaw F. Zurich, Switzerland Chemistry Warsaw Univemity .$ w GamefJn, Theodore W. Odessa LJSSR Warsaw, PoJand (Iniversiry of California 82 88 Lamhek, Joachkm Los Angeles. CA McGill U“iversiiy W 287 Stmon, Barry Martfa 80 I(J3 Gfffmam, Leonard Montreal, Ca”.ad.a California Institute of (Iniversily of Texas W 98 Luxemburg, Wffbefmua Tecfmology Austin, TX Anthonfus ]cWph”s Pasadem, CA “K ‘9 Goldachmkk, Davfd M. California Immule of 98 225 .Somfe. Stenhen [Illiversity of California TecbmJc)gy University if California Berkeley CA Pasadena, CA BerkeJey, CA 68 9- Gmtzer, George w 259 Magnns, WfJbelm Sfdf&s, John Robert University of Manitoba Polytcch”ic Immutc of 72 “~ University of California Winnipeg, Canada New York BerkeJey, CA 94 109 G rfffftbs, Pfdtf[p A. New York, NY Har\ard (University 92 13s Mkbael, Ernest Arthur 82 146 Steenrod, Norman E. C’ambndge, MA Uni. crsmy of Washington Princeton [J”ivernty 9’7 115 Gunnkng, JfoberI Cfffford %alde, WA Princeton, NJ Pnncetcm Univermty 85 lfJ2 Moor@, CslvhI C. ‘m 70 StefnherR, Robert Pnncekm, NJ University of Califomm University of CaJiiomia 94 11- ffau, Pbulp BerkeJey, CA Los Angeles, CA [ In,vers,ty “1 Cambridge 78 w Money, Charles Bmdfleld 87 loh Suffkvan. Demnk? Cambridge, UK University of Csdifomm lnstitut des Ha”tes Erodes h9 -3 HmymaII, Walter Kurt BerkcJey CA Scientitiq”es ( Iniversjty of Lo”dcm 89 294 NeMmamm, Jc.kn Von B.res-s”r-Yvette, France London, UK Institute for Advanced Study 73 13 Suzuki, Mkhko 82 88 Hfgman. Groham Prince! on, NJ University 01 IJlimms Oxford (University “2 113 NfkofsMf. Sergef Mffhffovkb (Irbana, IL Oxford, (IK StekJov Imtit”le of 94 112 “Hfronak., Hetsuke Mathematics 72 232 Szego, Gabor Harvard Unwerslly Moscow, (ISSR Stanford Il”tversity Cambridge, MA Smnford, CA M 85 Nussbnum,Roger David “tl 143 Hirsch, Motrk Wttffsm Rutgers (lntverwty 92 172 Szokefalvl.Nagy. Befa ( lnivermty of California New Bnmswwk, NJ University of Szeged BerkeJey, CA Szeged, Hungary 74 124 Pafafs. Rkfurd Sheldon 8“ 119 Hocbschffd, Gerhard P. 88 127 T.kesakl, Mammkbt ( Imvermty of California Brandeis Umverwty WaJ!ham, MA [University of CaJifomm Berkeley, CA Los AngeJes, CA 81 90 Hochster, Melvfn ‘4 82 Pedemom Gcrt Kjaergard [Imversi!y of Michigan University of Copenhagen 95 101 Trite, John T. Ann Arbor. Ml Copenhagen, Demtmrk Harvard l]”,”~~,ty RI 118 Hoffman, Kenneth 82 113 Peetre, Jaak Cambridge, MA Hampshire CoUege University of Lund 80 115“Tbompmt, lobs G, Amherst. MA Lund, Sweden University of Cambridge m 1[)() Humphreys, lames E. Cambridge, -6 79 Pelczynskl, Alekmuder UK [I”ivemity of Massach”se[[s Polish Academy of 74 74 TknmesfeJd, Fmntz G. Amherst, MA Smencm L)mversily of COJOflne ~h w K.dbon, Richard WaE.av/ PoJand CoJognc, FRG Vfncen: TIu, Jacques 11“,, em,y of Pe”nsylva”la 7J 96 P[elscb, Albrecbt 88 102 ColJege de Framce Phdadelphia, PA [inivermy of Jena Paris, France % 124 KeUey, John k Roy fens, GDR 1Jmversny of CaJdornm ~i 2?5 Reed, Mkbnel Cbarfes 83 124 Treves, Francoks Berkeley, CA Duke Umversity Rutgers University t)n 74 Kervdre, Mlchel A. Durham, NC New Brwmwick. NJ Umvcrmry of Geneva 74 1s! Rlesz. Frkdrfch 7) 83 Trtehcl, Ham Geneva, Switzerland (I”rv.msity of B“dapesf University of Jena ‘XI 94 Knebwcb, Manfred Budapest, Hungary Jena, G DR ( lmversty of Regemburg 95 11! Ronentbnf,fJaskeU P. 80 82 W &fbauseII, Frfedhefm Rcgensb.rg, FRG University of Texas Unwersi~ of BieJefeJd 82 121 . Kodafm, Kmdbfko Austin, TX Bielefeld, FRG [Imvers]ty of Tokyo 80 loft Warner, Garth W. Tokyo, Japan 70 109 Schechter, Murray Lehigh University University of Washingmn 69 525 KoJmogorov, Audrey Bethlehem, PA .%attk WA PUkofnevkb 1:SSR Academy of Sc!ences 83 182 Schoenberg, f,aac J. 7.5 Jv Wolf. Joseph Albert Moscow. USSR lJniversity of Wiscomm LJniverslty of CaJifomia % 169 Kowsmt,Bertmm Madison, WI BcrkeJey, CA Massachusetts lnstituie cd 72 86 Segal, Gmeme Bryce I(I3 189 Yosldn, Kosak~ TecbnoJogy Oxford lJnwerstlv Gakushwn Umversty Cambridge. MA Oxford, OK Tokyo, Japan
379 ogy.st 20 most-citedjournal articles. A more to the Nobel Prizes, for which researchers adequate- sample would be on the order of are eligible throu@out their lifetimes. 1,00@1,500 articles. But even this might not Also, the Fields Medal judges might be sufficientunless books were also included. sometimes seem to make arbitrary decisions During the period examind here, 1945-1954, on who is a “mathematician.” This was books may have km equally or more im- most recently illustrated in the 1990 awards. portant than journals as a means of com- Shigefumi Mori, Research Institute of Math- municating mathematical research. ematical Sciences, Kyoto University, Japan, An alternative approach would be to ex- was honored for developing the classifica- amine a list of most-cited authors rather than tion of complex algebraic varieties-pre- highest impact publications to see whether sumably, a contribution to “pure” mathe- Fields Me&1 winners are highly cited. In matics. 7 But the other winners could lx. 1982 we identified the 200 “pure” mathe- considered mathematicians or theoretical maticians who were most cited in 1978 and physicists. 1979.6 Through 1978, 24 individurds had Vladimir G. Drinfeld, Institute for Low received the Fields Medal. Fifteen of them Temperature Physics and Engineering, (63 percent) appeared on the list of 200 Khrtrkov, USSR, was recognized for his most-cited mathematicians. They are iden- research in algebraic geometry, number tified by asterisks in Tables 1 and 2, which theory, quantum groups, and other mathe- are reprint+ from that study. matical specialties that are related to Another author on *e list, Alain Cormes, theoretical physics. Vaughan F.R. Jones, Institut des Hautes Etudes ScientMques, University of California, Berkeley, worked Bures-sur-Yvette, France, won the Fields on knot theory, a branch of topology that Medal in 1982. Including Connes, the 16 has applications both to elementary particles Fields Medal winners were cited 3,137 times and DNA. Edward Witten, Institute for in a set of 64 “core” mathematics journals Advanced Study, Princeton, New Jersey, and 4,335 times in all SCljournrtls in 1978 was honored for his fundamental contribu- and 1979. Thus, the average rtunhr of tions to the development of string theory, citations per author was 1% and 271, re- which might shed light on the relationship spectively. In comparison, the 187 non- between gravity and other natural forces.T Fields winners received 22,578 core mathe- Witten has consistently appeared in our matics citations and 38,281 all SC1citations, recent studies of the most-cited physical- yielding per author averages of 121 and 205, sciences papers. g$’He also appeared on a respectively. These data indicate that Fields ‘‘shortlist” of 12 researchers forecasted to Me&1 wimers are indeed highly cited and win the Nobel Prize in physics that appeared have higher average impacts than the non- in 7he Scientist”. 10Similar lists of” nomi- winners. nees” for the Nobel Prizes in chemistry as It is worthwhile to note a few limitations well as medicine or physiology are being of the Fields Medal. The judges tend to limit prepared as we go to press. Last year 7he awards to mathematicians who are no more Scientist identified 20 likely candidates for than 40 years old. Theoretically, those who the 1989 Nobel Prize in medicine or make major contributions to mathematics in physiology, two of whom did go on to win later life would not necessarily be recog- it—J. Michael Bishop and Harold E. nized by a Fields Medal. This is in contrast Varmus.11
REFERENCES
1. Garfkfd E. Tbe new 1945-1954 SCf cumulation providea nnique access to the crucial postwar decade of acientitk and technologic+d achievement. Currenr Contents (27):3-10, 4 JuJy 1988, 2. Dixon B. Tbe 102 moat-citexf Iife-aciencea pubkmions in the new 1945-1954 science Cirarion Index. Part 1. Titiea, journals, and research fronta. Current Coruents (15):4-10, 10 April 1989, 3. —------Wonder drugs, cdl biochemistry, separation techniques bigldigbt major trends of pnat-World War JJ decade. Current Contents (16):3-10, 17 ApriJ 1989.
380 4. Brush S G. The most-cited physicat-scierrces publications in the 1945-1954 Science Cikaion Jr&x. Part 1, Current COnterrfs(20):7-17, 14 May 1990. 5. (krffeld E. Do Nobel prize winners write Ckation Classics? Essays of on in@motion sciem”w: towards scientogrqohy. Pbitadelphia: ISI Press, 1988. Vol. 9. p, 182-7. 6. —. The 200 “pure” mathematicians most cited in 1978 and 1979, including a list of moat-cited publications for the top 100. Current Contenrs (36):5-14, 6 September 1982. (Reprinted in: Ibid., 1983. Vol. 5. p. 66&75.) 7. Browne M W. 4 Imnorcd with Fields Medal in mathernntics. New York 7imes 22 August 1990, p, A17. 8. Grrrffeld E. ‘fIre mow-cited 1987 physical-sciences articles: supsrconductiviry superwxfes sutnmstrings. CurrerrfContents (18):3-14, 30 April 1990. 9. —. Tire most-cited 1986 physical-sciences articles: ozorw, comet Haney, and continued interest in superatrirrgs and superconductivity. current C2m!erm (6):3-14, 6 February 19g9. 10. MarteUo A. Twelve protitlc physicists: likely 1990 Nobel contenders. 77re .$cierrtim4(17): 16; 25-6, 3 September 1990. 11, Pemttebury D. Tire 1989Nobel Prize in medicine: 20 who deserve it. 17te Scientist 3(19):14; 16; 19, 2 October 1989.
The Most-Cited Physkal-Scietms Publications in the 1945-1954 Science CifdiOn Zndex. Part 2. Mathematics Stephen G. Brush Department of History and Institute for Physical Science and Technology University of Maryland College Park, MD 20742
This essay exeminw 20 highly cited papers in mathematics, based on the .SciertceCitorionIndex” cumulation for 1945-1954. Next week 42 most-cited papers in astronomy and tbe earth sciences wi13 be examined. These papers are compared with other publications (including some Itigblycited books) considered important by scientists and historians of science. The essay discusses some of the major trends, achievements, and researchers in mathematics in the period including World War II. .- Introduction Finding Highly Cited Do Citations Measure Importance? The Publicationsin Small Fields Case of Mathenmtka In Part 1 of this essay, I discussed 52 As noted in Part 1 of this essay, one highly cited publications in the physical should not simply rely on citation counts as sciences, based on the Science Citation a measure of the impmlance or quality of Znukx” (SCF’ ) cumulation for 1945-1954.1 a publication. Rather, it is desirable also to That list was composed rdmost entirely of obtain the independent judgments of the sci- publications in chemistry (25) and physics entific wrmmmity-for example, as irt- (25); there were only two in mathematics, dicated by Nobel Prizes-or of historians of and none in astronomy or the earth sciences. science. Thus, 48 percent of the most-cited Just as one cannot ignore the physical sci- physics publications and 40 percent of the ences merely because they generate fewer most-cited chemistry publications were citations than the iioiogical sciences,2 one authored or coauthored by a Nobel laureate, cannot simply ignore a8tmnomy, the earth although those publications were not neces- sciences, and mathematics merely because sarily the work for which they received the they generate fewer citations than physics Nobel Prize. 1 and chemistry. ISI@has therefore generated For mathematics, the closest equivalent additional lists of relatively highly cited to the Nobel Prize is the Fields Medal, papers in these smaller, less-cited fields. In awarded at the quadrennial International addition, I present lists of publications con- Congress of Mathematicians, beginning in sidered important by scientists or historians 1936. No medals were given between 1936 of science. and 1950; the medals awarded in 1936,
381 Table 1: Wlrmers of the Nelda Medat fn mathematics, awarded at tbe hrternatiooaf Congress of Mathematicians in 1936, 1950, and 1954, and their areas of research. Medalists are fisted in alphabetic order. Dates in paren- theses in the “Research Area” column give the time perind when the medal-winning work was done,
Year MeetaMat Awarded Research Ares
Ablfors L 1936 Complex-variable theory, quasiconfomnal mappings, Rienuum surfaces, meromorpbic Iimctions (1920s, 1930s). Onuglas J 1936 Solved Plateau problem (mininud surface) (J93 1), Kndaira K 1954 Harmutic integrals and harmonic forma with application to KaMerirmand algebraic varieties (1944- 1953). Schwartz L 1950 Tbcory of distributions (1945-1951). Selberg A 1950 Prime number themrem (1948-1949), Riemann zeea function (1940s). Serre J-P 1954 Complex variabIes, cohomology in a complex-anafytic sheaf ( 1950- 1951).
1950, and 1954 were for research by six The Moat-Cited Mathematics WIcka mathematicians published in the pericd from about 1930 to about 1952. These are listed The research areas of the Fields Medal in Table 1. winners and the most-cited papers published Table 2 presents 20 mathematics journal in mathematics journals indicate trends in articles that were most cited in the 1945-1954 pure mathematics during the 1930s and SCI. Comparing both tables, one w see that 1940s.Abstmet algebra and topol~ WE the none of the Fields Medal winners appear as most popular subjects. As Jean Dieudonn6, authors of the 20 most-cited mathematics University of Nice, France, expressed it in articles during this period. The most-cited his survey of modem mathematics, the journal article by a Fields winner is by Jean- emphasis was on studying the structure Pierre Serre, College of France, Paris.3 Its rather than the content of mathematical 27 citations from 1945 to 1954, however, objects. 5 Most of the highly cited mathe- are too few to put it on the Iist of 20 most- maticians are listed as “originators” of one cited mathematics papers, which were cited or more of the research specialties deseribed at least 30 times. Citations for the 1958 by Dieudorm&6 Fields Medal winners (Klaus F. Roth, Uni- The most-cited mathematics article is on versity of !mndon, UK, and Rem? Thorn, statistics and was authored by Henry B. University of Strasbourg, Frame) were even Mann and D.R. Whitney, Ohio State Uni- fewer, so including them would not make versity, Columbus. Most of its 109 citations any difference to our conclusion: the most from 1945 to 1954 are from biological and important research in mathematics, as judged medical joumrds, so one may question by awards of the Fields Medal, is not highly whether it should be included in a list of cited, and the most-cited publications in highly cited physical-sciences publications. mathematics do not contain the most import- Mann has described its origin in the problem ant research. of testing a dmg that was supposed tn protect Some mathematician wotdd undoubtedly against the common cold. T argue that Stefan Banach’s (University of One of the most-cited papers in math- Lvov, USSR) i?ekorie des operations [ink- ematics journals was by Milton Friedman sires is a emmterexrunple to this generaliza- (b. 1912), then with the National Resources tion, since it showed up on the list of 52 Committee, Washington, DC, who won the most-cited physical-sciences papers and is 1976 Nobel Prize for economics. Presum- generally regarded as a report of important ribly,his 1937paper on the use of rank order- original research. 1,4 Nevertheless, it did ing in statistical analysis was ordy a small not win the 1936 Fields Medal for which it part of the body of work for which he was was presumably eligible. honored, and the award of the Nobel Prize
382 Table 2: The 20 most-cfted papers from mmfmrnatics jorrraats covered fn tfse 1945-1954 SCf@ cmrmfation. Papsrs are listed in alphabetic order by fwst author. A =tatal number of 1945-1954 citations.
A Bibtbgrapldc Data
30 Bnrtl&t M S. On the thcmeticsl specification snd samplig properties of autucorrelatd time-series. J. Roy. Sm”st. Sot. Ser. B Metho. 8:2741, 1946. 31 E-whoa J. Applicationof tbe logistic tiurction to bio-assay. J. Amer. .$ratiw Assn. 39:357-65, 1944. 33 FrIedmsar M. The use of ranks tn avoid b assumption of normslity implicit in the analysis of verisnce. J. Amer. Statist. Amt. 32:675-701, 1937. 32 Iwasowa K. On some types of mpological groups. Ann. Math. 5&507-58, 1949. 61 Jacobson N. llre radical snd semi-simplicity for mWrrny rings. Amer. .), Math. 67:300-20, 1945. 38 JacobsonN Structuretheoryof simple rings without ftiteness assumptions. Tram. Amer. Math. WC. 57:228-45, 1945. 30 Ebfmtmrf S. Cnncreterepresentation of abstrsct (M)-spsces (A characterization of the space of continuous tiurcdons). Am. kfarh. 42:994-1024, 1941. 31 King R & Middletan D. The cylindrical snterrns; current snd impdrurce. Quarr. AppL Math. 3:302-35, 1946. 35 Lin C C. On the stability of two-dimensional parsffel flows. Psrt L-GenersJ theory. Quart. Appl. Math. 3:117-42, 1945. 109 Mann H B & WldtsMy D R. On a test of whether one of two random variables is stuchsstiwdly lsrgcr tbsrr the other. Arm Math. Wrtisr. 18:50-60, 1947. 30 Mfddtetoer D. Some gewcral results in the theory of noise through non-linear devices. Qaart. APpf. Math. 5:445-98, 1947. 32 Morm@an F D. Finite deformations of m efestic salid. Amer. 1 Math. 59:235-60, 1937. 41 Murray F J & won Neommm J. On rings of ~rators. Arm. Math. 37:116-229, 1936. 33 Neyman J. On a CISSSof ‘+conrsgious” distributions, applicable in entomology snd bacteriology. Ann. M@h. .$tatk 1035-57, 1939. 32 Wcnrad N E. Products of cocycles and extensions of nrsppirrgs. Ann. Marh. 48:290-320, 1947. ‘- 54 Stone M H. Applications of the theory of J3dean rings to general tqwlogy. Thans. AW. Math. sac. 41:375-4s1, 1937. 37 Stone M H. The theory of representations for Soalmrr algebrss. Tram. Amer. Math. SW. 40:37-111, 1936. 32 Wafd A. sequential tests of statistical hypotheses. Ann. Math. Sfatisl. 16:117-86, 1945. 61 Wiener N. Generalized hsrnmnic anafysis. Acts Math. 55:117-258, 1930. 38 Yates F. TIE snafysis of muftiple classifications with uneqmd numbers in the different classea J. Amer. Statist. “Arm 29:51-%6, 1934.
to hm cannot be viewed as a judgment that to significant publications that might ottter- he made a significant contribution to mathe- wise be overlooked. matics. Jacobsen’s two papers in 1945 presented TWOAmerican mathematicians published major advances in abstract algebra, espial- highly cited papers in pure mathematics: Iy the theory of associative rings.g He in- Nathan Jacobson (b. 1910), Yale University, troduced what is now tailed the “Jacobson New Haven, Comecticut, and Norbert radical” of a ring, defined ss “the ideal J(A) Wiener (b. 1894-d. 1964), Massachusetts of an awociative ring A which satisfies the Institute of Technology, Cambridge. Wiener following two requirements: 1) J(A) is the later became well known to the scientific Iargegt quasi-regular ideal in A; 2) the public for his work in communication quotient ring ~ =A/J(A) contains no non- theory. Jacobson’s work is hdliar only to zero quasi-regular iderds. ”9 Based on this mathematical experra. Curiously, neither is concept, the ‘‘Jacobgon ring” is defined as given much attention in works on the history “a commutative ring with unit element in of mcdem mathematics-perhaps Jacobson’s which any prime ideal is the intersection of contribution is considered too sprzialized, the maximrd ideals containing it, i.e., a ring Wiener’s too “applied.” Jn these cases, the any integral quotient ring of which has a SCZhelps the historian by calling attention zero Jacobson radical. ”10These ideas were
383 —
Tabfe 3: Chrormf@c dMr5n@mof@rMatioltda tes The leading Citation Classic@ located with for the 20 rnarbernatics papers most cited irr the the help of the Halmos list is A Course c-$ 1945-1954 scI@ cumulation. h-h%m Analysis by the Britishmathematician PubJJcatiOrr Number of Edmund ‘fhylorWhittaker (b. MB-d. 1956). Year’ Papers Whittaker was a specialist in differential 1930-1934 2 1935-1939 6 equations and was known for his discovery 1940-1944 2 of integral representations of solutions of 1945-1949 10 Laplace’s equation, including the Legendre and Bessel functions. He later wrote a major further developed in books by Jacobson and treatise on the history of optics and electro- others.ll-lq magnetism. 18 When Whittaker first pub- Wiener has described the circumstances lished A Cburse of Modern Analysis in 1902, of his work on generalizedharmonic analysis, it was, according to biographer Daniel leading to his 1930 paper on that topic, in Martin, University of Glasgow, UK, “the his autobiography. 1AHarmonic analysis is first book in English to present the theory the decomposition of time-dependent physi- of functions of a complex variable at a level cal processes or mathematical functions into suitable for undergraduate and beginning components with different frequencies, graduate students. ” 1$’ pioneered by the French mathematician George Neville Watson (b. 18864 1965), Joseph Fourier at the beginning of the nirte- a British mathematician who was art expert teenth century. The original stimulus for on complex variable theory, collaborated on Wiener’s work came from problems in elec- the preparation of the expanded second C& trical engineering, He was able to develop tion that appeared in 1915.zo,zl The book a rigorous theory based on modem math- became a standard reference work for the ematical techniques. His interest in practical properties of special functions and tech- applicationsled him to promote the harmonic niques used in mathematical physics. The analysis of time series as a key to many various editions were cited 420 times in the problems in science and engineering. Is.lb period 1945-1954, more than the beds by Seventeen of the 20 papers in Table 2 Banach and Harald Cram&, University of listed one author, and the remaining three Stockholm, Sweden, the only mathematics have two authom each. Sixteen authors were publications on the first list of 52 most-cited based at institutions located in the US, and publications for that period, 1 But it ap- two each were based in the UK and Japan. Table 3 shows the chronologic distribution TaMe4’flwjourmalsf .hatpuMfrkJthe20rwt-rfted of publication dates, and Table 4 lists the ~mp.mnbntipbm journals that published the 20 most-cited the 1989 irnpsct factors for tbe jrxu-rmls. Data were taken from the 1969 JC@. The figures at tbe right mathematics articles in the 1945-1954 SC[. indirate how rrrsnypapers from each journal appear in Table 2. The Most IrBfluentld MathLmrJ$Mcs Number of Pubkatioos Journal Papws Arm Math. (2.01) Table 5 lists 25 books considered “infhn- 4 ‘Arm. Math. Ststist. (N/A) 3 tial” by the mathematician PauJ Richard J. Amer. Statist. Assn. (1.17) 3 Halmos, University of Santa Clara, Califor- Qusre, AwL Maeb. (0.48) 3 nia. 17 ~~ shown is the num~r of ci~- Trsrrs. Amer. Maeb, Sm. (0.54) 3 Arrrer.J. Math. (0,55) 2 tions they received in the 1945-1954 SC1. Acts Matft. (O,%) 1 There is no algorithm for selecting math- J. Roy. Statist. Sot. ser. B Merbo. 1 ematics bcoks from the 1S1database, so it (1.15) is possible that there are other mathematics ‘Divided in 1973 into Arm, Probsb. (0.69) end Ann, books even more highly cited than these. statist. (0,97)
384 Table 5: Mathewrrdtm books published before 1955, from a tist of honks that P.R. Halrnos considered irrtluential (see reference 17). Citation totals inehrde 1945-1954 references to all editionz and trsnstetions. Publication years shown are those given by Hntmos; other bibliographic data sre taken from the Na”orroi Union C#alag. Brinks sre Iisted in slpbsbetic order by first author. A = 1945-1954 citations,
A Imbgraphic Data
167 Banach S. 71tff0rie&s opdrm”om lirkfaires (Theory of linear operations), Warsaw, Polsrrd: Z subwerrcji Funduszu kukury namdowej, 1932.254 p. 46 Birkiroff G. Lrrrice rheory. New York American Mathemsticsl Soeiely, 1940.155 p. 37 B6eher M & Dovef E P R. Irrrroriudorr to higher afgebra. New York: MacrniUsn, 1907.321 p. 0 Bofmenbtust H F. LecRues by H. F. Bohnentrlrr@ on tlrsory of Jimcrions of real variables, 1936-1937. Ann Arbor, Ml Edwsrds, 1937. 132 p. 1 Bwr%gton R S & Torrance C C. Higher rruuhm”cs with applicotkms to science ad engineering. New York McGrsw-HiU, 1939. S44 p. 21 Carathdodory C. Vorlesungen tier reelle Funktiorrerr (Treatise on real lirrctions). bipzig, Germany: Teubner, 1918, 718 p. 24 Cuurent R & MeShane E J. Vorlesungen Uber alfferential und hrtegralrechnrmg (Dtierential sud integral calculus). (McShane E J, trmrs.) New York: Nordemsror, 1938. 2 VOIS, 1 Diekeon L E. Modern algebraic theories. New York Senbnm, 1926.276 p. 8 Granvflle W A & Sndtb P F. Elements of the diflereti”af and inregrol catculra. Bostnn, MA: Gii, 1904.463 p. 14 Greves L M. 7?retfreory @functions of red wrrides. New York: h4cGr-sw-Hill, 1946. 3(XIp. 4 33atrrIaaP R. Finite dirrrensirmatvector spaces. Princ&on, NJ: Princeton University Press, 1942. 1% p. 5 Hardy G H. A course of pure mathsnratics. Csmbndge, UK: Cambridge University Press, 1908. 428 p. 18 Hmrsdorff F. Grunrfnlge der A4engedehre (Foundations of set theory). Leipzig, Germsny: Veit, 1914.476 p. 2 IGeerie S C. Irrtmddon to rrretanrarh.mrdcs. New York Van Nostrand, 1952.550 p. 6 Knopp K. Rurktionentheon’e @mction theory). Berlin, Germeny: de Groyter, 1930.2 vols. 23 Kolnmgoroff A N. Grondbegrifle &r IVahrscheinlichksitsredtrtung (lbundations of the theory of prubsbiliry). Berlin, Gemy: Springer, 1933.62 p. 0 Landau E. Grurralagen der Anrdysi.r(Poondations of analysis). IApzig, Germany: Akaderniscbe VerlagsgeseIlscheft, 1930.134 p. 30 L.ef-ets S. Algebmic topology. New York: American Mathematical Society, 1942. 108 Ssdrs S & Ban&h S. 37reory of the integral. Wsrssw, Poland: Z subwencji Fmrduszu kuhrry nerndowej, 1937. 347p. 1 Siegel C L & Belfrmm R. i%wrscenderrtalruarrbers. Prinmrnn, NJ: Princeton University Press, 1947.73 p. 24 Stmre M H. Linear tmns~~”ons in HiIberr space and their applicatiomr to analysis. New York: American Mathematical Wiety, 1932.622 p. 2 Townsend E J. Functionr of a complex variable, New York Holt, 1915, 3S4 p. 17 7mfWW;.Convergence and umyom”ty in topology. Princeton, N]: Princeton University press,
135 van der Waerden B L, Arttri E & Noether E. Moderns Algebra (Modem etgebre). Bertirr, Germany: Springer, 1931.2 vols. 420 WTdttaker E T. A course of modem analysis. Cambridge, LJfC University Press, 1902, 378 p. peared in severrd editions and reprintings, tant by scientists and historians of science. no one of which received enough citations In addition various trends, achievements, to put it on that list as a separate publication. aild researchers represented in these lists will be highlighted. Astronomy and the Earth Sciences ***** Next week’s essay will examine22 aatron- My thanks to Albert Gluckman and Lance omy journal articles and 20 earth-sciences Small for valuuble suggestions and to Eric papers that were most cited in the 1945-1954 lkrschwelljbr colle~”ng informdon used SC1. These lists will be compared with in preparing this essay. publications considered influential or impor- @19901s1
385 1. Brush S G. ‘k most-cited physical-sciences publications in the 1945-1954 Science Citation Index. Part 1. CurmrrrConkvrts (20):7-17, 14 May 19$X). 2. Garffeld E. The 102 most-cited life-sciences publications in the new 1945-1954 Science Cimtion fndcx. Parts I & 2. Current Contents (15):3-10, 10 April 1989; (16):3-10, 17 April 1989. 3. Serre J-P. Homulogie singuli&e des espaces fibres (Mr@ar homology. . of fiber spaces). Arm. Math. 54:425-505, 1951. - 4 Bmtwft S. 7Morie des op.4rd”ons lirkzires (Theory of linrar operations), Warawv, Poland: Z subwencji Furuiuazu Imhury narcdowcj, 1932.254 p. 5 Dieudrmm! J. Prcacnt trends in pure mathematics. A&m. Math. 27:235-55, 1978. 6 --—-—. A panorama of pure mathematics, as seen by N. Bourbaki New York: Academic Press, 1982.289 p. 7 Mann H B. Citation Claasic. Commentary on Arm. Math, Statist. 18:50-6Q, 1947. (Thackray A, comp.) Contemporary classics in physical, chemical, and earth sciences. Philadelphia: 1S1 Prcas, 1986. p. 299. 8 Small L. PeraunaJ communication. 1990. 9 Zhevbakov K A. Jacobson radical. ,!Owyclopedia of rrmthematics. Soston, MA: JGuwer, 15!?0. Vol. 5. p. 231. 10 Ekmifav V 1. Jacobamr ring. .!hycbpedia of mathematics. Buatmr, MA: Kluwer, 1990. Vol. 5. p. 231-2. 11 JSCObaOnN. Strucwre of rings. Providence, RI: American Mathematical Society, 1956.263 p. 12 —. Collected mathematical papers. F30stmr,MA: Birkhauaer, 1989.3 VOL. 13 Kacpilcwsky G. lhe Jacobson radicol of groap algebrar. New York: North-Holland, 1987.532 p. 14 Wkner N. I am a rrrathemotician: ths later lije of a prodigy. Garden City, NY: Doubleday, 1956.380 p, 15 -—-—-. Cybernetics. New York: Wiley, 1948.194 p. 16 Hekrra S J. John von Neurmmn and Norben Wiener: j+om mathematics to the technologies of lije and death. Cambridge, MA: MIT Press, 1980.547 p. 17 HalmoaP R. Some beaks of Auld Laug Syae. (Duren P, cd.) A century of mathematics in America, Part 1. Providence, Rf: American Mathematical Society, 1988. p. 131-74. 18, ——. A history of the theon’es of aethcr and electn”city. l-m Angeles, CA: Tomaah Fubliahers, 1987.2 VOIS, 19. MartirI D. Wbittaker, Edmund Taylor. Dictionary of scientific biography, New York: Scribners, 1980. Vol. 14, p, 31.S8. 20. Rankin R A. Watson, George Neville. Dictionary of scientific biogrophy. New York: Scribners, 1980. Vol. 14. p. 188-9. 21. Whittier E T & WsItsorr G N. ,4 course of modern analysis. Cambridge, UK: Cambridge University Press, 1915.560 p.
386