The 200 “Pure” Mathersmtisiam Most Cited iR 1978 and 1979, Including a List of Most-Cited Pubiicsttiorts for the Top 100
Number 36 September 6,1982
In our study of the 1,000 most-cited cians. Specifically, we examined those scientists publishing from 1965 to 1978,1 71 journals listed under the “mathemat- there were no mathematicians listed. In ics” subject category in the SCI Guide an earlier study of the 250 most-cited au- and List of Source Publications. We ex- thors in Science Citation Indexa (SCFW) cluded multidisciplinary journals, such from 1961 to 1975, only 13 were not in as Doklady Akademii Nauk SSSR and the life or physical sciences. z Almost all Comptes Rendus Hebdomadaires des of these were statisticians—not pure S;ances de 1‘Acad~mie des Sciences mathematicians, Sen”es A, that also publish large sections There are many reasons why mathe- on physics and astronomy, for example. maticians are “underrepresented’ on We were left with a list of 64 “pure” math these lists. These include the size of the journals, shown in Table 1. math literature and the related fact that All references appearing in the 1978 the average math paper contains fewer and 1979 volumes of these journals were references than papers in the life and processed. The cited authors were physical sciences. For example, the ranked by frequency of combined cita- average biochemistry paper contains tions in those two years. The list of cited three times as many references as the authors was then examined for homo- average math paper. j graphs—two or more individuals with One does not need to perform citation the same surname and initials. Finally, analyses to confirm the truism that we looked up citations they received mathematicians make important contri- from a[l journals indexed in SCI. This butions to the advance of science. And added citations from physicists, astrono- the literature of mathematics is now mers, theoretical biologists, and other quite large, In recognition of this fact, scientists publishing in the joumals from we’ve launched a new data base covering those fields. Table 2 shows the 100 most- pure and applied mathematics called cited mathematicians in 1978 and 1979 in ISI/CompuMath’M .4 To cover this alphabetical order. Also shown are their literature efficiently, we identified the institutional affiliations and the number most important pure and applied math of citations from both the “core” pure joumals.J Much earlier, we identified math journals and all SCI journals. the most-cited papers and books in While this method for identifying mathematics. ~~ But this is the first time highly cited pure mathematicians in our we’ve done a separate study of the most- data base isn’t perfect, it seemed the best cited math authors. approach. For example, the distin- We relied on the math journals listed guished French mathematician Reni+ in SC] in 1979 to identify the mathemati- Thorn does not appear in Table 2. In cians most cited by current mathemati- 1978 and 1979, Thorn’s publications
666 Table 1: Math journals indexed in the 1979 SCP used to were cited 404 times, but only 62 of these identify the top 100 most-cited mathcmaticimw 1978 and citations were from pure math journals. 1979. Non-journal items—books, proceed- Acts Mathematical Academiae Scieniiarum Hung.wicae ings, series, etc.—accounted for 264. Acts Mathematica—DjurshoJm Advances in Mathematics Similarly, Andrey Kolmogorov also does American Journal of Mathematics not appear on our list, although he has American Mathematical Monthly Annals of Mathematics been described as “the 20th century’s Archiv der Mathematik most influential Soviet mathemati- Arkiv for Matematik Bulletin de la %cieie Mathcmatique de France cian. ”T Kohnogorov’s publications were Bulletin of the American Mathematical Smiety cited 525 times in 1978 and 1979. Canadian Journal of Mathematics Commcntarii Mathematics Helwtici However, just 69 of these were from the Cmmmmicrdions in Algebra pure math journals in Table 1. Composition Ma fhenvmca Dtscrete Mathematics Several mathematicians we consulted Duke Mathematical Journal commented that many other “signifi- Fibcwacci Quarterly Minois Journal of Mathematics cant” people do not appear on the list. Indiana University Mathematics Journal When we extended the study to include Inven!iones Mathematical Israel Journal of Mathematics 200 authors, almost all of the mathemati- Journal d’Analyst Mafhematique cians mentioned were included. For ex- Journal fur die Reinc und Angewandte Mathematik Journal of Atgebra ample, Kolmogorov is included in Table Journal of Approximamm Theory 3, which lists the next 100 mathemati- loumal of Combhmtorial Theory Series A Journal of Combinatorial Theory Series B cians who were most cited in 1978-1979. Journal of Differential Equations (There are actually 103 names in Table 3 Journal of Functional Analysis Journal of Graph Theory because of a tie. ) But we are limited by Journal of Mathematical Analysis and Applications time and space tQ study only the top 100 lo.mal of Numfw Theory Journal of the London Mathematical Soclety— most-cited mathematicians in detail. Of Second Series course, there still might be some mathe- loumal of the Mathematical Society of Japan Manuscript Mathcmatica maticians perceived as signti~cant who Mathematical Scandinavia were not highly cited during the two Mathematical Notes Mathematical Proceedings of the Cambridge Philosophical years studied. Sociely Ten authors listed in Table 2 have Mathematics of the USSR—Izvestiia Mathematics of the USSR—Sbomik received the Fields Medal: L.V. Ahlfors, Mathematika 1936; L. Schwartz, 1950; J.P. Serre, ?vfathematische Annalen Mathematische Nachrichten 1954; L.V. Hormander and J. W. Milnor, Mathentatiwhe Zeitscbrift 1962; M.F. Atiyah and A. Grothen- Memoirs of tbe American Mathematical Society Michigan Mathematical Journal dieck, 1966; D.B. Mumford, 1974; and Monatsheftc fur Maihematik P. Deligne and D.G. Quillen, 1978. Five Nagoya Mathematical Journal Pacific Journal of Mathematics more Fields Medaliits appear in Table 3: Proceedings of lhe American Mathematical Society K. Kodaira, 1954; S. Smale, 1966; Proceedings of the Edinbwgh Mathematical Society Proceedings of the Indian Academy of Sciences— H. Hironaka and J.G. Thompson, 1970; Mathematical Sciences and C.L. Fefferman, 1978. The Fields Proceedings of the Japan Academy Series A— Mathematical Sciences Medal is awarded every four years by the Proceedings of [he Koninklijke Nederfandse Akademic International Mathematical Union to van Wetm,schappen Series A—Mathematical Sciences Proceedings of (he London Mathematical Society young mathematicians for their out- Proceedings of the Royaf Swiety of Edinburgh standing achievements. John Charles Section A—Mathematics Quarterly Journal of Mathematics Fields, former mathematics professor at Ricerchc di Matematica the University of Toronto, set up a trust Semigroup Forum Siberian Mathematical Journal fund for the medal in his will. The medal Studia Mathemalica was described in Science as “an award Transactions of the American Mathematical Soc)etv Topology comparable in many respects to the No- Zeitschrift fur Math. matische Logik .nd Gmndlage” bel Prize in the prestige it confers. ”s The der Mathematik
667 Table 2: The top IfU3mathemahc]ans most c,ted in 19“8 and 19“9 Asterisks indicate Fields Medal winners A = citatmns from the math core yxmnls i“ 19’ff! and !979. B = total ciwdmns from SCJ” Journals. in. 1978 and 1979. AB AB An 164 202 A&m& lokn Frank f03 hx) Couraat. Rkbard 284 461 firmly, Godfrey Harold llnl,ers:ty ~,[ Manchester New York [In,, ei-utv [Inivmsity of Cambridge Manchester, L!K New York, NY “ Cambridge, UK 164 265 Aumon, SJmxtel 128 ls~ Curfb, Cbarfes Whktle$ey fhl 2f - Harfsh-Cfmmdm Hebrew I :mverslty Umversity of Oregon Insotutc for Advanced Study Jerusalem, kracl Eugene, OR Princeton, NJ 11- f-l “Akffom, Lam Vskrfm 145 l-v) “Delkgne, P&me 13R 235 Hartmen, Pfdl!F Harvard ~!nivers~ly lnstiful des Hautes Etudes Johns Hopkins Ilniverstly Carnbndge, MA Scmntifiq.cs Llaltmmre, MD Ion 12” Alken. Erkk Msgnus Bures-wr-Yvette, France I’ll lt12 Hm-fsb.me, Roberi Cops [Imvcrmy of OSJU 148 26.3 Dfeudwme, Jean Akxnndre [I”iversity of CaJiforma Oslo, Norway Llniversity of Nice Berkeley, CA 14ff 15“ Artfn. Mkhad Kim, France 125 f38 Ha6se, Hebnut Ma,w.chusetts ln,tttuw of 346 435 Dfxmler, Jacques [I”iversity of Hamburg Technology ll”l, crs!ty “f Palls VI Hmnbur8, FRG fkmbndgc MA Paris. France l.i$ 23” HeJgason, SJgurdu? f M 164 Aichbacber, Mfckm! 111 13” Douglas, Ronald George Massachusetts lnsmute of Cafilorma JmlK”tc of stale On,v.ersl[y of Technology Technology New York Cwnbndge, MA ...... Pasadena,. ...CA. . . Stony Brook, NY 139 15- Hemmfn, Ism.1 N. .!>1 4+4 Aoy.0. mmtael r m.cu .324 514 Dun ford, !lefaon (i”,V~~SIN d [’h,cago Oxford (ln!\erslty Yak [’nwemry Ch,cago. IL Oxford f rK New Ha$en. CT 19.1 ?5- Hewitt, Edwfii f26 ,36 Ausfander, Msurice 101 824 Erdefyl. Arlbut [l”!WWIY of Washmgmn Brandeis (I”,vemty ~’”,”~r,lty of J-.di”burgh Sea!de, WA Walth~m, MA Edinburgh, lIK 1M XN Hfffe, Efnar 222 255 Barn, ffyme~ 2q\ 4/(5 Erdos, Paul 1 I“i.ersity of Cahfornia Cul.mbm I ‘nwerstty H“ngmia” Academy of La Jo)k4 CA Ncw York, NY Sctc”ccs IIY 161 Hlftoa, Peter Jofm Ill) -la BdfmsII, Rkkard Em.mI If.dapml. Hungary c.,, Wmtel’”Reserve [’mvcmity of So.lhem 119 12~ Felt, Wal[er [I”iverslty Cafifom]a Yale ~l”I\crsNy Ck, eland, OH Los Angeks. CA New Ha, e”, CT 115 f52 Hlrzebruch, Frfedrlch 13f 333 Berge, Claude lacques 161 35h Frfedman, Avnm [:niversily of Bon. CNRS North wmlem Um, em(y Bonn, FRG Pans, Franc. Fvanslon, IL 334 49 f ‘ Honnardcr, Lam 129 338 Bkkhoff, G.rrett I-- 220 Fuchs, Lmzfo volt., Harvard llmvcrslry Tulane lln]veruty Il”i,emifyof Lund Cambridge, MA New Orleans, LA Lund, Sweden 29- 3n- Bc.rel, Arms.d 2(1- -W Gelfand, Jzraff 1“8 !W H.ppert. Llertmm Jns!t!”m for Advanced Mofmevkh I ‘“t+erstty of Mmm Study Nfafhematics Jnstitute Mamz, FRG Pn”cmo., NJ (’$sR Academy of Scte”cm , , , ,23 Iwasaw., Kenkkhi 51- 723 Bourbaki. N Icofas Moscow [I SSR Pnnceto” 11.i\, Fra”m I(IS )12 GfaubermaII. Geoqe k~.C Princeton, NJ 13- If)? Brmwr, Rkbard Dagobert [I”,,ers,ty of Chica~o 2(II .343 J.cobsor., Nmtbsm Hsfiard ll”lWt,, !y (“hicago JL Yak [[nwcrsity Cambridge, MA 103 269 Gokbbem. Israel New Ha, en, CT 1[5 [20 Bredon. Glen E. T%udfkovlcb 225 285 fkapfmmky, IWJIUS Rutgers [’n,vers,ty Tel Avn (:mversi!y I ‘“ivers~ry of Ch,cago New Brunswick, NJ Tel A vi\’, Iwaef Chwago, JL 1‘.7 342 Brezk, Hafm 29.3 321 G omnsteka. DaIIkl 1.1[ tdn Kmdkt, %mw?f [l”,\ ms,ty of Pam VI Rutgers [Iniverslty Stanford l’ni\erstty F%s, Fm.ce Nmv Br.mwwk, NJ Stanford, CA Iw) 250 Browder. Feffx Earl f2h 131 Gmuerf, Hans 34.) 646 K*to, Todo [t”,, ~r,,ly of Chtcafy, [r”lv~r,lrY ~)f Gott,”gen 1I“tv Crstty ,>f Callfomia Chmigo, IL Gomngen, FRG Berkeley, CA 10! 140 Caldetcm, Alberto Pedro 4“9 5@ . Grotbendkeck, AkxuIdre 144 2(I1 Koha@d, Shosbkkd l“ntverstty of M 668 AB AB AB 22” 31 I Laug, Serge 113 2b9 potys, George ,o~ ,26 Spankr. Edwfn Henry Yak Umvermty S1anford University LJni\ ersify of Califorma New Ha\en, CT Stanford CA Berkeley, CA I08 404 L#x, Peter Lkvfd 13” 164 “Qufffen, Dank] G. 2S3 394 SfeJn. Efks M. New York Llmversily Massachusetts Insmute of Princefon Univerury New York, NY Tcchmiogy Princeton, NJ 150 1b7 Lfndensfrauss, Joram Cambridge, MA 104 112 sWaO, Rkhmd Gordon Hebrew L]nwersny 109 370 R~kalefJar, Ralph Tyrrefl Llniversi~ of Chicago ]erusakm, Israel U“ivmsify of Washington Chicago, IL 210 552 Lions, Jn.qnes.Louf? SCat[k, WA I3’ 339 Titcbmarsh, Edward Cbmfes College de France 224 349 Rudkl, Waker Oxford University Paris, France U“ivcrsify d Wmconsm Oxford. LJK 112 [40 Lorentz. George G. Madison, WI 104 I’M Tut[e, Wffffam Tbomns Llniversity d Texas 110 138 .%kal, Shdcbfro [I”i. emify of WaIerJ~ Austin, TX Nihon University Watcrko, Canada IJ? 249 Mackey, George Tokyo, Japan 145 lb2 Waft, Cbarfes Terence W Ldfefaw I I ! I S3 %to, Mfklo Ckgg Harvard Univerwty Kyoto (Jnivemify Un#.ers#ty of Lnerpool Cambridge, MA Kyoto, Japan Liverpool, LIK 125 1M MncLmw, Saundem 133 172 Schaefer, Hefnmt H. In” 248 Weff, Andre Umvemity of Chicago Univemify cd Tubtngen ]nstilute for Advanced Study Chicago, IL Tubingcn, FRG Princeton, NJ 105 133 Msy, 1. Peter 125 325 ‘Schwarfz, Laurent 110 487 Weyl. Hermanc University d Chicago Ecole Polylechmque [nsm.te for Advanced Study Chicago. IL Plaiscau, France Princeton, NJ 415 542 “Mffnor, John Wffkrd 390 463 “Serre, Jean- pkrre 131 Iw Wbffney, Hassler Institute for Advanced Study College de Fra”cc lnstitule for Ad\aaced Study Princeton, NJ Paris, France Princeton, NJ 206 228 “Mnmford, Davfd Bryant Ilil 185 Sfdmura, Gom 190 214 Zarkkl, Oscar Harvard Llni.ersity Princeton Unwerwy Harvard Umvermfy Cambridge, MA Princeton, NJ Cambridge, MA 119 14- Nagafa, Magayodd 129 I% SkgcJ, Cm+ Ludwkg 21.J 290 Zygmnnd. A.tmd Kyoto Llniversity Uni\erstfy of Gottingcn [l”l,em,~ of Ch,cago Kyoto, Japan Gottinge”, FRG Chicago, IL Table 3: The next {03 mathematimans most cited in 1978 and lq79 Asltrmks indicate Fields Medal wmmrs A= mtatmns from the math core journals in 19’f8 and 1979. B= Iotal citations from SCr Journals !“ 19”8 and 1979, AB AB AB ‘fO %3 Ammn, Herbmf .7 91 Bou$flefd. Afdrkfge Knfght 74 162 Cmndaff, Mkbael G. Umversiiy of Z“ricb LJntversity of Ilb.ois Universifv of WScomm Zurich, Switzerhmd Chicago, IL Madison,” WI 68 76 Amlfsur, Sbfmshon A. 83 Im Bowen, Robe?i E. 8“ 91 Day, Mabfcm M. Hebrew University Ll”,versify of Calif orma Umverwfy d Hfino]s Jerusalem, Jsrad Berkeley, CA Urbana, IL 71 80 Andreotd, Afdo 89 95 Brow&r. Wfffkm b9 89 Demazure. Mkbael lJ”ivmswy of Strmbcwrg Princeton Umvermfy Ecok Polytechmq.e Strasho.rg, Fnmce Princeton, NJ Pfaiseau, France 91 3f7 Arnold, Vktor Igorcvkh b9 76 Grkson, Letuum Axel 91 109 Dkkson, Leonard E. University of Moscow Edvard Universi~ of Chicago Moscow, USSR M1[tag-Lefffer Im[it.te Chicago, fL 94 123 Artfn. End! D!urshdm, Sweden ~o 92 Dfes(ef. knepb Umversify of Hamburg 103 111 Gssefs, John Wfffkm Scoft Kent SIatc Llmvermty Hamburg, FRG Llniversity of Cambridge Kent, OH 74 98 Arveson, Wfffkm Barnes Cambridge, UK 69 90 DoId, Afbrecflt University of California 87 142 Cherm Sfd@-Shen Universiw of Heidelberg Berkeley, CA University of Callfomia Heidelberg, FRG “ 83 90 Aosfrmder, Lomb Berkeley. CA Ico l-l Ekfenberg, Samnel City Univemify of New York 93 133 Cbevaffey,Cfoude Co fumbia LJniversity New York, NY’ Univcmify of Paris VIII New York, NY 99 J54 Ben, LJpman Paris, France 81 93 Everftt, WfUfam Norrfe Ccdumbla Lhiversity 76 194 CoddJngIoa, Zmf A. Ll”ivemtfy of D.ndee New York, NY University of Califomua Dundee, LIK 93 104 Bfng, R.ff. Los Angeles. CA Fcderer. ffetben University of Texas 78 87 Conner, Pfcrre Eucffde Brown Univemify Austin, TX Louisiana Sfate Un:vcrsty Promdencc, RJ 72 105 Boas, Rafph P. Baton Rouge, LA Ifm 121 “Fe fferomn, Cbarkt Leuk Northwestern University 83 113 Cannes, Afafn Princefon Llniversify Evanston, IL [nstltut des HaUtCS Etudes Princeton, NJ 93 [m Lfomdf. Fmti Fathemtone Sciendfiqucs 91 885 FeUer, Wfffkm Umversify of Edinburgh Bures.sur-Yvefte, France Princeton Univemify Edinburgh, UK 78 119 Coxeter, Harold Scott Princeton, NJ 79 118 Bwf, RaOUl MacDonald 70 76 FOX. Rafpb H. Harvard University University of Toronto Princeton University Cambridge, MA Toronto, Canada Princeton, NJ 669 AB AB AB Ml 9- Frob3kh, Albrech( 93 118 Kothe. Gowfrfed 9- 27 I %gal, JrvbIE Ezra [:n,\ersity of London University of Frankfurt Mas.wch.sc(ts Jns(ttute of London, (IK Frankfurt, FRG Technology ~.1 91 Gabrkl, Pferre 92 1~ Krefn, Mark G. Cmnbndgc MA (Inmersity of Zurich Institute of Physical $1 W Skrpfdt. Wacfaw F. Zurich, Swltz.erland Chemmry .5 ~, Warsaw [J”iversify Gameffn, Theodore W. Odessa, llSSR Warsaw Poland [Inivemity of Cahhmua ~~ n~ Lambek, loachfm LiIs Angeles, CA McGill Llniversity w 28” She., Barry Martfm w 103 Gfffman, Lemrmd Montreal, Canada Ca!ifomia lmtitule of [Iniversily of Texas W V8 Luxembq, Wffhefmus Technology Austin, TX Aritbonlus Josepkmw Pasadena, CA “8 w Goldsdmddt, Davfd M. Cafiiomia Institute 01 98 225 - sma!e, Ste.phez [ ‘nivei-sity of Cablom ia Technology Umversify of Cdiiomm Berkeley, CA Pasadena, CA Berkeley, CA hH 9- Gmtzer, George 99 2s9 M.gmas, Wfffmfm 77 S@IIl~, John Rober( tlrii\ersily 01 Ma”,toba Polylcchnic Inso!ule of 72 Winnipeg, Canada New York f,ntversify of CallJomia Berkcky, CA 94 I(F4Grfffitbs, Pb!JfJp A. New York, NY Hmard L1niversily 92 I35 MkhaeI, Ernest Arfhur 82 146 Steenrod, Norman E. Cam btidgc, MA [University of Wash,ngto” Pnnccton Llni\ erwty v- 11~ Gtumf~, Robert CfJfford Sea[!le, WA Princeton, NJ Princeton llnwers,ty 85 102 Moore, Calvfn C. “o “0 Stefmberg,RoberI Prmccton, NJ Llmversity of Cablc,mia [Imverwy “f Cabfom~ 94 11- Half. PfdJl~ Berkeley, CA Los AngeJcs,CA llntverstty of Cambridge .8 90 Momey, Cbmfes Bmdfkkf 8“ 10b Sdffvan, Derm!.? Cambridge, UK [Jni.crsity ofCalifomm Jns[itut des Ha”tcs Etudes 69 -3 H@yman, Walter Kurt Berkeley, CA Scientifiques lln,\ersity of London W+ 29’4 Neumann, John Von Burcs-sur-Y.ctrc, France London, [ lK Institute for Advanced Study “> ~~ -3 “3 Suzuki, Mkbfo Hfgman, Graham Princeton, NJ ( lni.msifyof JJIUKM flxford 1 lmverszty 72 113 NfkofskU, Sergei MJkhaUovkh LIrbana, fL Oxford, UK Steklov Institute of 94 112 -Hfronukn, He fsuke Mathematics ‘2 ?32 Szego, G.bor Harvard (university Moscow, LISSR Stanford O“i. ersity Cambridge, MA Stanford, CA M 85 Nmssbaum, Roger David 7b 143 Hfmcb. M.mrks Wffffxm Rutgers [I”ivcrsity 92 172 Szokekf.1.Nmgy,Bela Umv.rsity of Cahforma New Brumwick, NJ (,”iversify of Szegcd Berkeley, CA 74 124 Szeged, Hungary 8- 119 JJocbxbffd, Gerbard P. Pafab, RJcJurd Sb@Idon S4 12“ Takesakf, Mmamkbf [ Imvmsity of California Brandeis I!nwers,ty Wallham, MA (1.iversity of California Berkeley, CA Jms AngeJes, CA HI ‘+3 Hochwcr, Melvfn “4 82 Pedemon, Gerf Kj.aergmd [ Inwerslty of Mich]gan Univerm[y of Copenhagen 95 101 Tale, JrJfm T. Ann Arbor, Ml Copenhagen, Denmark Harvard [Ioivermty 81 118 Ho!fmrm, Kenzetb n2 113 Peetr.z,Jaak Cambridge, MA ..,. Hampshwe CoU.ge Umverwty of Lund t10 85 ‘-i Ilompaom,Jam b Amherst, MA Lund, Sweden Umversity of Cambridge 83 ILX) Hum#meys, James E. -76 79 Pelczynskl,Akksax?er Cambridge, llK University of Massachusetts Pohsh Academy of -4 74 Tfmsae4eM, F181MZG. Amherst, MA Scwnces Ilniversity of Cologne “6 99 Kadbon, Rkbmd Warsaw, Poland Cologne, FRG Vfncent tin 102 Tim. Jacqum t Ini%ersity of Pennsylvama ~1 96 Pkoch. Albrecbt CoJkge de Fra”cc Pbdadelpbm, PA Uruverwty of Jema Paris, France % 124 Kdfey, Iofm kc Roy Jena, GDR University of Cafifomn3 “1 225 Reed, Mkbd Cbades 83 130 Treves, Fmnccds Berkeley, CA Duke Umversiry Rutgers Universny M “4 Kerwafm,Mkhe! A. Durham, NC New Brunswick, NJ Univerwfy of G enc+a “4 151 Rksz, Frfedrfcb “1 f!J Trfebel. Ham Geneva, Switzerland University of Budapest University of Jena W 94 Kne!wch. Mardred Budapesl, Hungary Jena, GDR 1:nivem!y of Regemb.rg 95 Ill Rone.ILuJ, HmkeU P. 80 82 Wab?h.mwen, Frledfmh Regensburg, FRG Univemity of Texas Umversity of Bjckfeld 82 121 ‘Kodaka, Ktudhfko A“st,n, TX J3iekfeld, FRG [lmewy of Tokyo Scbechter.Mumy fUJ 108 Warner, Garth W. Tokyo, Japan University of Washington 69 525 Kofmogorov, Andrey Lehigh f. fniverstty Seattle, WA N fkofmevkb Bethlehem. PA (IS$R Academy of Sciences Scha+.ribeq,JsmacJ. 75 87 WofJ, Joseph Albest Moscow, USSR LJ”i.ersity of WMcomm lJniversMy of CaJtiomia 96 169 Kostant. Bertnm Madison, W 1 Berkeley, CA Massachusetts Insntute cd Segal, Gmeme Bryce I(KJ !89 Ymk?a, Komku Technology Oxford [J”iversity Gakushuin Unwerwty Cambridge, MA Oxford, UK Tokyo, Japan 670 . Table 4: Insm.tiond affdiallons of lhe top ICUJmost. cited hrst two medals were awarded in 193b. A mathemauclans of 19”8 and 1979 total of 24 mathematicians have won the Number of medal since then. The 1982 Fields Medal hmthutlon A utbors winners will be announced later this Uni\ersily of Chicago, [L 9 year. Harvard Univerw[y, Camhndge, MA b Table 4 lists the institutional affilia- Inslitute [or Advanced Study, Princeton, NJ b University of California 5 tions of the top 100 most-cited pure Berkeley (4) mathematicians. Some of the mathema- San D,ego (! I ticians who reviewed the list observed Yak University, New Ha\e”, CT 4 Massachusetts Institute of Techmlogy, that a few authors have retired or are Cambridge, MA 3 U.n erstty of Paris, France 3 deceased. Nevertheless, we feel it is im- V], Pierre c! Msne Curie ,2, portant and useful to show their former XJ, Pans-S”d (1) California Imfifute of Technology, Pasadena 2 institutional affiliations, Their work re- College de France, Pans 2 mains relevant to currently active math- Hebrew Uni. ersif y, Jerusalem, Jsrael 2 Kyoto Univers~fy, Japan 2 ematicians. Their institutions deserve to New York Unwersny, New York 1 be acknowledged. Oxford University, UK 2 Princeton Universny. NJ 2 Interestingly, we cannot credit any in- Rutgers Umvers!ty, New Brunswick, NJ 2 stitution with Nicolas Bourbaki’s S1anford lJniversny, CA 2 Tulane University, New Orleans, LA 2 work—’’he” is a secret group of mostly University of Gomngen, FRG 2 French mathematicians who publish LJniversfity vf Washi”g( on, Seartfe 2 Brandeis Um. ermy, Waltham, MA I under that collective pseudonym. Paul Brow” Unwerst!y, Pr.,\ Ide”ce, RJ 1 R. Halmos, Indiana University, Bloom- Case Western Reser. e U.i. ers)ty, 1 CleveJand. OH ington, claims that the membership of Cemre National de la Rechercbe J Bourbaki varies between ten and 20.9 At Scientific.e, Paris, France Columbia Ll”i.ersity, New York, NY f various times, several of the Bourbaki Duke Llni.ersiry, Durham, NC 1 members were affiliated with the Uni- Eccde Polytechmque, Plaiseau, France I Hungarian Academy of Sciencm. I versit y of Chicago, Uliiois; Northwest- Math Re+carch Institute, B“dapcw ern University, Evanston, Illhois; Co- Indwma Umverstty, Bloomington I Instiw! des Hautes Etudes Scientifiqucs, I lumbia University, New York: and the Bwss-mr-Y\ette, France University of Nancy, France. Andr6 Johns Hopkins Umvcrwfy, Balmnore, MD I Leningrad University, (ISSR 1 Weil is credited with being one of the Mathematics Imritute, LISSR Academy of 1 founding fathers of the group, and Jean Sciences, Mmcow Moscow Ccmtrol Problems [nsm.te, USSR 1 Dieudonn~ is described as “Bourbaki’s Niho” Unwersity, Tokyo, Japan 1 chief scribe almost from the beginning” Northwestern University, Evansfcm, JL 1 State University of New York, Stony Brook 1 of the group’s publications in the Tel A.m Unwersity, Israel I mid- 1930s,9 Weil, Dieudonn6, and Unwermty of Bonn, FRG 1 Unmerslty of Cambridge, UK 1 Halmos appear on the list in Table 2. Urm ersily of Edinburgh, UK 1 The University of Chicago heads our Unnerstty of Hamburg. FRG I LJn)+crs,ty of Liverpool, LIK I list with nine most-cited mathemati- Llni\ersity cd Londm, UK 1 cians. The Institute for Advanced Study, Llniversity of Lund, Sweden 1 University cd Mainz, FRG 1 Princeton, and Harvard University University of Manchester, lJK 1 follow with six each. The University of Lltm emit y of Michtgan, AmI Arbor f Univcrs]ty of Minnesmta, Minneapolis 1 California accounts for five, while Yale Unwersity of Mcmtpelhcr J], France 1 University has four. The University of LJnwcrsity of Nice, France 1 University of Oregon, Eugene 1 Pans and Massachusetts Institute of University of Oslo, Norway 1 Technology each have three. Twelve University of Southern Cafifomia, J Lns Angeles more institutions account for two each: U.wmmy 671 ty; Princeton University; Rutgers Uni- tion as a core document. Seventy-nine versity; Stanford University; Tulane are books. R. Courant and D. Hilbert’s University; University of Gottingen, Methods of Mathematical Physics, the Federal Republic of Germany; and Uni- oldest book on the list, was published in versity of Washington, Seattle. 1924. The four newest books on the list Of the 58 institutions listed, just under were published in 1973, and were au- half, 28, arelocatedin the US, and62 thored by H. Bri+zis, R.G. Douglas, Hor- authors are affiliated with them. Ten mander, and J. Lindenstrauss and mathematicians are affiliated with seven L. Tzafriri. In total, two books were French institutions, not counting Bour- published in the 1920s, five in the 1930s, baki. Seven authors did their work at six two in the 1940s, ten in the 1950s, 47 in UK institutions, and the Federal Repub- the 1960s, and 13 in the 1970s. lic of Germany accounts for five institu- Of the 21 papers on the list, one was tions and six authors. The USSR has published in the 1930s, three in the three institutions and authors. Both 1950s, 11 in the 1960s, and six in the Israel and Japan account for two institu- 1970s. The two most recent papers were tions with three authors each. Canada, published in 1977—Atiyahs “Instantons Hungary, Norway, Poland, and Sweden and algebraic geometry” and M. Sate’s each have one institution and one “Studies on holonomic quantum fields.” author. The oldest, “Congruent graphs and the Table 5 lists the most-cited publica- connectivity of graphs, ” by H. Whitney, tion as a primary author for each of the was published in 1932. 100 math authors, Also shown are the As you can see, mathematicians tend code numbers for lSI/Co mpuMa th re- to cite older literature. The so-called search fronts that include the publica- half-life of math research is much longer Tnfde 5: MosI-cLIcdpubhcauon a, a primary author for each of the top I(K) math a.lhor+ Pubhcation. v,hwh are m the cow of an [51 [’ompu, %[h’” research front ,pecralty arc followed hy (he rcwarch front speciidtv n.mhcr in hold. Tofsd.s[1 Chstlom 1978.1979 BffdJogmPfdc Data ~~ A(famt, J F, ,Jmhlt= h<,m<,ropy ond Re”erolIzeLI h 672 Tofal SCl Clmuolw 1978-1979 BfhffogmphkcD.is 104 Carfan H & EIJenhergS. Home.[ogmd alge-bm Princeton, NJ: Princeton Univermty Press. 1956 390 p 105 CJifford A H & Preston G B. The algebmic theory of semj~roup~ Providence, RI American Mathematical Society, ( 1%1) 1977, 216 p. S0.1206. 35 Cohn P M. Un,vt.rmf a(gebm New York: Harper & Row, I%5. 333 p, 398 Coamml R & HffberI D. Methoden der malhematimhen phymk. IMelhods of rnathemancol phymcs ) New York: Wiley, ( 1924) 1962.2 VOIS 92 Cartk C W & Refner L Represenmtton theory offmire groups and assocmrt w olgebms New York: Wiley, ( 1%21 1981.635 p 17 Deffgne P, Grfffftka P, Mor&an J & hdffvam D. Real hcmmtopy theory of Kdder manifolds. Invenr Ma!h 29245-74, 1975. 74 Dleudonme J. Fondemems de 1Qnalyse modern. (Foundations of modern analjsw. I Pans. Gauthier-Villms, 119f#3) 1963.374 p. 103 Dfxmkr J. Les algebres d’opemte.rs duns Iqmce Hdberrte” algebres de Won Neumann (Opem$or algebras m Hdberl s~ce Vo. Neumann algebra s.) Paris. Gauth]er-Villam. ( 19571 1%9. 363 p. 29 Dough R G. Banach algebra rechnques m the theory of Toep/trz opt=roIorz Providence, RI: American Mathematical Society, 1973.53 p. 469 DunIonf N & .Schwcrfz J T. Linear operafors. New York: Wdey, ( 19581197 I 3 vols, SO-l 539. 413 Erdelyl A, Msgnus W, Oberhcttfnger F & Trfcoml F G. Ba{eman manuscnp project. lff,gher rranscendenral funcr,on$.1 New York: McGraw-Hill, 1953 -55.3 >OIS 15 Erdoa P, Kc. C & Rado R. Intersection theorems for systems of fini[e sets. Q.arf J Ma/h 12313-20, 1961. 21 Felt W & Thompmon J G. Solvability of groups of odd order. Pac J Math 13:775-1029, 1%3, 164 Ftfedman A. Pantal dtfferenml eqwatmns of pambohc rype Melkume, FL: Kricger, ( 1964) 1976.262 p. 127 FIIeka L. lnfIn,te A belian groups. New York Academic Pres, ( 1970) 1973.2 VOIS.S0-1S04. 198 Geffaad J M & Sfdfov G F. Genem/ized functions, New York Academic Prex, (1964) 1967, 5 VOIS. 80-1S67. 23 Gfmherman G. Central elements in corefree groups. J A/gebm 4,403-20, 1966 38 Gokhberg J T & Krdn M G, Vvedenie v reom. li”ei”ykh twsmnosopnazhen”ykh Opemforov I{ntmduc~,on to the theory Of linear nO~e/ffld/Ornt Opemlors I Providence, Rf: American Mathematical Society. ( 1%51 1%’4 378 p 145 Gorematefn D. Ftntte groups New York: Chelsea, 11%7) 1980 527 p. 21 Gmneti H. Uber Modifikationen und exzeptionclle analytische Mengen. (Over.modification and exceptional analytical numbers. I Math Ann 146:331 -M, 1962. 59 GrothemdJeck A. Elements de geomerne olgebriq”e (Elements of ge=omelnc .Igebm. ) New York: Springer-Verlag. (1960) 19”1.454 p. 45 JJde J K. 0rd4.ory d,ffertvmd equarmns. Melbcmrne, FL: Krieger, ( 1%9) 1980. 3S4 p. 82 Haff M. The theory ofgroup$. New York: Chelsea, ( 1959) 19~6 434 p. 92 Hafmos P R. Measure rhecvy. New York: Springer-Verlag, 11961 I 1974 305 p. 272 Htrary F. Gmph rheory. Reading, MA: Addison-Wesley, 1969.274 p 146 H~rdy G H, Lftdewood J E & Pefys G. {mq.afities, Cambridge, UK: Cambridge Univerwty Press, ( 1934) 1952 324 p. 23 Hmfsh.Chandm. Discrefe series for semisimple Lie groups. 11. Acm Maih —D]”rsho(m I ICXI-111, 1966. S0-1626. Im Hmtman P. Ordinary differenna{ equations. New York: Wiley, 1964.612 p. 26 Hufahome R C. Residues and d.a/iry New York: Springer-Verlag, [%6. 423 p L7 Haase H & Kfohe W. K1.ssenzahl Abelscher Zahlkorper (Number of classes of Abe6an number groups. 1 New York F. Ungar, 1954. 212 p. 139 Hefgascm S. L3iffemniial gemnewy a“d sy”memic spaces. New York: Academic PreM, I%2. 486 p 17 Herstefn 1 N, Toptcs in nng theory. Chicago: University of Chicago Press, ( 1%5) 1%9, 121 p. 140 Hewftt E & ROM K A. A bstracr harmmtc analysis. New York Springer-Verlag, ( 1%3 I 1970.2 vols. I37 HffJe E. F“nctionaf cmalys,s and semi-groups Providence, RI. American Mathematical Society, ( 194811974528 p [6 Hffton P J & Wyffe S. Homofogy dwory. Cambridge, UK: Cambridge University Press, ( 19601 1%1. 4S4 p 49 Hfnebrnch F. TopologIcd melhods in algebrmc geomemy. New York Springer-Verlag, ( 1956 I I9“8. 232 p 105 Hormander L. An introduction m complex analysis tn se ver.al .mmb[es New York: Elsevicr, 1973.213 p I 54 Happen B. ,!ndliche Gruppen (Fini@ groups, ) New York: Springer- Verlag, 1%7 W6 p. 18 Jwasawa K. On Z] extensions of algebraic nurn6er fields. Ann Math 98246-326, 1973. S0-0943. 58 Jacobson N. Lies/gebms. Ncw York: Dover, (l%2) 1979.331 p. 44 Kapbmky l. Comm.torrveting, Chicago: University of Chicago Press, (1’468) 19”4. 129P. 4s Karffn S. Totcdpositiwry Stanford, CA. Stanford University Press, 1%8 2VOIS. 369 Kmto T. Perru,barion theory forltneoropcmtorr New York Springer-Vcrlag, (1966J 19f@. 619p. 168 Kobayashf S& Nomlzw K. Foundations o{dtfferenfia/ geomet,y New York. Wiley, 1963.329p 64 Kmsno$efskffM A. Topologwal mezhodstn thelheory of.onl,near tntegmleq”alio.$ New York: Macmillan, 19&4 395 P. SO-J816. ] 27 Krmmowmklf(, Topologw (Topology .) New York: Academ,c Press, (1933) 196& 2v015 125 L8dyzbemskak OA& Umltaeva N N. Lineinye tkvaziline,nye umvneni{a eIltpticheskogo tip. iLtnear a.dq”a~tljneor el/!pttc eq”attons. )New York Academic Press. (19641 1963. 495P. 71 LmgS.A/gebm Reading, MA. Addison-Wesley, 1965 508p, 71 J.u PD. Integrals of nonlinear equations of evolution and solitary waves. Comm.n Pure App/ M.(h 21:467JJ0, 19&. SfI-lf!d3. 673 Tefal .SCI Cltaflonl 1978.1979 Bfblkogrqddc D.fa 31 ~&~e=~mu*a I& T~lfi L, Cfo,,,ra/ Bana,h,pace, New York Sprmger-Ver&A~, 19”3. 243p. 115 Lions] L. Q.elq.e.r melhodes derexolulion de, prohleme~a.x hm!ls nonh.eatre.r (Some method.r for the re.”lutt 674 Table 6: Titles of Lr//CompuM.fh ‘n research fronts that include most-cited works by the top lfM math authors among their core documents. The names of the mathematicians in this study whose mos-cited publication is included in the research from are show” in parentheses. Research Front Number Research Front Name so-tm39 Adams-No\~kov spectral sequence, Brown-Peterson homology, Mora,a K-theory, and complex cobord~m (Adams J F) fUM3295 Rational singularities, elliptic singularities, and normal singularities of surfaces (Arti” M) ao-ow Standard compamtls and standard subgroups of finite simple group (Ascbbacher M) 8C-033C Yang-MUls gauge theories, Euclidean self-dual solutions, and instantons IAtiyah M F) S04547 U[traprcducts, power series equations, and curves with large tangent space ( Zariski 0} 8Mfi58 Blocks of characters and the stmcture of finite groups (Brauer R) S0-0943 P-adic L-functions, cyclotomic fields, and Iwasawa invariant (fwasawa K I eQ-120h Semigroups: structure theorems, inverse semigroups, divisibility, lattice of ideals; repres.entnrions, ededding theorems, and free $emigroups (Clifford A HI &3-I 539 Controllability and observability for distributed-parameter systems in Banach spaces (Dunford N) 80-1626 Repres-sntations, characters, and discrete series for semK1mple Lie groups (Harish-Chandra I W-1793 Finite gm”ps with trivial class groups, a mmnal integral basis theorem, periodk projective resolutions, and locally free class group+ of groups of prime power order (Swan R G ) sf-l W4 Infectivity, projectivity, torsion, md other properties of Abefia” groups (Fuchs L I 801816 Spectral theory for nonhnear operators in normed spaces (Krasnoselskii M A) W1843 Evolution equations, Backlund transformations for a higher order Korteweg-Devries equation, and nonlinear partial differential equations solvable by inverse-scattering tran?.forms (Lax P D ) SG1S67 Localization in quantum field theory: Fourier hyper functions, the Bogolyubov axiomatic approach. and a relativistic invariant fotmu fation of causality {Geff and 1 MI f02ttas Studies on holonomic quantum fields (Sato MI W-2937 Cauchy problems, eigenspaces, and general solutions of differential equations (Schwartz L I W2908 Distrib.tim !hemy, generalized f“”ctiom, differemial operators, and compact groups (Schwartz L) most surprising result to one who is not a have given a different perspective on mathematician is the dominance of current mathematical research. This will books. This is a result I might have ex- be easy to do in a future study based on pected in the humanities or social sci- even more up-to-date information. ences, or even in engineering. However, the results were not so surprising to the ***** many mathematicians who examined the list. Several commented that they would My thanks to Dorothy Silver and have preferred that we limit the list to Alfred Welljams-Dorof for their help in journal articles. Such an approach might the prepamtion of this essay. 01982,s( REFERENCES 1. Gsrffeld E. The 1,CWfcontemporary scientists most-cited 1%5- 197S. Part 1. The basic list and introduction. Current Contents (41):5-14, 12 October 1981. 2. ------The 250 most-cited primary authors, 1961-1975. Part I. How the names were selected. .ESS.YSof an information scientist, Phdadelphki: 1S1 Press, 1980. Vol. 3. p. 326-36. (Reprinted from: Current Contents (49):5- 15, 5 December 1977. ) 3. ------Journal citation studies. 36. Pure and applied mathematics journals: what they cite and vice versa Current Contents ( 15):5-13, 12 April 1982, 4. ------lSf/CompuMath, muftidiscipfimtry coverage of applied and pure mathematics, statistics. and computer science, in print andlor online-take your pick! Current Contents ( 10):5-10, 8 March 1982. 5. ------Highly cited works in mathematics. Part 1. “Pure” mathematics. EMQyJ of an information scientist. Phlladelphla: 1S1 Press, 1977. Vol. 1. p. 504-8. (Reprinted from: Current Contents (47):5-9. 2f November 1973. ) 6. ------Highly cited works in mathematics, Part 2. “Applied’ mathematics. ,%says of an in~ormation $cientist. Phfiadelphla: 1S1 Press, 1977. Vol. 1. p. 5fM-13, (Reprinted from: Currenf Confenfs (4t):5-9, 28 November 1973. ) 7. Gnedenko B V. Kolmogorov, A ,N, Encyclopedia Britannica. Chicago: H.H. Benton, 1976. Vol. 10. p. WI-3. 8. Mrm(ow G D. The Fields Medals (1): relating the continuous and the ducrete. Science 202:297-8, 1978. 9. Hafnms P R. “Nicolas Bourbaki. ” Sri. Amer. 196:88-91; 93-4; 96:99, 1957. 675