Study of History of Mathematics PDF
Preview Study of History of Mathematics
■ THES TUDOYF T HEH ISTORY OFM ATHEMATICS :ind THES TUDOYF T HEH ISTORY ■ OFS CIENCE (Twov olumbeso unasd o ne.) by GeorgSea rton DOVERP UBLICATIOlN!raS@, t NEW YORK THES TUDOYF T HEH ISTORY OFM ATHEMATICS by GeorSgaer ton DOVER PUBLICATIONS, INC. NEW YORK COPn.teld'• 1936 llY nnt Pl'l'.sro.tN"t Al\"D l"lt.l.1.0\\"S OF KA.1VAJU) 00U.Z<U: rmn LIBRARY [[l1�11� 8517 Tht.S new Do�r �luuu ani puon!UlNt lll •�7. is :an un:abnd� :and un:altcnd rtpublitahon pf the 6nt cd(u()n or. Tia� Study of tht Hutorr tJ/ Jf•thffMtu=1. >nd Th� Stauly o/ lbe HJSll"l'T o/ SttmN'. tht- tll"D '\'Olumc:s btulg bound as one PREFACTEO T HED OVERE DITION Ia mg ratteofD uolv ePru blicationsa ta fr oerl aissuing, tivleolwyp rinceew,e ditoifot nhse tsweo little books of minweh ihcha vleo nbge eonu otf p riEnatc.oh ft hecmo n tainnvsop arfitrss:at t,e xetx plaitnhmieen agn ionftg h e histoofsr cyi e(noctreh e hoifsm taotrhye maatnidsc,es c)o nd, ab ibliofgarcaiphlyia tdadtiitnsigto undaTilhe essb.ei bliog� raphaireneso tu p-tob-udtac toen ttahieens sendtoiwanl tot imoeffi rsptu blicRaetaidowenhr.osa rseu fficiienntly quisiwtiilbvleae b lteoc ompltehteeema sbiylr ye ferring to myb ooHko ruAs ,G utiodt ehH ei stoofSry c iepnucbel,i shed byC hronBioctaa nWiaclat,hM aams,is n.1 ,9 5B2u.et v etnh at inso atb soluupt-etlo-yfd oaurtp e-,t o-dianat nee vnaensess cent qualiinat w yo rclhda ngaisfn agas sto urRse.a dwearnst ing thvee rlya tiensfto rmoantt ihoheni stoofsr cyi esnhcoeu ld consruelgtu lianar p luyb lliicb roarbr eyt,st teiral thl o me, thceu rrennutm berI soiAfsnI , n ternatQiuoanratRlee.. r ly viedwe vottote hdHe i stoofSry c i>e endcietbeyId .B ernard CoheWni,d enLeirb r1a8rC9ya, m bri3d8Mge,a ss. Them aitnh iintsgo u nderstthaaintnad w ordlodm inated bys cienmteitfihcoa dnsdi nventtihhoein sst oofsr cyi ence shoubletd h kee ystoofhn ieg heedru cation. Chris1t9m5a4s GEORGSEA RTON CONTENTS THE STUDYO F THEH ISTORYO F MATHEMATICS 3 NOTE ON THE STUDY OF THE HISTORYO F MODERN . . . . . .. . . . . . . . 29. . MATHEMATICS BIBLIOGRAPHY I.G enetrraela tis.e . s 41 . . . . . . . . . . . . . . IIH.a ndbooks 4 4 IIIT.r eatdiesveostt oet dh hei stoofsr pye cial brancohfme aste hmati•c s. . .4 6. . . . IV.M athemiantt hineci stn eeeannttdhw entieth . . - . . . . . centu.r ie.s . .. . . 49 V.P hiloasnomdpe htyh loodg.oy ... . . 3 . 5 VI.B ibliog..r ap.h .y . . . .. . . . .5 5. A.G uidBe.sE. n cyclopCa.Le adrigaes . cataloDg.Ju oeusr.n als VII. Joountr hhneia sltsofo m rayt hema.t i5.c s 9 VIICIe. ntorfre ess ea.r c..h . . . . . . . . 61 A.A cadeomfsi ceisee .Bn .Mc athematical sociCe.tI inetse.r nactoinognrDae.lsI snes. stitauntldei sb raries Biograopfmh oidenesm r athemat.i 6c7i ans APPENDIX. . . . . .. . .. . . .. . . . . . . 0.5 INDEX I THES TUDY OFT HEH ISTOROYF MATHEMATICS T HE remarks ,vhich I have made on another occasion ,vith reference to the history of science 1 would apply equally ,veil to the history of mathematics; there is no need of repeating them. Ho,vevcr, the history of any special science suggests ne,v considerations. As long as the history of science ,vas conceived as the sum of the histories of special sciences, the relationship bcrureen the former and the latter ,vas simple enough. The history of each special science ,vas simply a part of a ,vhole; a part which could easily be removed and isolated. Ho\vcvcr, that old Whewel lian conception had to be abandoned, as it ,vas borne in gradually upon scholars that one of the most valuable as- pccts of the history of science ,vas the study of the inter relationships bcnvecn different branches and their mutual enrichment. The history of science could no longer be conceived as a sum of particular histories, but rather as an organic in tcgra tion, whence no part could be abstracted ,vithout damage. Moreover the history of each science is necessarily more technical than that of science as a whole, more concerned ,vith scientific than with cultural continu ity. As it deals ,vith a more lillllted group of ideas it can hope to follow these more closely. To be sure, these differ ences are quantitative rather than qualitative, and would vary considerably from one historian to another. The one might write a history of science of a very abstract type; the other, a history, say, of chemistry, which would contain fewer technicalities than humanities. In general, however, we should expect the opposite. 1 G. Sarton, The Study of the Hfrto,y of Scitnct1w ith an Introductory Bibliography (Cambridge, Harvard University Press 1936). See also Tiu History of Science 1 Va.nu the History of Mt dicine (Isis, vol. 23, pp3.1 3 -320, I 935). I 4 THE STUDY OF THE HISTORY OF MATHE�fATIC:S The history of mathematics essentially different from JS the history of other sctenccs m its rclationshtp wtth the his tory of science, because 1t never was an integral part of the latter 1n the Wlte,-vcl11an sense The reason for thts ob is Vious mathemat!_CS being far more esoterJc_ than_ the 01hez:.. ences, 1ts histo_ry can only be told to a .select group_oL !:!, _ mifia� It true that there are 1n every science certain is questions which are more difficult to explain than others, or cannot be explained without long prehmmaries, but those questions are almost exclusively recent ones, 1n the case of mathematics, on the contrary, the difficulties began very early There are problems wh.tch exercised the nunds of men 1n the fifth century B C and cannot be entirely ex plained to the non•mathemattcians of to-day, and it is lm• possible to make the latter realize the grandeur and beauty of Greek mathematics One might thus oppose the history of mathematics to the htstory of science, and thts s.s often done for praetteal rea• son! The teacher of the .htstory of �c.tence bcJng obbged to omit mathematical questions -cspcciaUy the most interest ing ones-, because only a part of hts audience could be ex:• pccted to understand them, 1t is natural enough to organize separate courses devoted to the history of mathematics There arc then at least two courses (or two series of courses) compieung one another, the history of science and the hIS tory of mathematics It a p1ty that this should be so, for the history of mathe 1S matics should really be the kernel of the history of culture Take the mathematical developments out of the history of science, and you suppress the skeleton which supported and kept together all the rest Mathematics g1ves to science its innermost uruty and cohes1on, rhlch can never be entirely replaced with props and butt« es or with roundabout con nections no matter how many of these may be introduced t On the other hand, the histonan of mathematics, re membering that his activity complementary to that of the 1S VARIOUS KINDS OF lfATHE�iATICAL HISTORY 5 historian of science, ,vill not attempt to do over again the latter's task, and he may even feel inclined to take of his subject too technical and too narrow a view. There O\\rn fore, it is \\'ell to insist that he should seize every occasion to indicate the relationships between mathematics and other sciences, and to insist that these relationships have always been reciprocal: mathematical problems being often the result of physical needs, vvhile mathematical elaboration gave ph ics, and, gradually, other sciences, not only means ys of discovery of almost miraculous potency, but also perfect models of anal is and synthesis. ys Some historians of mathematics, with a strong bent for hu�nism, are \villing to consider not only other scientific J activities than the purely mathematical, but the whole gamu�. So much the better. Others, movfrig1n1he opposite direction, feel that the history of mathematics it self - not tosp eak of the history of science - is too com• plicated a subjeancd,t ,,-vis hing to avoid the endless intri cacies of the mathematical tree, they select one branch of it, and study its development in more or less complete iso lation from the others. Thus the historian may be led to investigate the development of algebra across the ages, or the amplifications of a single idea, like the idea of number, function, or group. Such abstraction in historical research, as opposed to the more natural procedure of considering each fact as it occurs in due chronological order, is very arbitrary. It is perhaps \vorth \vhile to examine the matter a little more carefully. The filiation of ideas is some\vhat like the filiation of in dividuals, except that the intricacy is even greater. Any individual A thinking only of his o\vn genealogy has a sim ple pattern in his mind like our figure but that pattern is 1, obviously a false one, from every point of view except that of his own unimportant personality. In reality, the pattern is enormously more complicated, for each couple may have had more than one child, each person may have married 6 THE STUDY OF THE lllSTOltY OF ?.tATHEt.tAncs more than once, and marriages bcnveen cousins have in• troduced ne\V cross rclat1onsh1ps The complete picture of a man's family hkc a net,.vork ,vhtch, 1f 1t be dra\vn com.. is pletcly even for only a fc,v gcncrattons, 1s almost mex.. trzcabJe Of course the� nothing to prevent any ind1 .. JS vidu.al from selecting 1n that net\vork and dra,-ving more . • • • • • • • • • • • • • • • ,. n� �: l! l! A! A� A! l� �: lt l! Af �: A fig t heavily the hncs which concern him unmcdiately, the blood hnes, but the personal pattern thus abstracted from the whole ne tworJ.. 1s of no interest except to rum.self Now the fihat1on of ideas nccessar1ly more comph• lS cated for the biological pattern rigorously luruted by the t JS rule that each 1nd1vidual has nvo parents, neither more nor less, \vhdc each idea may cc::sult from the f of more us1on than nvo others, or on the contrary may be the fruit of a kind of parthenogenesis 'Whenever the rustorian tries to relate the hLStorv of a single group of 1deas he 1s obliged to abstract one pattern from a networl of endless complexity, SECRET HISTORY 7 ands ucahna bstrahcot,ivoenv,c r iinmtt aeybr eei,ss t ing ahvaayrsb ittroaa d reyg ree. The stuodfsy p ecbiraaln cohfme ast hemoarto ifsc pse cial mathemaitdieciaavssle ruys efuilht,e lfoponsrte o u nder statnhdo psaer tiicduelmaaosrr dee epbluyit,ts hounlodt bea llot,ovc eodn fushei sotuorpr eircsaple cTthiehv ies. torimaunst tr tyo k eeipnm intdh ceh ronolsougcicceasl sionno otf t hiosrt haitd eaab,s trfarcottemhd re e sbtu,t oft hmea iind easo,ft haeilmnlt hemiurt uraell ationships andi nt hediirv ecrosnen ec,vit tiho ntsh e rest of life. Manyt imheasv Iec ompatrhehedi stoofsry c ie,nvciet h a� crehti sttohryae,c cooufan d te veloptmaekniptnl ga ce mysteriiontu hsdela yr kn,evshsti,hl meea joroifpt eyo ple armeo rien teraensdmt oerdie m mediaaffteeclbtyy e tdh e evenhtasp penionntg h bea ttloerfi eftlohdre u omrb, yt he vicissoiftt huedoie,rsrns elavnedfs a milFioesrso .c ieties, eveansf oirn diviodnumeau lsmst,a kaes hadrips tinction bet\vetehnte h in,gvsh iacrhte h e muorsgtea nntdt hose whiacrhte h meo sitm portTahnetts.he i ngnso btya arney meanst hsea meT.h em osutr gennetc esissti olt iyvt eo, remaailni tvheai,ts ,e atstol, e teop ,hb aep ptyop, r ocreate childarnedon b,t asienc ufroiortn yef 'asm iTlhya.mt e ans physiobluosgyi,n aensdss p,o ratn,do fteenno uwgahr . Hov1evtehrme,o sitm portthainantrg es tnoso att oinsef'ys physiolnoegeidbcsua,ttl oi ncretahcseue l thuerrail tage ,vhihcabhse ebne queattohu esT.dh eu rgetnhti nagrse obvieonuosu agnhd,m en'esff orttoos b tatihnefi ml tlh e whohlie stopriicctauolrn ece;a h na rdsleayen ytheilnsge . Yeatl tlh tei mseo mmee np ursiunte h dea rknseescsr,e tly, thfeu lfilmtehnetii nrote fec ltludeasli reosfh uamanndi ty's highpeusrtp ose. Itfh hei stoofsr cyi einascs eec hriestt tohretynh, e history ofm athemaitsdi ocusbs leyc raes te,c wrietth ai sne cret, fotrh ger owotfmh a themaitusi ncksn onwonot n ltyot he
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