Celebratio Mathematica

Marshall Harvey Stone

Marshall Stone and
the internationalization of
the American mathematical research community

by Karen Hunger Parshall

The year 1938 was one of cel­eb­ra­tion and self-con­grat­u­la­tion with­in the Amer­ic­an math­em­at­ic­al re­search com­munity. Fifty years earli­er, four Columbia gradu­ate stu­dents and two Columbia fac­ulty mem­bers had met in New York City in or­der “to es­tab­lish a math­em­at­ic­al so­ci­ety for the pur­pose of pre­serving, sup­ple­ment­ing, and util­iz­ing the res­ults of their math­em­at­ic­al stud­ies” ([e2], page 4). With­in two dec­ades, this ex­tremely mod­est, loc­al en­ter­prise had grown in­to a na­tion­al or­gan­iz­a­tion that sup­por­ted two pub­lic­a­tions, its Bul­let­in star­ted in 1891 and its Trans­ac­tions first pub­lished in 1900, as well as re­gion­al sec­tions in the mid­w­est, on the west coast, and in the south­w­est ([e22], pp. 266–268 and 401–415). By 1938, the lead­er­ship of that or­gan­iz­a­tion had re­cog­nized that the time was ripe both for chron­ic­ling its his­tory and for show­cas­ing the con­tri­bu­tions to the store of math­em­at­ic­al know­ledge made by the mem­bers of the vi­brant and self-sus­tain­ing na­tion­al com­munity of re­search­ers that it defined. To these ends, the Com­mit­tee on Pub­lic­a­tions of the Amer­ic­an Math­em­at­ic­al So­ci­ety (AMS) ar­ranged for the pub­lic­a­tion of both the his­tory of the So­ci­ety’s first fifty years [e2] and a volume that aimed — by en­list­ing some of Amer­ica’s lead­ing math­em­aticians to tell the tales — “to re­veal what has been ac­com­plished in Amer­ica since the found­ing of the So­ci­ety, and … to ac­quaint math­em­aticians with cur­rent prob­lems and re­search in many fields” ([e13], pre­face). The lat­ter volume, the Semi­centen­ni­al Ad­dresses of the Amer­ic­an Math­em­at­ic­al So­ci­ety, con­tained top­ic­al es­says on al­gebra, al­geb­ra­ic as­pects of the the­ory of dif­fer­en­tial equa­tions, har­mon­ic ana­lys­is, the cal­cu­lus of vari­ations, geo­metry, to­po­logy, Di­rich­let prob­lems in har­mon­ic ana­lys­is, and hy­dro­dynam­ics, all of which em­phas­ized — subtly or not so subtly — Amer­ic­an con­tri­bu­tions against the back­drop of ma­jor achieve­ments in the vari­ous fields.

There was, however, noth­ing subtle about the boos­t­er­ist­ic in­tent of the volume’s cul­min­at­ing es­say. There, George Dav­id Birk­hoff, the mid-cen­tury doy­en of Amer­ic­an math­em­at­ics, self-con­sciously took on “Fifty Years of Amer­ic­an Math­em­at­ics” and told a story of poin­tedly Amer­ic­an ac­com­plish­ments across many math­em­at­ic­al areas, es­pe­cially, in his view, in his own area of ana­lys­is [e1].1 As Birk­hoff and his fel­low con­trib­ut­ors to the semi­centen­ni­al volume saw it, in fifty years Amer­ic­an math­em­at­ics had put it­self on the map; that is, in fifty years Amer­ic­an math­em­aticians had suc­ceeded in be­com­ing fully com­pet­it­ive with those European coun­ter­parts who had for so long been con­sidered the math­em­at­ic­al stand­ard-bear­ers. An Amer­ic­an math­em­at­ic­al re­search com­munity had reached ma­tur­ity.

In light, then, of the suc­cesses so proudly high­lighted in 1938, it is per­haps not sur­pris­ing that some with­in that ma­ture na­tion­al com­munity sensed that the mo­ment was pro­pi­tious for fuller Amer­ic­an par­ti­cip­a­tion in the de­vel­op­ment of math­em­at­ics in­ter­na­tion­ally, es­pe­cially giv­en the in­flux in­to the United States of math­em­at­ic­al tal­ent from Europe that had be­gun in the 1930s.2 For these out­ward-look­ing Amer­ic­an math­em­aticians, such par­ti­cip­a­tion meant not only the con­tinu­ation and cre­ation of re­search agen­das in which math­em­aticians from many na­tions could and would par­ti­cip­ate from a tech­nic­al point of view, but also the cre­ation of so­cial and in­sti­tu­tion­al ties that would foster a glob­al­ized com­munity of math­em­aticians united in a com­mon set of val­ues and goals, an in­ter­na­tion­al math­em­at­ic­al com­munity,3 but the agenda was not purely in­ter­na­tion­al. That cadre wanted to es­tab­lish the United States as a lead­er in shap­ing an in­ter­na­tion­al — as op­posed to a European or a West­ern or an East­ern — math­em­at­ic­al world. If Europe, and es­pe­cially Ger­many, had been the math­em­at­ic­al stand­ard-bear­er of the late nine­teenth and early twen­ti­eth cen­tur­ies, then the United States was poised, un­der ap­pro­pri­ately tal­en­ted and en­er­get­ic act­iv­ists, to as­sume that role in the mid-twen­ti­eth cen­tury. Per­haps chief among those Amer­ic­an math­em­aticians who worked so ef­fect­ively and so self-con­sciously to­ward this end at mid-cen­tury was Mar­shall Har­vey Stone.

The making of an American mathematical leader

Mar­shall Stone was born in New York City on 8 April 1903 to Har­lan Fiske and Ag­nes Har­vey Stone.4 By the time of Mar­shall’s birth, Har­lan Stone had not only es­tab­lished him­self in the prom­in­ent Wall Street law firm of Wilmer and Can­field but had also taken on an ad­junct teach­ing post at his — {alma ma­ter}, the Columbia Law School. He juggled these two com­pet­ing in­terests un­til 1905, when the de­mands of a busy prac­tice forced him to give up teach­ing. By 1910, however, Columbia had suc­ceeded in call­ing him back for the in­flu­en­tial post of Dean of the Law School a po­s­i­tion he held un­til 1923 when, tired of aca­dem­ic polit­ics and fed up with ad­min­is­tra­tion, he ac­cep­ted the head­ship of the lit­ig­a­tion de­part­ment back at his old law firm. He held this post in private prac­tice for only one year. In 1924, he was ap­poin­ted At­tor­ney Gen­er­al of the United States, then As­so­ci­ate Justice of the U.S. Su­preme Court a year later in 1925, and fi­nally Chief Justice of the U.S. Su­preme Court in 1941.5 Mar­shall Stone thus grew up in a priv­ileged, edu­ca­tion­ally minded, and polit­ic­ally ex­tremely well-con­nec­ted fam­ily.

The young Stone pro­gressed rap­idly as an in­tel­lec­tu­al, en­ter­ing Har­vard in 1919 at the young age of six­teen, gradu­at­ing summa cum laude in 1922, and earn­ing his Ph.D. un­der G. D. Birk­hoff in 1926 for a thes­is on “Or­din­ary Lin­ear Ho­mo­gen­eous Dif­fer­en­tial Equa­tions of Or­der \( n \) and the Re­lated Ex­pan­sion Prob­lems”. A string of po­s­i­tions — at Columbia, Har­vard, and Yale — promp­ted Stone’s fath­er to write to him in 1932 that “you … are get­ting to the time in life when you should not be mak­ing many more changes, and you will give ser­i­ous con­sid­er­a­tion this time to the prob­lem, where you are go­ing to spend the rest of your life”.6 Ap­par­ently tak­ing his fath­er’s ad­vice, Stone fi­nally settled again at Har­vard in 1933, be­com­ing a full pro­fess­or there in 1937 and con­tinu­ing in that po­s­i­tion un­til his move to chair the De­part­ment of Math­em­at­ics at the Uni­versity of Chica­go in 1946.

Mar­shall Stone’s peri­pat­et­ic early ca­reer in no way af­fected his abil­ity to gen­er­ate first-rate math­em­at­ic­al re­search. His earli­est work, like his dis­ser­ta­tion, was very much in the Birk­hof­fi­an ana­lyt­ic tra­di­tion, one fo­cused on or­tho­gon­al ex­pan­sions and es­pe­cially on ex­pan­sions in terms of ei­gen­func­tions of lin­ear dif­fer­en­tial op­er­at­ors. By 1929, however, Stone had moved in­to the ab­stract the­ory of un­boun­ded self-ad­joint op­er­at­ors in Hil­bert space. This new work cul­min­ated in 1932 with the pub­lic­a­tion by the Amer­ic­an Math­em­at­ic­al So­ci­ety of his massive treat­ise, Lin­ear Trans­form­a­tions in Hil­bert Space and Their Ap­plic­a­tions to Ana­lys­is [1], [8], a book that has been deemed “one of the great clas­sics of twen­ti­eth-cen­tury math­em­at­ics” ([e32], page 17). In it, Stone suc­ceeded in ex­tend­ing Dav­id Hil­bert’s spec­tral the­or­em from bounded to un­boun­ded op­er­at­ors. As George Mackey put it in his ac­count of Stone’s math­em­at­ic­al ac­com­plish­ments, “[t]his ex­ten­sion was made ne­ces­sary by the prob­lem of mak­ing math­em­at­ic­ally co­her­ent sense of the newly dis­covered re­fine­ment of clas­sic­al mech­an­ics known as quantum mech­an­ics. Here an im­port­ant part of the prob­lem was dis­cov­er­ing the ‘cor­rect’ defin­i­tion of self-ad­joint­ness for un­boun­ded op­er­at­ors. This cor­rect defin­i­tion is rather del­ic­ate and the ex­ten­sion of the older the­ory of Hil­bert and oth­ers was a ma­jor task” ([e32], page 18). By the mid-1930s, Stone had shif­ted areas again to ex­plore Boolean al­geb­ras and their links both to to­po­logy and to the the­ory of rings. Again, in Mackey’s view, “[t]he dis­cov­ery of these con­nec­tions has had sig­ni­fic­ant con­sequences for all three sub­jects” ([e32], page 19), among them, Stone’s proof in 1948 of the so-called Stone–Wei­er­strass The­or­em, which gen­er­al­ized Wei­er­strass’s nine­teenth-cen­tury res­ult on ap­prox­im­at­ing ar­bit­rary con­tinu­ous func­tions on a fi­nite in­ter­val uni­formly by poly­no­mi­als [4], [3]. The depth and breadth of Stone’s re­search had already been re­cog­nized a dec­ade earli­er in 1938 with his elec­tion to the Na­tion­al Academy of Sci­ences at the age of only thirty-five.

Stone’s in­volve­ment in the Amer­ic­an math­em­at­ic­al scene was not lim­ited to his re­search, however. Like his ad­viser, he was an act­ive par­ti­cipant in the broad­er or­gan­iz­a­tion­al goals of the Amer­ic­an math­em­at­ic­al re­search com­munity.7 In par­tic­u­lar, Stone served in the 1930s on the ed­it­or­i­al boards of the three lead­ing Amer­ic­an re­search journ­als, the Trans­ac­tions of the Amer­ic­an Math­em­at­ic­al So­ci­ety, the Amer­ic­an Journ­al of Math­em­at­ics, and the An­nals of Math­em­at­ics. Moreover, from 1936 to 1942 he was an act­ive mem­ber of the gov­ern­ing Coun­cil of the AMS and from 1936 un­til 1939 a key mem­ber of the or­gan­iz­ing com­mit­tee for what would have been an In­ter­na­tion­al Con­gress of Math­em­aticians (ICM) in Cam­bridge, Mas­sachu­setts in 1940, the first to have been held in the United States since the of­fi­cial in­sti­tu­tion of the ICMs in Zürich in 1897.8 It was in the lat­ter ca­pa­cit­ies that Stone began to fo­cus on in­ter­na­tion­al re­la­tions in math­em­at­ics, sparked per­haps by the trips abroad he had taken with his fam­ily from the time he was a boy, by his own first-hand ex­per­i­ences as a par­ti­cipant at an in­ter­na­tion­al to­po­logy con­fer­ence held in Mo­scow in 1935 ([e10], page 540), and by the lar­ger Amer­ic­an de­bate over isol­a­tion­ism versus in­ter­na­tion­al­ism that re­sumed in earn­est in the late 1930s and early 1940s [e11].9

Looking beyond the American mathematical community

As a mem­ber both of the AMS Coun­cil and of the ICM or­gan­iz­ing com­mit­tee, Stone in­creas­ingly grappled with the ex­i­gen­cies of try­ing to foster free math­em­at­ic­al in­ter­change in an ever-worsen­ing in­ter­na­tion­al polit­ic­al arena. In Feb­ru­ary of 1940, for ex­ample, after it had be­come clear that plans for the ICM would have to be put on hold for the in­def­in­ite fu­ture due to the polit­ic­al situ­ation in Europe, Stone draf­ted a let­ter to the Coun­cil of the AMS that in­cluded an “Ap­peal from the Amer­ic­an Math­em­at­ic­al So­ci­ety to sis­ter sci­entif­ic or­gan­iz­a­tions in all parts of the world”. That ap­peal asked not only for aid in ”the pre­ser­va­tion of the cul­tur­al val­ues and the ef­fect­ive or­gans of sci­entif­ic re­search throughout the world dur­ing these days of de­struc­tion” but also for help “es­pe­cially for those sci­ent­ists who, by the for­tunes of war, may fall pris­on­er or may come un­der new flags, to the end that their in­di­vidu­al suf­fer­ings may be mit­ig­ated and their sci­entif­ic activ­ity con­tin­ued to the be­ne­fit of all men”.10 The Coun­cil voted un­an­im­ously to dis­trib­ute Stone’s ap­peal and sent it on to some thirty-nine math­em­at­ic­al so­ci­et­ies in­ter­na­tion­ally.

By the end of 1940, however, re­sponses had only been re­ceived from Ger­many and Switzer­land. Writ­ing on be­half of the Deutsche Math­em­atiker-Ver­ein­i­gung, Wil­helm Süss ex­pressed the hope “that des­pite the em­phat­ic wishes for war of our former en­emy, Eng­land, the war can soon be brought to an end without too much in­jury to the sci­entif­ic stand­ards or to the sav­ants in the war zone”.11 The reply from Switzer­land was more prag­mat­ic and more im­me­di­ate. Soph­ie Pic­card, as a mem­ber of both the Swiss and Pol­ish math­em­at­ic­al so­ci­et­ies, urged the Amer­ic­an math­em­at­ic­al com­munity to do whatever it could to se­cure entry visas “for the dur­a­tion of the war” for the two Pol­ish math­em­aticians, Waclaw Si­er­piński and Kazi­mierz Kur­atowski, since “for polit­ic­al reas­ons, the Swiss au­thor­it­ies do not grant entry visas in­to Switzer­land to Poles ex­cept when they have visas for oth­er coun­tries where they are per­mit­ted to go and settle”.12 Of course, as then AMS Sec­ret­ary Ro­land G. D. Richard­son, ex­plained in a reply on 22 Novem­ber 1940, the Amer­ic­an math­em­at­ic­al com­munity was already hard at work try­ing to place dis­placed schol­ars. “[T]here are”, he noted, “ap­prox­im­ately sev­enty-five refugee math­em­aticians in this coun­try, some of whom per­haps fifty have ac­quired some sort of per­man­ent po­s­i­tion”. Yet, he ad­ded, “[w]hile this en­riches the cul­ture of this coun­try, it does, as you will read­ily un­der­stand, raise very con­sid­er­able dif­fi­culties. Our young men are not happy over this situ­ation”.13 For his part, Stone was clearly frus­trated by the un­der­whelm­ing re­sponse to his ap­peal, an ini­ti­at­ive that he viewed as vi­tal for math­em­aticians in­ter­na­tion­ally. By year’s end, he had sought and re­ceived per­mis­sion from the AMS both to draft a reply to Süss, even though he did “not ex­pect any im­me­di­ate res­ults from con­tinu­ing the cor­res­pond­ence”, and to “eli­cit some re­sponse from the Lon­don Math­em­at­ic­al So­ci­ety”. In his view, his “Eng­lish col­leagues ha[d] a def­in­ite ob­lig­a­tion in that mat­ter and … we should ex­pect an ac­know­ledg­ment at least”.14 By the sum­mer of 1941 with the United States’s entry in­to the war and with the ef­forts of Stone and oth­ers, such as AMS Pres­id­ent (in 1941 and 1942) Mar­ston Morse, to mo­bil­ize the Amer­ic­an math­em­at­ic­al com­munity in the ser­vice of the coun­try, more broadly in­ter­na­tion­al ini­ti­at­ives like the “ap­peal” were forced to take a second seat.15 Nev­er­the­less, when Stone him­self as­sumed the pres­id­ency of the AMS in Janu­ary of 1943 for the two-cal­en­dar-year term from 1943 to 1944, his agenda for the Amer­ic­an math­em­at­ic­al com­munity in­cluded, not sur­pris­ingly, great­er vis­ib­il­ity for Amer­ica’s math­em­aticians in the war ef­fort and in­creased activ­ity in ap­plied math­em­at­ics dir­ec­ted to­ward spe­cif­ic war­time prob­lems, but also the main­ten­ance and en­hance­ment of in­ter­na­tion­al math­em­at­ic­al con­tacts in so far as the war al­lowed. The lat­ter ob­ject­ive fo­cused — as did Amer­ic­an dip­lo­mat­ic ef­forts of the early 1940s such as the At­lantic Charter signed by Frank­lin Roosevelt and Win­ston Churchill in Au­gust of 1941 and the De­clar­a­tion of United Na­tions signed in Janu­ary of 1942 by the United States, Great Bri­tain, the USSR, China, and the rep­res­ent­at­ives of some twenty-two oth­er coun­tries — on plan­ning ahead for the post­war world.16 For Stone, as for the na­tion at large, Lat­in Amer­ica rep­res­en­ted an area both ripe for con­tact and re­l­at­ively ac­cess­ible giv­en the war­time theat­ers of activ­ity in Europe and the Pa­cific. Moreover, the coun­tries in the Amer­icas had been a fo­cal point of Amer­ic­an for­eign policy at least since 1933.

The American mathematical community and U.S. foreign policy: Mathematical good neighbors in Latin America

When Roosevelt was elec­ted Pres­id­ent of the United States in 1932, the coun­try was in the depths of an eco­nom­ic de­pres­sion. Not sur­pris­ingly, the new pres­id­ent de­voted al­most all of the just-over-1800-word in­aug­ur­al ad­dress he de­livered on 4 March 1933 to do­mest­ic is­sues. The fifty-four words of the speech that were not fo­cused in­ward, however, served to shape the coun­try’s for­eign policy throughout his un­pre­ced­en­ted twelve years in the pres­id­ency. Roosevelt pledged that, “[i]n the field of world policy”, he would “ded­ic­ate this na­tion to the policy of the good neigh­bor — the neigh­bor who res­ol­utely re­spects him­self and, be­cause he does so, re­spects the rights of oth­ers — the neigh­bor who re­spects his ob­lig­a­tions and re­spects the sanc­tity of his agree­ments in and with a world of neigh­bors” ([e5], page 3). Just over a month later on 12 April in a speech giv­en be­fore the Pan-Amer­ic­an Uni­on, Roosevelt made ex­pli­cit that among those “good neigh­bors” would be the coun­tries of Lat­in Amer­ica. As he put it, “[y]our Amer­ic­an­ism and mine must be a struc­ture built of con­fid­ence, ce­men­ted by a sym­pathy which re­cog­nizes only equal­ity and fra­tern­ity. It finds its source and be­ing in the hearts of men and dwells in the temple of the in­tel­lect” ([e5], pp. 4–5).

The U.S. gov­ern­ment made mani­fest its no­tion of the “good neigh­bor” al­most im­me­di­ately through trade, through its policy of non-in­ter­ven­tion in Lat­in Amer­ic­an polit­ic­al af­fairs, and through its pro­mo­tion of “a com­mon de­fense against out­side threats” to North, Cent­ral, and South Amer­ic­an in­terests ([e5], page 124). Con­com­it­antly, some U.S. sci­ent­ists came to em­brace Roosevelt’s vis­ion in the form of inter-Amer­ic­an in­tel­lec­tu­al par­ti­cip­a­tion and co­oper­a­tion. With the fin­an­cial aid and en­cour­age­ment of private found­a­tions — such as those es­tab­lished by oil mag­nate John D. Rock­e­feller and in­dus­tri­al­ist Si­mon Gug­gen­heim — as well as with gov­ern­ment­al sup­port after the es­tab­lish­ment in 1940 of the Of­fice of Inter-Amer­ic­an Af­fairs (OIAA), they act­ively fostered sci­entif­ic re­la­tions throughout the Amer­icas in the late 1930s and in­to the 1940s.17 Among the earli­est sci­entif­ic “good neigh­bors” were the as­tro­nomer Har­low Shap­ley, the ex­per­i­ment­al physiolo­gist Wal­ter Can­non, and the math­em­atician George D. Birk­hoff, all of Har­vard Uni­versity ([e21], es­pe­cially, pp. 467–522).18 In par­tic­u­lar, Birk­hoff ex­pli­citly cast his in­ten­tions of es­tab­lish­ing math­em­at­ic­al li­ais­ons with Lat­in Amer­ica in the con­text of broad­er Amer­ic­an for­eign policy. In a let­ter on 21 Janu­ary 1941 to Henry Moe, sec­ret­ary of the Gug­gen­heim Found­a­tion and head of the Com­mit­tee of Inter-Artist­ic and Cul­tur­al Re­la­tions of the OIAA, Birk­hoff offered the opin­ion “that Pres­id­ent Roosevelt has been the first Amer­ic­an Pres­id­ent to real­ize the ex­traordin­ary im­port­ance and value to us, as well as to them, of a closer cul­tur­al and eco­nom­ic rap­proche­ment between us. If I do go [to Lat­in Amer­ica], I should there­fore sed­u­lously aim to co­oper­ate with the pur­poses which our gov­ern­ment has in mind in unit­ing the demo­cra­cies of the west­ern world.”19 Birk­hoff’s trip did ma­ter­i­al­ize a year later in the spring of 1942, and he suc­ceeded both in gain­ing an over­view of math­em­at­ic­al Lat­in Amer­ica and in for­ging ties with math­em­aticians to the south.20 Fol­low­ing his re­turn, he strongly en­cour­aged his former Har­vard stu­dent and then Har­vard col­league, Mar­shall Stone, to con­tin­ue the ex­ample of math­em­at­ic­al good-neigh­bor­li­ness with a trip of his own. As a math­em­atician already con­vinced that act­ive in­ter­na­tion­al­iz­a­tion was key to the vi­tal­ity of his field and as the Pres­id­ent-elect of the Amer­ic­an Math­em­at­ic­al So­ci­ety in 1942, Stone was a nat­ur­al choice for Birk­hoff to hand­pick as his suc­cessor in Lat­in Amer­ica. Stone re­solved to use his new lead­er­ship po­s­i­tion with­in the Amer­ic­an math­em­at­ic­al com­munity to help real­ize the ideal of the math­em­at­ic­al good neigh­bor more fully.

Plans co­alesced quickly. By 10 June 1943, Stone was writ­ing to his wife from New York City, where he had been meet­ing with Henry Moe in his ca­pa­city as a func­tion­ary in the Of­fice of Inter-Amer­ic­an Af­fairs. Moe, who had co­ordin­ated and un­der­writ­ten Birk­hoff’s 1942 Lat­in Amer­ica trip un­der the ae­gis of the OIAA, played the same role for Stone in 1943, se­cur­ing war­time air pas­sage for him from Miami to Lima, Peru, on 13 June and ar­ran­ging his it­in­er­ary from there to Bolivia and Ar­gen­tina with a sci­entif­ic side trip to Ur­uguay and an ex­cur­sion to Paraguay and Brazil to view the Iguassu Falls.21 Al­though Stone de­livered a two-month-long course of lec­tures on Boolean al­geb­ras and their con­nec­tions to to­po­logy in Buenos Aires — his home base throughout the months of Ju­ly, Au­gust, Septem­ber, and early Oc­to­ber — he also gave spe­cial lec­tures by in­vit­a­tion in the vari­ous cit­ies he vis­ited, uni­ver­sally wel­comed and cel­eb­rated as the Pres­id­ent of the Amer­ic­an Math­em­at­ic­al So­ci­ety. In Lima, for ex­ample, where he so­journed in mid-June and was made Doc­tor hon­oris causa of the Uni­ver­sid­ad May­or de San Mar­cos ([e7], page 138), Stone lec­tured in Span­ish on “Al­gebra and Lo­gic”, high­light­ing the role of Boolean al­geb­ras in con­nect­ing these two fields. In La Plata, Ar­gen­tina, later in his stay, he took as his top­ic “Math­em­at­ics in Mod­ern Sci­ence and Tech­no­logy” and pushed the same point in a Lat­in Amer­ic­an con­text that he had been hon­ing while a ci­vil­ian con­tract­or, first to the Navy De­part­ment and then to the War De­part­ment in Wash­ing­ton, namely, that math­em­at­ics has a crit­ic­al role to play in the mod­ern world. These talks, to­geth­er with his more spe­cial­ized series of lec­tures, com­prised the form­al, in­tel­lec­tu­al com­pon­ent of his vis­it and were re­por­ted on by the Span­ish math­em­atician in ex­ile, Ju­lio Rey Pas­tor, in the pages of the Rev­ista de la Unión Matemática Ar­gen­tina later in 1943 [e7].22 In ad­di­tion to lec­tur­ing, however, Stone also met and talked with stu­dents and fac­ulty and par­ti­cip­ated in the meet­ing of the Unión Matemática Ar­gen­tina on 10 Ju­ly 1943 [e6].

As a res­ult of his ex­per­i­ences, Stone, like Birk­hoff, came away with dis­tinct im­pres­sions of the Lat­in Amer­ic­an math­em­at­ic­al scene. He opened the six­teen-page, typescript re­port he sub­mit­ted to Henry Moe on 13 April 1944 by first re­flect­ing broadly on “our cul­tur­al re­la­tions with Lat­in Amer­ica”, a top­ic he con­fessed to be­ing “very deeply in­ter­ested in” and on which he had “a num­ber of ideas”.23 In light of the fact that Moe’s of­fice dealt with cul­tur­al re­la­tions with Lat­in Amer­ica in the broad­est sense, Stone first made clear those areas in which he felt inter-Amer­ic­an con­tact would be most fruit­ful. “It seems to me”, he wrote, “that the great need in Lat­in Amer­ica is for sci­entif­ic and tech­no­lo­gic­al de­vel­op­ment, and that we on our side have far more to give in the sci­entif­ic and tech­no­lo­gic­al fields than in most oth­ers”. In an­oth­er echo of the line of ar­gu­ment­a­tion for math­em­at­ics that he had honed in Wash­ing­ton, Stone ad­ded that “[i]t goes without say­ing that sound tech­no­lo­gic­al de­vel­op­ment is not without sim­ul­tan­eous de­vel­op­ment in fun­da­ment­al sci­ence”.

The prob­lem, of course, was how best to foster such inter-Amer­ic­an tech­no­lo­gic­al and sci­entif­ic in­ter­ac­tion in light of the “good neigh­bor” policy. Stone made his case with polit­ic­al savvy. “If one be­lieves, as I do”, he stated, “that the sound­est re­la­tions between na­tions will res­ult from mu­tu­al as­sist­ance without thought of profit or the cre­ation of per­man­ent ob­lig­a­tions, then one can con­clude that any­thing we can do to pro­mote sci­ence and tech­no­logy in Lat­in Amer­ica will con­trib­ute in the long run to the good of all. It is ex­ceed­ingly im­port­ant”, he con­tin­ued, “… that whatever the United States un­der­takes should be done in the spir­it of help­ful­ness and not at all in the hope of in­flu­en­cing the in­tern­al or ex­tern­al polit­ics of the vari­ous coun­tries to which we give as­sist­ance. It is also of the very first im­port­ance that every step we take should be de­signed to dis­cov­er and cul­tiv­ate self re­li­ance in our Lat­in Amer­ic­an fel­lows”. This goal could be ac­com­plished re­l­at­ive to sci­ence in gen­er­al and math­em­at­ics in par­tic­u­lar in at least two ways in Stone’s opin­ion.

First, bar­ri­ers should be broken down between na­tions to al­low for the “free ex­change of in­tel­lec­tu­al activ­ity at pro­fes­sion­al and uni­versity levels”. This would not only al­low those trained in one Lat­in Amer­ic­an coun­try to move more eas­ily to an­oth­er, but also foster great­er cross-fer­til­iz­a­tion of ideas. Second, Stone con­ten­ded that “some­what more can be ac­com­plished for the time be­ing”, in the case of math­em­at­ics, “by bring­ing to the United States on trips of study and in­vest­ig­a­tion a great­er num­ber of Lat­in Amer­ic­ans in­ter­ested in math­em­at­ics than we send of North Amer­ic­an math­em­aticians to Lat­in Amer­ica”. Al­though he had very much profited from his trip to and ex­per­i­ences in Lat­in Amer­ica, Stone well knew that this had been pre­cisely the strategy that North Amer­ic­an stu­dents and pro­fess­ors had ad­op­ted re­l­at­ive to Ger­many from the clos­ing dec­ades of the nine­teenth cen­tury through the out­break of World War I.24 They had traveled abroad for their high-level math­em­at­ic­al train­ing, they had im­por­ted key as­pects of the Ger­man, and es­pe­cially Prus­si­an, edu­ca­tion­al sys­tem in­to the United States, and, by the out­break of World War II, they had suc­ceeded in es­tab­lish­ing a math­em­at­ic­al com­munity com­pet­it­ive on the in­ter­na­tion­al math­em­at­ic­al scene.25 What Ger­many had been to the United States at the turn of the twen­ti­eth cen­tury, the United States could be to Lat­in Amer­ica at mid-cen­tury.26

Stone’s platforms for the internationalization of mathematics

Dur­ing his pres­id­ency of the AMS, Stone worked to en­cour­age not only U.S.–Lat­in Amer­ic­an con­tacts but also broad­er in­ter­na­tion­al math­em­at­ic­al co­oper­a­tion. In Oc­to­ber 1944, for ex­ample, he re­ceived a re­quest from Fre­d­er­ick Sil­ber of the Of­fice of War In­form­a­tion to make “a col­lec­tion of re­print art­icles se­lec­ted from ap­pro­pri­ate journ­als” to send to math­em­aticians in France anxious, fol­low­ing the lib­er­a­tion of Par­is in Au­gust of 1944, to re­sume their math­em­at­ic­al re­searches.27 Al­though Stone him­self was un­able to un­der­take the task ow­ing to the press of his own work with­in the War De­part­ment, he sug­ges­ted that “[t]he most nat­ur­al way for French math­em­aticians to sat­is­fy their curi­os­ity would be for them to re-es­tab­lish dir­ect con­tacts with Amer­ic­an math­em­aticians, with many of whom they have old per­son­al re­la­tions, with a view to ob­tain­ing our re­cent math­em­at­ic­al lit­er­at­ure and open­ing up in­di­vidu­al sci­entif­ic cor­res­pond­ence. The soon­er the obstacles to in­aug­ur­at­ing this state of af­fairs can be cleared away, the hap­pi­er all con­cerned will be!”28 Giv­en that more ground­work might be needed in or­der for this more nat­ur­al course of events to un­fold, Stone pro­posed that “[i]n the mean­time … the best and most ef­fi­cient way to ac­quaint French math­em­aticians with what has been go­ing on in the out­side world since 1940 would be to put in­to their hands enough back volumes of Math­em­at­ic­al Re­views … to sup­ply each of the cent­ral math­em­at­ic­al lib­rar­ies of France at­tached to uni­versit­ies or sci­entif­ic in­sti­tutes”. Moreover, he offered, “[i]f you can provide one or two cu­bic yards of ex­press ship­ping space, I am sure that you will find our So­ci­ety will­ing and able to coöper­ate in oth­er re­spects”.

Stone’s over­tures on be­half of the AMS were not lim­ited to the French. On 8 June 1944, AMS Sec­ret­ary J. R. Kline let him know that the AMS had just re­ceived “a cable­gram of greet­ings from the So­viet sci­ent­ists”,29 and wondered wheth­er “it would be prop­er for you and me to pre­pare a friendly cable­gram of greet­ings and good wishes” in re­turn and to “ex­press the hope that with­in the near fu­ture it will be pos­sible to re­sume nor­mal sci­entif­ic re­la­tions and to have con­fer­ences on sub­jects of vi­tal math­em­at­ic­al im­port­ance”. Stone replied un­equi­voc­ally. “By all means”, he wrote, “reply to the Rus­si­an sci­ent­ists in the spir­it you sug­gest — em­phas­iz­ing our de­sire for cor­di­al sci­entif­ic re­la­tions in peace­time”.30 A year later, Stone and Kline were still en­gaged in es­tab­lish­ing in­ter­na­tion­al math­em­at­ic­al con­tacts, Kline from his po­s­i­tion as AMS Sec­ret­ary, but Stone as chair of the AMS’s War Policy Com­mit­tee and no longer as Pres­id­ent of the AMS.31 On 23 June 1945, Kline urged Stone to “see what gov­ern­ment­al as­sist­ance can be se­cured in the re­new­al of con­tacts with math­em­aticians in the formerly oc­cu­pied coun­tries”.32 “I ima­gine”, he con­tin­ued, “the prob­lem will be more dif­fi­cult in con­nec­tion with the Pol­ish math­em­aticians than with the Dutch, Nor­we­gi­ans, and Danes. This is an im­port­ant item and should be care­fully dis­cussed by the War Policy Com­mit­tee soon”. Stone whole­heartedly agreed. Even though he was ex­tremely busy, he replied that “I think if I can get some pro­gress … on the ex­ten­sion of our for­eign re­la­tions dur­ing my off mo­ments I shall be con­tent”.33 As Stone had wanted the Amer­ic­an Math­em­at­ic­al So­ci­ety to take the lead in 1940 with his “Ap­peal … to sis­ter sci­entif­ic or­gan­iz­a­tions in all parts of the world”, so he saw the AMS play­ing a lead­ing role in help­ing the math­em­aticians of France, Po­land, and else­where re­cov­er from a war that had been waged on their soils.34 Stone and oth­ers with­in the AMS did not em­brace their in­ter­na­tion­al­ist agenda in a va­cu­um. Throughout World War II, in­ter­na­tion­al­ists in Amer­ic­an polit­ics such as Re­pub­lic­an pres­id­en­tial can­did­ate (in 1940) Wendell Willkie and Demo­crat­ic con­gress­man and later sen­at­or J. Wil­li­am Ful­bright pressed an agenda dir­ec­ted to­ward a post­war world of in­ter­na­tion­al co­oper­a­tion. Where­as the League of Na­tions, which was formed in the af­ter­math of World War I without the ad­her­ence of the United States, had failed to pre­vent World War II, the United Na­tions chartered in San Fran­cisco in June of 1945 as a res­ult of much Amer­ic­an in­ter­na­tion­al­ist agit­a­tion and spade­work would serve to main­tain world peace in the af­ter­math of World War II. It was in­cum­bent upon the United States, moreover, as a world lead­er to work to ef­fect this new world or­der [e11]. As with the coun­try as a whole, so with the coun­try’s math­em­aticians, at least that is how Stone and oth­ers saw it.

After the war, Stone con­tin­ued his in­ter­na­tion­al­ist agenda both with­in the AMS and from the po­s­i­tion he as­sumed in 1946 as chair of the De­part­ment of Math­em­at­ics at the Uni­versity of Chica­go. One of the trans­form­a­tion­al de­part­ments in the early his­tory of re­search-level math­em­at­ics in the United States ([e22], pp. 261–426), the Chica­go Math­em­at­ics De­part­ment of the in­ter­war years was pro­duct­ive, if no longer as much on the cut­ting edge as it had been at the turn of the cen­tury. Le­onard Eu­gene Dick­son and A. Ad­ri­an Al­bert main­tained high pro­files in al­gebra, but the pro­gram in the cal­cu­lus of vari­ations that had be­gun un­der Os­kar Bolza had largely played it­self out in the hands of Bolza’s stu­dent, Gil­bert Ames Bliss ([e22], pp. 445–446). In a post­war ef­fort to re­store not only the Math­em­at­ics De­part­ment but also the whole Uni­versity to its former luster, Chica­go Chan­cel­lor Robert Maynard Hutchins entered in­to ne­go­ti­ations with Stone to bring him from Har­vard to Chica­go, prom­ising him es­sen­tially free rein re­l­at­ive to fu­ture ap­point­ments in the de­part­ment.35 By 16 May 1946, those ne­go­ti­ations had suc­ceeded, and Stone was ex­plain­ing to Kline that he had “just writ­ten Mr. Hutchins, telling him that I am ready to ac­cept his of­fer. I think that there is a real chal­lenge and a real op­por­tun­ity out there … You would give me much needed guid­ance”, he con­tin­ued, “if you could find the time to put down on pa­per some of your ideas as to what a really first-class de­part­ment of math­em­at­ics should be like in this mod­ern world and some of the names of math­em­aticians who should be in it!”36 The goal was noth­ing short of a “first-class de­part­ment” in the “mod­ern world”, and, by Stone’s lights, that meant a de­part­ment that united some of the best math­em­aticians not just na­tion­ally but in­ter­na­tion­ally. For Stone, a “first-class de­part­ment” in the “mod­ern world” was one that re­flec­ted an in­ter­na­tion­al­ized com­munity, that is, a glob­al­ized com­munity of math­em­aticians, which shares a set of val­ues or goals and which, at the same time, op­er­ates at the highest levels of math­em­at­ic­al achieve­ment.

In or­der to at­tain this at Chica­go, Stone con­sul­ted with trus­ted friends and col­leagues such as Kline and John von Neu­mann, but, as Stone put it in his “Re­min­is­cences of Math­em­at­ics at Chica­go”, he was largely “an auto­crat in mak­ing [his] re­com­mend­a­tions” ([6], [7], page 187). He knew who he wanted, and he ne­go­ti­ated hard both with the Chica­go ad­min­is­tra­tion for fin­an­cing and with his can­did­ates to per­suade them to join in his vis­ion for what has been called the “Stone Age” at Chica­go [e19].

Stone’s ini­tial list of tar­get hires was as­ton­ish­ing in its au­da­city as well as in its qual­ity. “I have con­cluded”, he wrote mat­ter-of-factly to E. C. Col­well, the Pres­id­ent of the Uni­versity of Chica­go, on 25 Ju­ly 1946, “that our choice should be made among the fol­low­ing five math­em­aticians:

  • Saun­ders Mac Lane, As­so­ci­ate Pro­fess­or, Har­vard Uni­versity

  • John von Neu­mann, Pro­fess­or of Math­em­at­ics, In­sti­tute for Ad­vanced Study

  • An­dré Weil, presently Vis­it­ing Lec­turer, Uni­versity of São Paolo

  • Hassler Whit­ney, Pro­fess­or of Math­em­at­ics, Har­vard Uni­versity

  • Oscar Za­r­iski, Re­search Pro­fess­or of Math­em­at­ics, Uni­versity of Illinois”.

In Stone’s view, moreover, Whit­ney and Weil would have con­sti­tuted “the best pair we could se­lect from the list un­der con­sid­er­a­tion”.37 Al­though ul­ti­mately un­suc­cess­ful in scor­ing his hoped-for Whit­ney/Weil coup, Stone did make a string of spec­tac­u­lar ap­point­ments, some of which drew from this ini­tial list. He hired the Amer­ic­ans Paul Hal­mos in 1946 and Saun­ders Mac Lane in 1947, the ex­pat­ri­ate French­man An­dré Weil and the Pol­ish har­mon­ic ana­lyst Ant­oni Zyg­mund, also both in 1947, the Amer­ic­ans Irving Segal and Ed­win Span­i­er in 1948, and the Chinese dif­fer­en­tial geo­met­er Shi­ing-Shen Chern in 1949.38 Zyg­mund, moreover, em­braced Stone’s “good neigh­bor” agenda, vis­it­ing Lat­in Amer­ica in 1948, meet­ing Al­berto Calderón, and en­cour­aging the young Ar­gen­tine to pur­sue his doc­tor­al work at Chica­go un­der his su­per­vi­sion. In the late 1940s and early 1950s, Stone ex­pan­ded these loc­al ef­forts at in­ter­na­tion­al­iz­a­tion in­to a truly world­wide in­ter­na­tion­al­ist agenda, of which the Amer­ic­an com­munity would be a part, through his work in con­junc­tion with the AMS both to bring the In­ter­na­tion­al Con­gress of Math­em­aticians to the United States and to found an In­ter­na­tion­al Math­em­at­ic­al Uni­on.

Plans to or­gan­ize what would have been the 1940 ICM in Cam­bridge, Mas­sachu­setts, were re­vived as early as Feb­ru­ary 1946 by the so-called “Emer­gency Com­mit­tee” of the AMS con­sti­tuted for this pur­pose and chaired by Mar­ston Morse with Stone as one of its mem­bers. On 16 Feb­ru­ary, that com­mit­tee “voted, five to one, that”, while “it would be too soon to hold the In­ter­na­tion­al Con­gress in 1948”, “the pos­sib­il­ity of hold­ing an open Con­gress in 1950 should be ex­plored”.39 Moreover, “[u]pon the mo­tion of Pro­fess­or Stone, it was voted that a rep­res­ent­at­ive of the Emer­gency Com­mit­tee should be sent to Europe in 1947, to in­vest­ig­ate the at­ti­tude of the European math­em­aticians to­ward a Con­gress in 1950 of the type men­tioned above”. Re­lated is­sues dis­cussed at least pre­lim­in­ar­ily at the same meet­ing were the “[i]nter­na­tion­al co­oper­a­tion prob­lems raised by the United Na­tions Edu­ca­tion­al, Sci­entif­ic and Cul­tur­al Or­gan­iz­a­tion [UN­ESCO]” and, in par­tic­u­lar, “the as­so­ci­ated prob­lem of the re­viv­al of the In­ter­na­tion­al Math­em­at­ic­al Uni­on [IMU]”.40 As is well known, the IMU had been cre­ated in 1920 in the af­ter­math of the First World War amid great polit­ic­al tur­moil and had ul­ti­mately suc­cumbed to geo­pol­it­ics in 1932. Al­though oth­er in­ter­na­tion­al sci­entif­ic uni­ons also date from the im­me­di­ately post-World War I era — for ex­ample, the In­ter­na­tion­al As­tro­nom­ic­al Uni­on (IAU) and the In­ter­na­tion­al Uni­on of Pure and Ap­plied Phys­ics (IUPAP) were foun­ded in 1919 and 1922, re­spect­ively — the IMU was unique. Its con­stitu­ency, the world’s math­em­aticians, had of­fi­cially re­jec­ted it as their rep­res­ent­at­ive and in so do­ing had forced it out of ex­ist­ence in 1932 (see be­low). Nev­er­the­less, thoughts of re­sur­rect­ing an IMU sur­faced al­most im­me­di­ately fol­low­ing the close of World War II and in the con­text of the broad­er edu­ca­tion­al ob­ject­ives of the newly formed United Na­tions. In par­tic­u­lar, in a let­ter to Ro­land Richard­son, Joseph Need­ham, Brit­ish bio­chem­ist, soon-to-be noted his­tor­i­an of Chinese sci­ence, and first head of UN­ESCO’s Nat­ur­al Sci­ence di­vi­sion, had sug­ges­ted in 1946 that the Amer­ic­an Math­em­at­ic­al So­ci­ety “take the lead in re­con­sti­t­ut­ing the In­ter­na­tion­al Math­em­at­ic­al Uni­on”.41 As AMS Sec­ret­ary J. R. Kline con­fided to Stone, however, “I feel strongly that we should not be a party to a Uni­on which ex­cludes math­em­aticians be­cause of na­tion­al and ra­cial ties, just as we feel that the Con­gress must be an open Con­gress. There will surely be”, he noted, “some knotty prob­lems be­cause of the con­nec­tion with the State De­part­ment and UN­ESCO”. Moreover, he asked, “[w]hat would be the re­la­tion between the Con­gress and the In­ter­na­tion­al Math­em­at­ic­al Uni­on?” All of these were com­plex prob­lems in­ter­twined with in­ter­na­tion­al polit­ics. Stone, as the chair (from 1945 to 1948) of the Policy Com­mit­tee as well as ini­tially of the Fin­an­cial Com­mit­tee of the 1950 ICM, act­ively grappled with them and oth­er ques­tions of an in­ter­na­tion­al nature from 1946 in­to the early 1950s.42 As the cor­res­pond­ence between Stone and Kline makes clear, one of the most crit­ic­al is­sues at this junc­ture was that of the open­ness of the pro­posed ICM to math­em­aticians from all na­tions. In 1920 when the IMU was foun­ded at the Stras­bourg ICM, math­em­aticians from the former Cent­ral Powers had been ex­cluded from par­ti­cip­a­tion in both the Con­gress and the IMU largely at the in­sist­ence of the French. This ex­clu­sion­ary policy, at least re­l­at­ive to the ICMs, was main­tained at the Toronto Con­gress in 1924, but dropped by the Itali­ans for the Bo­logna Con­gress in 1928. The fact that it was main­tained by the IMU, however, res­ul­ted in the IMU’s dis­sol­u­tion by the math­em­aticians present at the next ICM held in Zürich in 1932. By con­trast, as late as 1949, Ger­many and Aus­tria had nev­er been mem­bers of the In­ter­na­tion­al As­tro­nom­ic­al Uni­on. This owed, however, not to the IAU’s of­fi­cial policies but rather to “either … gov­ern­ment­al veto, or … the ob­stin­ate re­fus­al of their lead­ing academies to ad­here to the In­ter­na­tion­al Coun­cil of Sci­entif­ic Uni­ons [IC­SU]” ([e8], page 9).43 The facts that the ICMs had been so tightly linked to the IMU and that the IMU as an in­sti­tu­tion was viewed as polit­ic­ally tain­ted gave math­em­aticians in the 1940s pause. If an IMU were re­con­sti­t­uted un­der the UN­ESCO rub­ric as Need­ham pro­posed and if it were to serve as an um­brella or­gan­iz­a­tion for the ICMs as it had in the 1920s, then the pre­vail­ing sen­ti­ment, at least among the Amer­ic­ans, was that it could not be ex­clu­sion­ary. Un­less and un­til that non-ne­go­ti­able point was cla­ri­fied, the AMS, as the or­gan­izer of the 1950 Cam­bridge ICM, wanted the mat­ter of the ICM to re­main sep­ar­ate from that of the IMU, even though it hoped for fin­an­cial sup­port from UN­ESCO for the ICM. Stone laid out the Amer­ic­an po­s­i­tion clearly in 1947. “In gen­er­al”, he as­ser­ted, “it ap­pears that in­ter­na­tion­al con­gresses … tend … to be con­sti­tuted without ref­er­ence to mem­ber­ship in the spon­sor­ing uni­on…. Un­less in­struc­ted in some oth­er sense, Amer­ic­an rep­res­ent­at­ives in dis­cus­sions of any pro­posed uni­on should be ex­pec­ted to main­tain the in­de­pend­ence of the Con­gress, should any al­tern­at­ive form of or­gan­iz­a­tion be sug­ges­ted”.44 Writ­ing in his ca­pa­city as chair of the Policy Com­mit­tee and at the re­quest of No­bel Prize-win­ning phys­i­cist Ar­thur H. Compton, one of the two Amer­ic­an rep­res­ent­at­ives chosen by the State De­part­ment to at­tend a meet­ing of UN­ESCO in Lon­don in Novem­ber 1946, Stone laid out his “views on the way in which UN­ESCO could pro­mote the de­vel­op­ment of math­em­at­ics on the in­ter­na­tion­al front”.45 In par­tic­u­lar, he stressed that “the chief in­ter­na­tion­al prob­lem of math­em­at­ics seems… to be what might be called the prob­lem of com­mu­nic­a­tions” and that “UN­ESCO [could] help the de­vel­op­ment of math­em­at­ics most ef­fect­ively by”, among oth­er things, “elim­in­at­ing or min­im­iz­ing the vari­ous obstacles, polit­ic­al and eco­nom­ic, which threaten to make the travel of schol­ars and stu­dents between the na­tions of the world ex­tremely dif­fi­cult even after the con­di­tions of peace are es­tab­lished”.46 Al­lud­ing to the sev­er­al plans of an in­ter­na­tion­al nature then un­der way — not the least of which in the view of Stone and the Policy Com­mit­tee was for the Cam­bridge ICM in 1950 — he closed with the as­sur­ance that “[t]he math­em­aticians of the United States will watch with the very greatest in­terest the de­vel­op­ments in UN­ESCO which may have a bear­ing on their pro­fes­sion­al activ­it­ies”.

Six months to a year later, speak­ing be­fore the Com­mit­tee on In­ter­na­tion­al Sci­entif­ic Uni­ons of the Na­tion­al Re­search Coun­cil, Stone was even more poin­ted. “[I]n con­sid­er­ing Amer­ic­an ad­her­ence to a Uni­on”, he stated firmly, “it must be borne in mind that we want noth­ing to do with an ar­range­ment which ex­cludes Ger­mans and Ja­pan­ese as such”. “We are fear­ful”, he con­tin­ued, “that the motive back of the great activ­ity of the French to­ward the form­a­tion of a Uni­on is polit­ic­al, and to pro­mote the ex­ten­sion of French cul­tur­al dom­in­a­tion over the satel­ite [sic] na­tions of Europe”. Moreover, he “em­phas­ized as one of the ser­i­ous prob­lems in re­la­tion to the form­a­tion of an In­ter­na­tion­al Math­em­at­ic­al Uni­on, the in­ab­il­ity of the out­side world to com­mu­nic­ate with Rus­si­an sci­ent­ists, and poin­ted to the great im­port­ance of in­clud­ing the Rus­si­ans in any in­ter­na­tion­al or­gan­iz­a­tion which may be set up”.47 As Kline ex­plained to one of his many cor­res­pond­ents, the Amer­ic­an ef­forts re­l­at­ive to the form­a­tion of a new IMU were mo­tiv­ated by the fact that “if we do not par­ti­cip­ate …, the Europeans will pro­ceed to set up a Uni­on alone. In that case, we may be forced to join a group in whose prin­ciples we do not agree or re­main out­side the fold en­tirely”.48 Clearly, neither of these was an ac­cept­able op­tion for an Amer­ic­an math­em­at­ic­al re­search com­munity poised and ready to shape and to par­ti­cip­ate in an in­ter­na­tion­al math­em­at­ic­al arena.

By 1948, Stone along with Kline and Mar­ston Morse had con­sti­tuted an of­fi­cial sub­com­mit­tee of the Policy Com­mit­tee to ex­plore the re­form­a­tion of an IMU. As early as 1947, Stone as well as the oth­er mem­bers of the com­mit­tee had be­gun so­li­cit­ing math­em­aticians in­ter­na­tion­ally —  Har­ald Bo­hr in Den­mark, W. V. D. Hodge in Eng­land, Al­bert Châtelet and Henri Cartan in France, Hassler Whit­ney, Norbert Wien­er, and Her­mann Weyl in the United States, among oth­ers — as to their views, par­tic­u­larly on the mat­ter of a pro­posed IMU. Al­most all49 agreed whole­heartedly with the Amer­ic­an con­cep­tion of an open IMU, di­vorced as thor­oughly as pos­sible from the geo­pol­it­ics of the day. As Bo­hr put it, re­port­ing on a meet­ing on the IMU is­sue held in Par­is in the sum­mer of 1947 and which Whit­ney at­ten­ded as the Amer­ic­an rep­res­ent­at­ive, “the present opin­ion of the Dan­ish and, I think, also the Scand­inavi­an and Swiss math­em­aticians who took all rather the same view in Par­is is that we are in­ter­ested in a Uni­on of real in­ter­na­tion­al char­ac­ter, but we are not in fa­vour [of] the idea of form­ing a Uni­on con­sist­ing only of a cer­tain group of na­tions, as we think that such a quasi-in­ter­na­tion­al Uni­on may give rise to fu­ture dif­fi­culties”.50 Des­pite turf and polit­ic­al is­sues that arose as early as 1948 between Stone as head of the IMU sub­com­mit­tee and Gar­rett Birk­hoff as chair of the ICM or­gan­iz­ing com­mit­tee, slow but steady pro­gress con­tin­ued on lay­ing the ground­work for the IMU. Everything had to be done with the ut­most care and de­lib­er­a­tion. In March of 1949, just a month be­fore the found­ing of the North At­lantic Treaty Or­gan­iz­a­tion (NATO), for ex­ample, Kline in­quired of Stone “[a]t what stage do you feel that you can start com­mu­nic­a­tions with the Ger­mans, Ja­pan­ese, and Aus­tri­ans?” and offered the opin­ion that “we should not delay too long the ap­proach to these groups, al­though I real­ize that the French will have to be handled care­fully be­fore the ap­proach to the Ger­mans is at­temp­ted”.51 Clearly, Kline and Stone were well aware of and acutely sens­it­ive to in­ter­na­tion­al polit­ic­al real­it­ies. “Ger­many” was a di­vided na­tion, and at least of­fi­cially, West Ger­many “would be treated as the rep­res­ent­at­ive of all Ger­man cit­izens” [e33], page 243; the French were once again vo­ci­fer­ous — as they had been after World War I — in their op­pos­i­tion to the in­clu­sion of Ger­many in post­war polit­ic­al and mil­it­ary al­li­ances and ef­fect­ively blocked ef­forts to in­clude it in NATO in 1949 ([e33], pp. 243–245); the Aus­tri­ans, al­though strictly con­sidered one of the na­tions conquered by Ger­many dur­ing the Second World War, had nev­er­the­less fought with Ger­many in the First World War and had made im­port­ant con­tri­bu­tions to the Nazi Party, not the least of which was Hitler him­self; the Ja­pan­ese, of course, had bombed Pearl Har­bor and had then been bombed in­to sub­mis­sion fol­low­ing Hiroshi­ma and Na­ga­saki. To say the least, it was a rad­ic­ally changed in­ter­na­tion­al polit­ic­al land­scape from that of just a dec­ade earli­er, and this new polit­ic­al real­ity could not be ig­nored by the math­em­aticians re­gard­less of how much they might have wished to con­duct their work in an apolit­ic­al en­vir­on­ment. By Au­gust, the Ja­pan­ese and Aus­tri­ans had been con­tac­ted, there had been no “trouble about hav­ing [them] set up Na­tion­al Com­mit­tees on the Uni­on”, and Stone had sug­ges­ted that the time would soon be ripe to move “in the mat­ter of the Ger­mans”.52 In fact, he was able to re­port that “con­sid­er­able pro­gress ha[d] been made in the mat­ter of per­suad­ing the vari­ous coun­tries to ap­point com­mit­tees to con­sider the ques­tion of the es­tab­lish­ment of an In­ter­na­tion­al Math­em­at­ic­al Uni­on”, and that such “[c]om­mit­tees ha[d] been formed in Eng­land, Hol­land, In­dia, Bel­gi­um, Den­mark, Italy, Nor­way, Egypt, Greece, Hun­gary, and France”.53 This pro­cess was fur­ther fa­cil­it­ated at the end of Au­gust 1949, when Stone em­barked on an around-the-world trip that aimed not only at es­tab­lish­ing his own math­em­at­ic­al con­tacts but also at “ne­go­ti­at­ing in per­son with the na­tion­al com­mit­tees study­ing the Uni­on prob­lem”.54 De­part­ing from Chica­go on 27 Au­gust, his first stop was Ja­pan, where he had been giv­en per­mis­sion by Gen­er­al Douglas Ma­cAr­thur, Com­mand­er of Al­lied Powers, to en­gage with the math­em­aticians of the former en­emy na­tion. He spent an in­tense two weeks lec­tur­ing at uni­versit­ies in Osaka, Kyoto, Nagoya, and Tokyo and en­ter­ing in­to dis­cus­sions with his Ja­pan­ese coun­ter­parts. As he de­scribed his wel­come, “[a]lthough Ja­pan­ese math­em­aticians had been able through cor­res­pond­ence since 1945 to break down the war-time isol­a­tion, I came as the first for­eign aca­dem­ic vis­it­or in the field of math­em­at­ics for many years; and I was re­ceived ac­cord­ingly”.55 Among the is­sues he dis­cussed was, of course, the pro­posed IMU, and he could proudly re­port that his vis­it “con­trib­uted in a quite spe­cif­ic way to the res­tor­a­tion of the pro­fes­sion­al bonds between the math­em­aticians of Ja­pan and those of oth­er coun­tries”. Fol­low­ing his de­par­ture, he ex­plained, “the Ja­pan Sci­ence Coun­cil com­pleted the ar­range­ments thus ini­ti­ated by ap­point­ing a spe­cial Com­mit­tee to rep­res­ent Ja­pan in the dis­cus­sions of the new Uni­on”.

From Ja­pan, Stone pro­ceeded to Vi­et­nam, Thai­l­and, Java, Singa­pore, and Ceylon (mod­ern-day Sri Lanka), be­fore ar­riv­ing for a sev­en-month stay and ex­tens­ive lec­ture and sight­see­ing tour of In­dia. With the In­di­an leg of his jour­ney com­pleted, he re­turned to the United States in May of 1950 via Egypt and France, where he gave more lec­tures and par­ti­cip­ated (in Nancy) in an even­ing of food and math­em­at­ic­al con­ver­sa­tion with mem­bers of the élite math­em­at­ic­al col­lect­ive, Bourbaki. In all of these ven­ues, Stone took the op­por­tun­ity not only to ac­quaint him­self with what was be­ing done in math­em­at­ics in­ter­na­tion­ally but also to broad­cast in­form­a­tion and to ex­change ideas about the IMU. In par­tic­u­lar, he dis­cussed the pro­posed IMU stat­utes and bylaws that had been in cir­cu­la­tion since the time of his de­par­ture for Ja­pan.

Stone, son of a former Su­preme Court Chief Justice and broth­er of a law­yer, had draf­ted a con­sti­tu­tion for an IMU in the sum­mer of 1949 for the con­sid­er­a­tion and com­ment of the vari­ous na­tion­al com­mit­tees that had been formed. By the end of the sum­mer of 1950, when the Uni­on con­fer­ence was held in New York City just in ad­vance of the ICM in Cam­bridge, this doc­u­ment had been duly re­vised based on the many sug­ges­tions re­ceived both dir­ectly and in­dir­ectly from com­mit­tees in­ter­na­tion­ally. Con­sensus on it was quickly reached at the meet­ing in the form of an “En­abling Res­ol­u­tion” that then set the wheels in mo­tion for the ad­her­ence to the pro­posed new uni­on by the re­quired min­im­um of ten coun­tries.56 If these events sur­round­ing the re­form­a­tion of the IMU re­flec­ted a cer­tain post­war spir­it of co­oper­a­tion — among math­em­aticians at least — so, too, did the 1950 In­ter­na­tion­al Con­gress of Math­em­aticians in Cam­bridge with which dis­cus­sions of the IMU had been so in­ter­twined. The ICM was ul­ti­mately a large event — more than doub­ling the pre­vi­ous at­tend­ance re­cord — with over 1700 math­em­aticians present over the week from 30 Au­gust to 6 Septem­ber. Still, the Cam­bridge ICM was not as thor­oughly an in­ter­na­tion­al af­fair as its or­gan­izers had hoped. Only 290 of the 1700 math­em­at­ic­al par­ti­cipants were from out­side North Amer­ica. At least two things were to blame: the cost of travel was high, and, as Kline ex­plained in his Sec­ret­ary’s Re­port to the Con­gress, “[m]athem­aticians from be­hind the Iron Cur­tain were uni­formly pre­ven­ted from at­tend­ing the Con­gress by their own gov­ern­ments which gen­er­ally re­fused to is­sue pass­ports to them for the trip” ([e9], 1: 122). The Cold War had be­gun al­most im­me­di­ately after the end of World War II and lay be­hind the So­viet Uni­on’s de­cision to re­strict travel to the West and es­pe­cially to the United States. What was not to blame, however, was either a lack of in­terest or an ab­sence of good­will among math­em­aticians. The Con­gress had, for ex­ample, re­ceived a cable­gram which was read at the open­ing ce­re­mon­ies from Sergei Vavilov, noted phys­i­cist and Pres­id­ent of the Academy of Sci­ences of the USSR, which thanked the Con­gress or­gan­izers for their “kind in­vit­a­tion”, offered the “[h]ope that [the] im­pend­ing con­gress will be [a] sig­ni­fic­ant event in math­em­at­ic­al sci­ence”, and wished them all “suc­cess in [the] Con­gress activ­it­ies” ([e9], 1: 122). Four years later, and des­pite the fur­ther es­cal­a­tion of the Cold War as mani­fes­ted by the Korean War, five So­viet math­em­aticians were al­lowed to par­ti­cip­ate in the ICM held in Am­s­ter­dam ([e24], page 118).

The in­ter­na­tion­al spir­it in evid­ence at the Cam­bridge ICM in 1950 per­sisted in­to 1951, when the ma­gic num­ber of ten coun­tries was reached re­l­at­ive to ad­her­ence to the pro­posed IMU. The “pro­posed IMU” then be­came the “new IMU”, which began its work of­fi­cially as an ad­her­ing mem­ber of the In­ter­na­tion­al Coun­cil of Sci­entif­ic Uni­ons a year later at its first Gen­er­al As­sembly meet­ing held in Rome in 1952 ([e24], pp. 79–88). Eight­een coun­tries were rep­res­en­ted of­fi­cially at that first meet­ing — Aus­tralia, Aus­tria, Bel­gi­um, Den­mark, Fin­land, France, Ger­many, Greece, Great Bri­tain, Italy, Ja­pan, the Neth­er­lands, Nor­way, Peru, Spain, Switzer­land, the United States, and Yugoslavia — while Po­land and Por­tugal sent ob­serv­ers. Not sur­pris­ingly, per­haps, giv­en the key role he had played in its re­form­a­tion, Mar­shall Stone was the chair of the U.S. del­eg­a­tion, which also con­sisted of Ein­ar Hille, J. R. Kline, Saun­ders Mac Lane, and Gor­don T. Why­burn.57 These del­eg­ates to­geth­er with those from the oth­er coun­tries rep­res­en­ted spent the three days from 6–8 March in spir­ited dis­cus­sion as to the activ­it­ies that should define the new IMU. In par­tic­u­lar, Stone pro­posed that the IMU: 1) pub­lish a world dir­ect­ory of math­em­aticians, 2) pro­duce a reg­u­lar news­let­ter that would ap­prise math­em­aticians in­ter­na­tion­ally “of its activ­it­ies and also of the activ­it­ies of in­di­vidu­al math­em­aticians, par­tic­u­larly the news of math­em­aticians about to travel abroad and con­sequently [be] avail­able for lec­tures”, and con­duct stud­ies of 3) “the costs of print­ing and the prob­lem of more prompt pub­lic­a­tion of re­search pa­pers”, 4) “meth­ods of fa­cil­it­at­ing the ex­change of math­em­aticians between na­tions”, and 5) prob­lems sur­round­ing the is­sue of ab­stract­ing and re­view­ing of math­em­at­ic­al pub­lic­a­tions.58 All of these sug­ges­tions were greeted with en­thu­si­asm, and com­mit­tees were ap­poin­ted to ex­plore them.

The Gen­er­al As­sembly ended with the elec­tion of the first Ex­ec­ut­ive Com­mit­tee of the new IMU. Again, per­haps not sur­pris­ingly, Stone was elec­ted Pres­id­ent with Émile Borel France First Vice Pres­id­ent, Erich Kamke of Ger­many Second Vice Pres­id­ent, En­rico Bompi­ani of Italy Sec­ret­ary, and W. V. D. Hodge of Great Bri­tain, Shoki­chi Iy­anaga of Ja­pan, and Børge Jessen of Den­mark Mem­bers-at-Large.59 “It was the un­an­im­ous opin­ion of the United States del­eg­a­tion”, Stone re­por­ted, “that the meet­ings were a de­cided suc­cess. All mem­bers of the Gen­er­al As­sembly were sin­cerely in­ter­ested in the pro­mo­tion of in­ter­na­tion­al coöper­a­tion in the ad­vance­ment of Math­em­at­ics”, and, moreover, “[t]he at­mo­sphere … was sci­entif­ic and not polit­ic­al”.60 The new IMU, un­like the old, had man­aged, at least at its found­ing, not to let polit­ics in­ter­fere with its broad­er goals.61 As IMU Pres­id­ent from 1952 through 1954, Stone worked di­li­gently not only to es­tab­lish an ad­min­is­trat­ive routine but also to define an agenda for the new or­gan­iz­a­tion that would put math­em­at­ics and its pro­mo­tion, in so far as pos­sible, above con­tem­por­an­eous geo­pol­it­ic­al con­cerns. In par­tic­u­lar, un­der his lead­er­ship, the IMU in­sti­tuted its pro­gram of IMU-sponsored con­fer­ences and ad­op­ted the pro­mo­tion of math­em­at­ics edu­ca­tion as one of its ini­ti­at­ives ([e24], pp. 105–113). Stone had be­come sens­it­ive to the im­port­ance of the lat­ter at least as early as the U.S.’s entry in­to World War II in con­nec­tion with his work both as a con­tract em­ploy­ee for the De­part­ment of the Navy and on the War Policy Com­mit­tee of the AMS. At that time, the is­sue was the role of ap­plied math­em­at­ics in the col­lege and uni­versity cur­ricula, but with the war’s con­clu­sion, he very quickly turned to broad­er edu­ca­tion­al con­cerns. Scarcely a year after he had stepped down as AMS Pres­id­ent, Stone had writ­ten dir­ectly to then Pres­id­ent of the Math­em­at­ic­al As­so­ci­ation of Amer­ica (MAA), Cyr­us C. Mac­Duffee, to voice his opin­ion on cer­tain “edu­ca­tion­al as­pects of our pro­fes­sion” that he viewed as “of fun­da­ment­al im­port­ance”, among them: “the status of math­em­at­ics in the sec­ond­ary cur­riculum; the ad­apt­a­tion of col­lege math­em­at­ics courses both to pro­gress in math­em­at­ics and to the chan­ging con­cep­tions of lib­er­al edu­ca­tion; the un­even stand­ards to be found in col­lege math­em­at­ics cur­ricula and teach­ing; the re­vi­sion of gradu­ate pro­grams in light of ad­vances in high­er math­em­at­ics”.62 Al­though Stone would soon tackle the last of these is­sues in the con­text of the re­vamp­ing of the gradu­ate pro­gram that he over­saw at the Uni­versity of Chica­go, in his view, “ur­gency of such prob­lems is greatest at the lower levels and di­min­ishes pro­gress­ively as the high­er levels are reached”. For that reas­on, he urged the MAA, of which he was a mem­ber, to play a more act­ive role in bridging the gap between sec­ond­ary and col­lege-level math­em­at­ics. As he put it, “[s]ince the in­terest in col­lege math­em­at­ics ex­tends in­ev­it­ably to the inter-re­la­tions of sec­ond­ary and col­lege math­em­at­ics, my con­cern in­cludes a sense of dis­sat­is­fac­tion with the com­par­at­ive in­activ­ity of the As­so­ci­ation in re­spect to the status of math­em­at­ics in the sec­ond­ary cur­riculum”.

The “in­activ­ity” he sensed re­l­at­ive to the MAA in 1945 would not be re­flec­ted in the IMU un­der his watch. As early as the found­ing of the Gen­er­al As­sembly in Rome in 1952, Stone had ar­gued for the cent­ral­ity of math­em­at­ics edu­ca­tion in the IMU’s agenda. “The prob­lem of de­term­in­ing the place of math­em­at­ics [in so­ci­ety] can­not be di­vorced from tech­nic­al con­sid­er­a­tions con­cern­ing teach­ing meth­ods”, he averred. “If we judge by the res­ults, we must find it dif­fi­cult to es­cape from the con­clu­sion that our at­tempts to teach math­em­at­ics as part of a pro­gram of mass edu­ca­tion have so far been, to put it bluntly, a co­lossal fail­ure, trace­able to our ig­nor­ance and com­pla­cency in re­spect to the art of teach­ing” ([e24], page 109). As a cor­rect­ive to this situ­ation, the IMU sub­sumed what came to be called the In­ter­na­tion­al Com­mis­sion on Math­em­at­ic­al In­struc­tion (ICMI) as a sub­com­mis­sion. A com­mis­sion con­cerned with math­em­at­ics edu­ca­tion had been in ex­ist­ence off and on since the Rome ICM in 1908 and had act­ively in­volved such dis­tin­guished math­em­at­ic­al fore­bears as Fe­lix Klein, Guido Castel­nuovo, and Jacques Hadam­ard. Re­viv­i­fied per­man­ently in 1952, ICMI ex­per­i­enced some ini­tial ten­sions with­in the IMU as Stone worked to define and cla­ri­fy the re­la­tion­ship between com­mis­sion and sub­com­mis­sion, but it nev­er­the­less began its work of fos­ter­ing math­em­at­ics edu­ca­tion, most prom­in­ently through the pub­lic­a­tion of the journ­al, L’En­sei­gne­ment mathématique.63 At the same time that he en­gaged in es­tab­lish­ing a sol­id ground­work for the IMU, Stone sought not only to ex­tend his per­son­al grasp of the is­sues con­front­ing math­em­at­ics edu­ca­tion in­ter­na­tion­ally but also to sat­is­fy his ever-grow­ing Wan­der­lust. In 1953, he ap­plied for fund­ing from both the John Si­mon Gug­gen­heim Found­a­tion and the Amer­ic­an Philo­soph­ic­al So­ci­ety to con­duct a study of the (West­ern) edu­ca­tion of nat­ive peoples in co­lo­ni­al Africa. With “the teach­ing of math­em­at­ics at all levels” as a par­tic­u­lar fo­cus, Stone aimed to ap­ply the prin­ciples of op­er­a­tions re­search to co­lo­ni­al Afric­an edu­ca­tion­al or­gan­iz­a­tions “with a view to throw­ing some light on the dy­nam­ics of the in­ter­ac­tion between West­ern and nat­ive cul­ture at” what he deemed “one of their most sig­ni­fic­ant and in­trins­ic­ally in­ter­est­ing points of con­tact”.64 As Stone saw it, this ini­ti­at­ive — which ul­ti­mately took him from Decem­ber 1953 through March of 1954 to the cit­ies of Khar­toum, Kam­pala, Nairobi, and Dar-es-Sa­laam as well as to mod­ern-day Zi­m­b­ab­we, Zan­zib­ar, the Cent­ral Afric­an Re­pub­lics, the Re­pub­lic of the Congo, Cameroon, the Ivory Coast, Guinea, and Seneg­al — was con­son­ant with the goals of the U.S. gov­ern­ment’s so-called Point Four Pro­gram. Stem­ming from the ideals of the At­lantic Charter of 1941, but form­ally ini­ti­ated by Tru­man in 1949 and ex­ten­ded by Eis­en­hower in 1953, the Point Four Pro­gram aimed to provide, es­pe­cially eco­nom­ic, aid to un­der­developed coun­tries.65 “It may be em­phas­ized”, Stone ar­gued, “that a bet­ter un­der­stand­ing of cul­tur­al in­ter­ac­tions such as this is im­per­at­ive for the fu­ture of man­kind, and is in­dis­pens­able for the suc­cess of con­crete un­der­tak­ings, such as the Point Four pro­grams, cal­cu­lated to de­flect the course of his­tory from those paths to­ward dis­aster which can be only too plainly iden­ti­fied by our gen­er­a­tion”. Stone also had broad­er per­son­al ob­ject­ives in­to which this trip and this ini­ti­at­ive fit, however. At least as early as 1946, he had be­gun to en­vi­sion a pro­ject on the ap­plic­a­tion of sci­entif­ic prin­ciples to state­craft and for­eign re­la­tions.66 Stone, as an in­ter­na­tion­al­ist math­em­atician, saw the po­ten­tial of math­em­at­ics edu­ca­tion as a means for fos­ter­ing the growth and de­vel­op­ment not only of math­em­at­ic­al com­munit­ies in­ter­na­tion­ally, but also of more ef­fect­ive re­la­tions between coun­tries in a post­war world.

From a national to an internationalized mathematical community

The ef­forts of Mar­shall Stone and oth­ers from the late 1930s in­to the mid 1950s to ef­fect an in­ter­na­tion­al math­em­at­ic­al com­munity lay squarely with­in the con­texts of the ini­ti­at­ives that the Amer­ic­an Math­em­at­ic­al So­ci­ety ex­pli­citly ar­tic­u­lated for the broad­er Amer­ic­an math­em­at­ic­al re­search com­munity as well as of na­tion­al and in­ter­na­tion­al polit­ics. Where­as oth­er sci­entif­ic dis­cip­lines, such as as­tro­nomy and phys­ics, had man­aged to main­tain throughout the in­ter­war peri­od at least a semb­lance of the more form­al­ized in­ter­na­tion­al com­munit­ies they had be­gun to foster in the 1920s, math­em­at­ics had not. The world’s math­em­aticians had ex­pressly re­jec­ted the ex­clu­sion­ary policies of their In­ter­na­tion­al Math­em­at­ic­al Uni­on and had ab­ol­ished it in 1932. As a res­ult, while the as­tro­nomers and phys­i­cists could re­sume their in­ter­na­tion­al sci­entif­ic re­la­tions in the con­text of ex­tant ad­min­is­trat­ive struc­tures in the post­war world, the math­em­aticians, were they act­ively to foster or­gan­ized in­ter­na­tion­al math­em­at­ic­al re­la­tions at all, would have to either re­cre­ate such struc­tures ex ni­hilo or settle upon some oth­er way to achieve their ends in a geo­pol­it­ic­al con­text rad­ic­ally altered from that of the 1920s.67 Who, if any­one, would take the lead?

Be­gin­ning in the United States in the 1930s, the AMS, as the rep­res­ent­at­ive of what had be­come a ma­ture and am­bi­tious math­em­at­ic­al re­search com­munity, worked to bring the 1940 ICM to Cam­bridge, Mas­sachu­setts. In 1942, even as World War II raged, the AMS Coun­cil at the ur­ging of G. D. Birk­hoff “au­thor­ized and re­ques­ted” AMS Pres­id­ent Mar­ston Morse “to ap­point a com­mit­tee of three to in­vest­ig­ate the whole mat­ter of re­la­tions with math­em­aticians in oth­er coun­tries in this hemi­sphere”.68 A year later as AMS Pres­id­ent, Mar­shall Stone fol­lowed Birk­hoff’s math­em­at­ic­al “good neigh­bor” tour of Lat­in Amer­ica with one of his own in an ef­fort to main­tain this in­ter­na­tion­al ini­ti­at­ive, and he was fully aware that the ini­ti­at­ive was in step with broad­er U.S. policies. With the close of the war in 1945 and in the con­text of in­ter­na­tion­al polit­ic­al ini­ti­at­ives such as the United Na­tions and the North At­lantic Treaty Or­gan­iz­a­tion, Stone and the AMS were im­me­di­ately back at work on their ex­pli­citly in­ter­na­tion­al­ist agenda. Writ­ing to J. R. Kline on 17 June 1945, Stone in­quired of the AMS Sec­ret­ary “what steps, wheth­er form­al and of­fi­cial or not, have been taken to­wards re­new­ing our sci­entif­ic ties with math­em­aticians in pre­vi­ously oc­cu­pied ter­rit­or­ies (in­clud­ing those now oc­cu­pied by our side)”. He ven­tured to sug­gest that, giv­en his con­nec­tions in Wash­ing­ton, he might be able to “do a little ex­plor­a­tion of the pos­sib­il­it­ies of gov­ern­ment­al as­sist­ance”.69 By 1946, Stone was not only the chair of the De­part­ment of Math­em­at­ics of the Uni­versity of Chica­go, where he im­ple­men­ted a plan of pro­gram re­new­al that hinged on at­tract­ing some of the best math­em­aticians in­ter­na­tion­ally to Chica­go, but he was also the chair of the AMS’s Policy Com­mit­tee charged with a full range of do­mest­ic and in­ter­na­tion­al math­em­at­ic­al is­sues, among the lat­ter of which were plans for the first post­war ICM as well as for a re­viv­al of the IMU. The Cam­bridge ICM in 1950, but more im­port­antly the be­gin­ning of the work of the new IMU in 1952 with Stone as Pres­id­ent, marked the self-con­scious trans­form­a­tion of the Amer­ic­an math­em­at­ic­al re­search com­munity from a na­tion­al com­munity ori­ented to­ward fos­ter­ing math­em­at­ics at home to an in­ter­na­tion­al­ized one sens­it­ive to the vi­cis­situdes of world polit­ics and fo­cused not only on par­ti­cip­at­ing act­ively in but also in­flu­en­cing the math­em­at­ic­al en­deavor world­wide.


For per­mis­sion to quote from archives held in the Mar­shall Stone Pa­pers and in the Pa­pers of the Amer­ic­an Math­em­at­ic­al So­ci­ety, I thank the John Hay Lib­rary at Brown Uni­versity. My thanks also go to Tim En­gels, Holly Snyder, and the staff at the John Hay Lib­rary for their help dur­ing my stay in Provid­ence and to my col­league in the Corcor­an De­part­ment of His­tory, Joe Kett, for his sage coun­sel.


[1] M. H. Stone: Lin­ear trans­form­a­tions in Hil­bert space and their ap­plic­a­tions to ana­lys­is. AMS Col­loqui­um Pub­lic­a­tions 15. Amer­ic­an Math­em­at­ic­al So­ci­ety (New York), 1932. Re­pub­lished (with ab­bre­vi­ated title) in 1990. JFM 58.​0420.​02 Zbl 0005.​40003 book

[2] M. Stone: “Sci­ence and state­craft,” Sci­ence 105 (1947), pp. 507–​510. Ad­dress of the re­tir­ing vice-pres­id­ent, Sec­tion A, AAAS, 1942, de­livered at Bo­ston, Decem­ber 27, 1946. article

[3] M. H. Stone: “The gen­er­al­ized Wei­er­strass ap­prox­im­a­tion the­or­em (con­tin­ued),” Math. Mag. 21 : 5 (May–June 1948), pp. 237–​254. Second of two parts, con­tin­ued from pre­vi­ous is­sue. article

[4] M. H. Stone: “The gen­er­al­ized Wei­er­strass ap­prox­im­a­tion the­or­em,” Math. Mag. 21 : 4 (March–April 1948), pp. 167–​184. First of two parts, con­tin­ued in fol­low­ing is­sue. MR 0027121 article

[5] M. Stone: “In­ter­na­tion­al re­la­tions in math­em­at­ics,” pp. 31–​39 in Men and in­sti­tu­tions in Amer­ic­an math­em­at­ics. Edi­ted by J. D. Tar­wa­ter, J. T. White, and J. D. Miller. Gradu­ate Stud­ies 13. Texas Tech Uni­versity, 1976. incollection

[6] M. H. Stone: “Re­min­is­cences of math­em­at­ics at Chica­go,” Univ. Chica­go Mag. (Autumn 1976), pp. 30. article

[7] M. H. Stone: “Re­min­is­cences of math­em­at­ics at Chica­go,” pp. 183–​190 in A cen­tury of math­em­at­ics in Amer­ica, part 2. Edi­ted by P. Duren, R. A. As­key, and U. C. Merzbach. His­tory of Math­em­at­ics 2. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1989. Re­prin­ted from Univ. Chica­go Mag. (Au­tumn, 1976). MR 1003127 Zbl 0682.​01014 incollection

[8] M. H. Stone: Lin­ear trans­form­a­tions in Hil­bert space. AMS Col­loqui­um Pub­lic­a­tions 15. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1990. Re­pub­lic­a­tion (with ab­bre­vi­ated title) of the 1932 ori­gin­al. MR 1451877 Zbl 0933.​47001 book