Celebratio Mathematica

Marshall Harvey Stone

Stone age of mathematics at the Midway

by Felix E. Browder

After its found­a­tion as a dis­tin­guished de­part­ment by E. H. Moore in the 1890s, the single most de­cis­ive event in the his­tory of the De­part­ment of Math­em­at­ics at the Uni­versity of Chica­go was the as­sump­tion of its chair­man­ship by Mar­shall Har­vey Stone in 1946. Stone ar­rived in Chica­go from a pro­fess­or­ship at Har­vard as the newly ap­poin­ted An­drew MacLeish dis­tin­guished ser­vice pro­fess­or of math­em­at­ics as well as chair­man of the de­part­ment. With­in a year or two, he had trans­formed a de­part­ment of dwind­ling prestige and vi­tal­ity once more in­to the strongest math­em­at­ics de­part­ment in the U.S. (and at that point prob­ably in the world).

This re­mark­able trans­form­a­tion, which en­dowed the de­part­ment with a con­tinu­ing vi­tal­ity dur­ing the tri­als of the fol­low­ing dec­ades, is un­par­alleled, to the writer’s know­ledge, in mod­ern aca­dem­ic his­tory for its speed and dra­mat­ic ef­fect. This was no easy vic­tory on the basis of great in­fu­sions of out­side money. It was com­pletely a tri­umph of Stone’s sure­ness of judg­ment and his de­term­in­a­tion and strength of char­ac­ter in get­ting done what he knew had to be done.

Stone’s ac­count of the trans­form­a­tion which he led is un­par­alleled for its candor and its ob­jectiv­ity (des­pite the strong fla­vor of Stone’s per­son­al­ity) and for its re­mark­ably open present­a­tion of the pro­cess by which aca­dem­ic de­cisions are reached and lead­er­ship ex­er­ted. The cent­ral prob­lem of aca­dem­ic life for in­sti­tu­tions which as­pire to ex­cel­lence and to great­ness is pre­cisely the dif­fi­culty of achiev­ing that ex­cel­lence and that great­ness.

With­in every aca­dem­ic in­sti­tu­tion, policy lead­er­ship falls in­to two pat­terns. The most com­mon pat­tern, which is the basis of the on­go­ing routine of the in­sti­tu­tion’s ex­ist­ence, falls with­in the ra­tion­al-bur­eau­crat­ic mold (to use the clas­sic­al ter­min­o­logy of Max Weber) in terms of ra­tion­al­ized gen­er­al policies and pro­ced­ures to be ap­plied uni­formly to an ar­ray of cases in the con­text of a bal­ance of spe­cial in­terests and in­flu­ences. The oth­er pat­tern, which is less com­mon, is that of cha­ris­mat­ic lead­er­ship in which the in­di­vidu­al judg­ment and per­son­al qual­it­ies of the ad­min­is­trat­or play a fun­da­ment­al role in both the choice and nature of the policy de­cisions which are made, and in their ac­cept­ance by those who are af­fected by them. Stone’s ac­count gives us a pic­ture of the most highly de­veloped form of cha­ris­mat­ic lead­er­ship, one which turned out to be enorm­ously suc­cess­ful. What is most in­ter­est­ing about it is the ques­tion it raises about the role of cha­ris­mat­ic lead­er­ship in the search for aca­dem­ic ex­cel­lence.

To my know­ledge, there is no case in which aca­dem­ic ex­cel­lence in any reas­on­ably high de­gree has been achieved and main­tained without an in­fu­sion of cha­ris­mat­ic lead­er­ship, either pub­lic or be­hind the scenes. Yet to an ever great­er de­gree, it has be­come in­creas­ingly in­com­pat­ible with the grow­ing pres­sures and struggles of in­terests that tend to dom­in­ate the or­gan­ized life of our uni­versit­ies.

When Mar­shall Har­vey Stone ar­rived at the uni­versity in 1946 to play such a dis­tinct­ive role, he was a re­l­at­ively young man (43) and a math­em­atician of great dis­tinc­tion and great repu­ta­tion. He had spent most of his aca­dem­ic life at Har­vard, get­ting his­gree there in the late 1920s with the dom­in­ant per­son­al­ity of the Har­vard de­part­ment, George Dav­id Birk­hoff, who had him­self been a stu­dent of E. H. Moore at Chica­go. Stone had done fun­da­ment­al work in a num­ber of widely known dir­ec­tions, in par­tic­u­lar on the spec­tral the­ory of un­boun­ded self-ad­joint op­er­at­ors in the Hil­bert space and on the ap­plic­a­tions of the al­geb­ra­ic prop­er­ties of Boolean al­geb­ras in the study of rings of con­tinu­ous func­tions. He was an in­ner mem­ber of the coun­try’s math­em­at­ic­al es­tab­lish­ment, hav­ing ob­tained a full pro­fess­or­ship at Har­vard as well as such hon­ors as elec­tion to the Na­tion­al Academy of Sci­ences. He was pro­foundly in­volved in the grow­ing trend to­ward put­ting math­em­at­ics re­search and edu­ca­tion on an ab­stract or ax­io­mat­ic found­a­tion, and was sharply in­flu­enced by the ef­forts of the Bourbaki school in France in this dir­ec­tion, which achieved a ma­jor im­pact in the years after the end of World War II.

Most im­port­ant of all, Stone was a man of force­ful char­ac­ter and un­ques­tioned in­teg­rity, with a strong in­sight in­to the math­em­at­ic­al qual­ity of oth­ers.

Stone’s fun­da­ment­al achieve­ment at Chica­go was to bring to­geth­er a fac­ulty group of un­pre­ced­en­ted qual­ity. In the seni­or fac­ulty he ap­poin­ted four very di­verse men with widely dif­fer­ent per­son­al styles and math­em­at­ic­al tastes. The most im­port­ant of these was un­doubtedly An­dré Weil, the dom­in­ant fig­ure of the Bourbaki group, who was one of the de­cis­ive taste-makers of the math­em­at­ic­al world, as well as the bril­liant re­search math­em­atician in his own work.

S. S. Chern, who was to be the cent­ral fig­ure of dif­fer­en­tial geo­metry in the world, was brought from his haven at the Prin­ceton In­sti­tute after his de­par­ture from China.

Ant­oni Zyg­mund, who be­came the cent­ral fig­ure of the Amer­ic­an school of clas­sic­al Four­i­er ana­lys­is, which he was to build up single-handed, came from the Uni­versity of Pennsylvania.

Saun­ders Mac Lane, who had been Stone’s col­league and sym­path­izer in the ab­stract pro­gram as ap­plied to al­gebra, came from a pro­fess­or­ship at Har­vard.

To­geth­er with Ad­ri­an Al­bert, who had been Dick­son’s prize stu­dent at Chica­go and a long­time mem­ber of the Chica­go de­part­ment, these men formed the cent­ral group of the new Stone de­part­ment at the uni­versity.

To do full justice to the kind of re­volu­tion that Stone brought about in Chica­go math­em­at­ics, one needs to per­form the un­edi­fy­ing task of ac­know­ledging the de­cay of the de­part­ment in the late 1930s and early 1940s. The great prestige and in­tel­lec­tu­al vi­tal­ity that had been cre­ated un­der the long reign of E. H. Moore as chair­man had not been main­tained after his re­tire­ment from the chair­man­ship at the end of the 1920s. His suc­cessors, G. A. Bliss and E. P. Lane, were not Moore’s equals in either math­em­at­ic­al in­sight or stand­ards. Es­pe­cially un­der Bliss’s re­gime, a strong tend­ency to in­breed­ing was in ac­tion, and as the great eld­er fig­ures of the de­part­ment died or re­tired, they were not re­placed by young­er math­em­aticians of equal caliber. Some of the most prom­ising of those who came in­to the de­part­ment soon left. There was one prin­cip­al ex­cep­tion: Ad­ri­an Al­bert. But des­pite his dis­tinc­tion as an al­geb­ra­ist in the Dick­son tra­di­tion, Al­bert at that time had neither the in­flu­ence nor the vis­ion to bring about the kind of rad­ic­al trans­form­a­tion that the de­part­ment needed, and that Stone brought about.

The in­sights that Stone provides in his firsthand ac­count of his great achieve­ments and of how they were brought about provide us once more with a dra­mat­ic vin­dic­a­tion of the de­cis­ive im­port­ance of the spe­cial qual­it­ies of sig­ni­fic­ant in­di­vidu­als as the ma­jor agents of the de­vel­op­ment of aca­dem­ic in­sti­tu­tions. In aca­dem­ic terms, Mar­shall Stone served as a great re­volu­tion­ary and a great tra­di­tion­al­ist. The re­volu­tion he made is the only kind which has a per­man­ent sig­ni­fic­ance — a re­volu­tion that founds or ren­ov­ates an in­tense and vi­tal tra­di­tion.