Celebratio Mathematica

Gilbert Ames Bliss

Calculus of variations  ·  U Chicago

Graduate student at Chicago in the twenties

by W. L. Duren, Jr.

As an un­der­gradu­ate at Tu­lane in New Or­leans, 1922–1926, I was pro­grammed to go to the Uni­versity of Chica­go and study ce­les­ti­al mech­an­ics with F. R. Moulton. My teach­er, H. E. Buchanan, had been a stu­dent of Moulton. That was an ex­ample of the great strength of the Uni­versity of Chica­go. Its PhD gradu­ates made up a large part of the fac­ulties of uni­versit­ies throughout the Mis­sis­sippi Val­ley, Mid­w­est and South­w­est. So they sent their good stu­dents back to Chica­go for gradu­ate work. I went there first in the sum­mer of 1926 and came to stay in 1928. In the in­ter­im I stud­ied Moulton’s Ce­les­ti­al Mech­an­ics and some of his pa­pers in or­bit the­ory. I met Moulton at a sec­tion­al meet­ing of the MAA where he was the in­vited speak­er. He was a man of great charm and en­ergy and was most en­cour­aging to me. But by the time I got to Chica­go in 1928 Moulton had resigned. I was told that he felt it was an eth­ic­al re­quire­ment, since he and his wife were get­ting a di­vorce. On the ad­vice of T. F. Cope, an­oth­er former stu­dent of Buchanan, who was work­ing with Bliss, I turned to Bliss as an ad­visor in the cal­cu­lus of vari­ations.

It was a down cycle for math­em­at­ics at Chica­go. All the great schools have their downs as well as ups, partly be­cause great men re­tire, partly be­cause their lines of in­vest­ig­a­tion dry up. At Chica­go at that time a young stu­dent could see the hol­d­overs of the great peri­od, 1892–1920, in Eliakim Hast­ings Moore, of­fi­cially re­tired, Le­onard E. Dick­son, round­ing out his work in al­gebra, Gil­bert A. Bliss, busy with ad­min­is­tra­tion and plan­ning for the pro­jec­ted Eck­hart Hall. Also there was Her­bert E. Slaught, teach­er and doer, one of the ori­gin­al or­gan­izers of the Math­em­at­ic­al As­so­ci­ation of Amer­ica and its Monthly, even if he played only a sup­port­ing role in math­em­at­ics it­self. He had an ex­tro­vert, friendly per­son­al­ity that reached out and got hold of you, wheth­er he was or­gan­iz­ing a de­part­ment so­cial or the Math­em­at­ic­al As­so­ci­ation of Amer­ica. He was the teach­er of teach­ers and key fig­ure in Chica­go’s hold on edu­ca­tion in the mid­w­est and south. Every gradu­ate de­part­ment needs a man like Slaught if it is for­tu­nate enough to find one. He was be­ing suc­ceeded by Ral­ph G. Sanger, a stu­dent of Bliss, an out­stand­ing un­der­gradu­ate teach­er, though not the or­gan­izer Slaught was.

The Uni­versity of Chica­go was foun­ded in 1892 with sub­stan­tial fin­an­cial sup­port from John D. Rock­e­feller. Wil­li­am Rainey Harp­er, the first pres­id­ent, had bold edu­ca­tion­al ideas, one of which was that the United States was ready for a primar­ily gradu­ate uni­versity, not just a col­lege with gradu­ate school at­tached. Harp­er brought E. H. Moore from Yale to es­tab­lish his de­part­ment of math­em­at­ics. Moore’s gradu­ate teach­ing was done in a re­search labor­at­ory set­ting. That is, stu­dents read and presen­ted pa­pers from journ­als, usu­ally Ger­man, and tried to de­vel­op new the­or­ems based on them. The gen­er­al sub­ject of these sem­inars was a pre-Banach form of geo­met­ric ana­lys­is that Moore called “gen­er­al ana­lys­is.” It was it­self not al­to­geth­er suc­cess­ful. But even if gen­er­al ana­lys­is did not suc­ceed, Moore’s sem­inars on it gen­er­ated a sur­pris­ing num­ber of new res­ults in gen­er­al to­po­logy, among them the Moore the­or­em on it­er­ated lim­its and Moore–Smith con­ver­gence. Moore’s sem­inars also pro­duced some out­stand­ing math­em­aticians. His earli­er stu­dents had in­cluded G. D. Birk­hoff, Os­wald Veblen, T. H. Hildebrant and R. L. Moore, who took off in dif­fer­ent math­em­at­ic­al dir­ec­tions. R. L. Moore de­veloped the teach­ing meth­od in­to an in­tens­ive re­search train­ing re­gi­men of his own, which was very suc­cess­ful in pro­du­cing re­search math­em­aticians at the Uni­versity of Texas.

I stud­ied gen­er­al ana­lys­is with oth­er mem­bers of the fac­ulty in­clud­ing R. W. Barn­ard, whom Moore had des­ig­nated as his suc­cessor and whose notes re­cord the second form of the the­ory, (Am. Philo­soph­ic­al Soc., Mem­oirs, v. 1, Phil­adelphia, 1935). In­stead of tak­ing the gen­er­al ana­lys­is courses, my old friend E. J. Mc­Shane, from New Or­leans, worked in Moore’s small sem­in­ar in the found­a­tions of math­em­at­ics. Al­though he was of­fi­cially a stu­dent of Bliss, I think he was in a sense Moore’s last stu­dent.

Moore him­self was me­tic­u­lous in man­ners and dress. He would stop you in the hall, gently re­move a pen from an out­side pock­et and sug­gest that you keep it in the in­side pock­et of your jack­et. Nobody thought of not wear­ing a jack­et. But Moore was less gentle if you used your left hand as an eraser, and he dis­played tower­ing an­ger at in­tel­lec­tu­al dis­hon­esty. To un­der­stand him and his times one must read his re­tir­ing ad­dress as Pres­id­ent of the So­ci­ety [Sci­ence, March 1903]. In those days the So­ci­ety ac­cep­ted re­spons­ib­il­ity for teach­ing math­em­at­ics and Moore’s ad­dress was largely de­voted to the or­gan­iz­a­tion of teach­ing, the cur­riculum, and the ideas of some of the great teach­ers of the time, Boltz­man, Klein, Poin­caré, and, in this coun­try, J. W. A. Young and John Dewey, whose ideas Moore sup­por­ted by pro­pos­ing a math­em­at­ics labor­at­ory. This ad­dress was ad­op­ted as a sort of charter by the Na­tion­al Coun­cil of Teach­ers of Math­em­at­ics and re­pub­lished in its first Year­book (1925). By the time I got to Chica­go the As­so­ci­ation had been formed to re­lieve the So­ci­ety of con­cern for col­lege edu­ca­tion, and NCTM to re­lieve it of re­spons­ib­il­ity for the school cur­riculum and train­ing teach­ers. In the top uni­versit­ies only re­search brought prestige, even if a few, like Slaught, up­held the im­port­ance of teach­ing.

L. E. Dick­son’s stu­dents ten­ded to identi­fy them­selves strongly as num­ber the­or­ists or al­geb­ra­ists. I felt this par­tic­u­larly in Ad­ri­an A. Al­bert [sic], Gor­don Pall and Arnold Ross. All his life Al­bert strongly iden­ti­fied him­self, first as an al­geb­ra­ist, later with math­em­at­ics as an in­sti­tu­tion and cer­tainly with the Uni­versity of Chica­go. I re­mem­ber him as an ad­vanced gradu­ate stu­dent walk­ing in­to Dick­son’s class in num­ber the­ory that he was vis­it­ing, smil­ing and self con­fid­ent. He knew where he was go­ing. Dick­son was teach­ing from the gal­ley sheets of his new In­tro­duc­tion to the The­ory of Num­bers (Uni­versity of Chica­go Press, 1929) with its nov­el em­phas­is on the rep­res­ent­a­tion of in­tegers by quad­rat­ic forms. I think he re­ques­ted Al­bert to sit in for his com­ments on this as­pect. He was tre­mend­ously proud of Al­bert. I re­mem­ber A\( ^3 \) too with his beau­ti­ful young wife, Frieda, at the per­en­ni­al de­part­ment bridge parties. He had su­perb men­tal powers; he could read a page at a glance. One could see even then that as heir ap­par­ent to Dick­son he would do his own math­em­at­ics rather than a con­tinu­ation of Dick­son’s, however much he ad­mired Dick­son.

In the con­ven­tion­al sense Dick­son was not much of a teach­er. I think his stu­dents learned from him by emu­lat­ing him as a re­search math­em­atician more than be­ing taught by him. Moreover, he took them to the fron­ti­er of re­search, for the sub­ject mat­ter of his courses was usu­ally new math­em­at­ics in the mak­ing. As Ant­oinette Hu­s­ton said, “He made you want to be with him in­tel­lec­tu­ally. When you are young, reach­ing for the stars, that is what it is all about.” He was good to his stu­dents, kept his prom­ises to them and backed them up. Yet he could be a ter­ror. He would some­times fly in­to a rage at the de­part­ment bridge games, which he ap­peared to take ser­i­ously. And he was re­lent­less when he smelled blood in the or­al ex­am­in­a­tion of some hap­less, cringing vic­tim. He was an in­defatig­able work­er and in pub­lic a great show­man, with the flair of a rough and ready Tex­an. An en­dur­ing bit in the le­gend is his blurt: “Thank God that num­ber the­ory is un­sul­lied by any ap­plic­a­tion.” He liked to re­peat it him­self as well as his ac­count of his and his wife’s hon­ey­moon, which he said was a suc­cess, ex­cept that he got only two pa­pers writ­ten.

The theme of beauty for its own sake was ex­pressed more sur­pris­ingly by an­oth­er Tex­an who worked in mech­an­ics and po­ten­tial the­ory, W. D. Mac­Mil­lan. Ac­cord­ing to the story he had come to Chica­go as a ma­ture man, without a col­lege edu­ca­tion, to sell his cattle. Hav­ing sold them, he went to Chica­go’s Yerkes Ob­ser­vat­ory to see the Texas stars through the tele­scope. He was so fas­cin­ated that he stayed on to get his de­grees in rap­id suc­ces­sion, all summa cum laude. Then he re­mained as a mem­ber of the fac­ulty. One day in his course on po­ten­tial the­ory he wrote some im­port­ant par­tial dif­fer­en­tial equa­tions on the board with ob­vi­ous pleas­ure, draw­ing the par­tial de­riv­at­ive signs with a flour­ish. Stand­ing back to ad­mire these equa­tions, he said: “That is just beau­ti­ful. People who ask, ‘What’s it good for?’, they make me tired! Like when you show a man the Grand Canyon for the first time and you stand there as you do, say­ing noth­ing for a while.” And we could see that old Mac was really look­ing at the Grand Canyon. “Then he turns to you and asks, ‘What’s it good for?’ What would you do? Why, you would kick him off the cliff!” And old Mac kicked a chair halfway across the room. He was a prodigy, a good lec­turer, an ab­so­lutely fas­cin­at­ing per­son­al­ity with a twink­ling wit. Some of his work was out­stand­ing, yet he had few doc­tor­al stu­dents.

Ce­les­ti­al mech­an­ics was be­ing car­ried on by the young Wal­ter Bartky, who was, I think, Moulton’s last stu­dent. But ce­les­ti­al mech­an­ics had gone in­to a bar­ren peri­od and Bartky with his su­perb tal­ents turned to oth­er ap­plic­a­tions of dif­fer­en­tial equa­tions, to stat­ist­ics and to ad­min­is­tra­tion.

Lawrence M. Graves was the prin­cip­al hope of the de­part­ment for car­ry­ing on the cal­cu­lus of vari­ations, which he did in the spir­it of func­tion­al ana­lys­is. He was my fa­vor­ite pro­fess­or be­cause he knew a lot of math­em­at­ics, knew it well, and in an un­as­sum­ing way was glad to share it with you. Al­though he taught Moore’s gen­er­al ana­lys­is, he poin­ted out the dif­fi­culties in it to me. His own brand of func­tion­al ana­lys­is was more ori­ented to­wards the use of the Frêchet dif­fer­en­tial in Banach space.

Re­search in geo­metry at Chica­go was a con­tinu­ation of Wyl­cz­in­ski’s pro­ject­ive dif­fer­en­tial geo­metry. There was no to­po­logy, though we heard that Veblen’s stu­dents stud­ied something called ana­lys­is sit­us at Prin­ceton. I knew so little about the sub­ject that years later when I wanted to pre­pare for Morse the­ory I spent months study­ing Kur­atowski’s point set to­po­logy be­fore it dawned on me that what I wanted was al­geb­ra­ic to­po­logy. E. P. Lane and his stu­dents car­ried on the study of pro­ject­ive dif­fer­en­tial geo­metry us­ing rather crude ana­lyt­ic­al meth­ods, that is, ex­pan­sions in which one neg­lected high­er or­der terms. We who were not Lane’s stu­dents ten­ded to look on it with dis­dain as be­ing non-rig­or­ous. But the struc­ture of the the­ory was beau­ti­ful, I thought. Lane was hon­est about the short­com­ings of the meth­ods, though he did not know how to over­come them.

Lane was a very fine man. I had come to Chica­go in 1926 to run the high hurdles in the Na­tion­al In­ter­col­legi­ate Track and Field Meet at Sol­diers Field. I placed in the fi­nals and some mem­bers of the U.S. Olympic Com­mit­tee urged me to keep work­ing for the 1928 Olympics. So I worked on the Stagg Field track un­til an ac­ci­dent set off a series of leg in­fec­tions. I was very sick in Billings Hos­pit­al in the days be­fore an­ti­bi­ot­ics and it was Lane who came to the hos­pit­al to see me and make sure that I got the best avail­able care. The only way I was ever able to ex­press my thanks to him was to do a sim­il­ar ser­vice to some of my own stu­dents in later years. I guess that is the only way we ever thank our teach­ers.

Bliss was an out­stand­ing mas­ter of the lec­ture-dis­cus­sion. He could come in­to a class in cal­cu­lus of vari­ations ob­vi­ously un­pre­pared, be­cause of the de­mands of his chair­man­ship, and still de­liv­er an el­eg­ant lec­ture, draw­ing the stu­dents in­to each de­duc­tion or cal­cu­la­tion, as he looked at us quiz­zically and waited for us to tell him what to write. His stu­dents learned their cal­cu­lus of vari­ations very thor­oughly. Yet we did not work to­geth­er, ex­cept in so far as we presen­ted class as­sign­ments. Each re­search stu­dent re­por­ted to Bliss by ap­point­ment. The sub­ject it­self had come to be too nar­rowly defined as the study of loc­al, in­teri­or min­im­um points for cer­tain pre­scribed func­tion­als giv­en by in­teg­rals of a spe­cial form. Gen­er­al­iz­a­tion came only at the cost of ex­cess­ive nota­tion­al and ana­lyt­ic com­plic­a­tions. It was like de­fin­ing the or­din­ary cal­cu­lus to con­sist ex­clus­ively of the chapter on max­ima and min­ima. A sure sign of the dec­ad­ence of the sub­ject was Bliss’s pro­ject to pro­duce a his­tory of it, like Dick­son’s His­tory of the The­ory of Num­bers. The his­tory reached pub­lic­a­tion only in the form of cer­tain theses im­bed­ded in Con­tri­bu­tions to the Cal­cu­lus of Vari­ations, 4 vols, 1930–1944, Uni­versity of Chica­go Press.

It is per­haps sur­pris­ing that this nar­rowly pre­scribed re­gi­men turned out men who did im­port­ant work in en­tirely dif­fer­ent areas as, for ex­ample, A. S. House­hold­er did in bio­mathem­at­ics and nu­mer­ic­al ana­lys­is, and Her­man Gold­stine did in com­puter the­ory. Among all of us Mag­nus Hestenes has been most faith­ful to the spir­it of Bliss’s teach­ing in car­ry­ing on re­search in the cal­cu­lus of vari­ations. Yet when Pontry­agin’s op­tim­al con­trol pa­pers re­vived in­terest in the sub­ject many years later, stu­dents of Bliss were eas­ily able to get in­to it. Op­tim­al con­trol the­ory really con­tained re­l­at­ively little that was cor­rect and not in the cal­cu­lus of vari­ations. In fact, op­tim­al con­trol was an­ti­cip­ated by the thes­is of Carl H. Den­bow, loc. cit.

Quantum mech­an­ics was break­ing wide open in the twen­ties. Bliss him­self got in­to it with his stu­dents by study­ing Max Born’s el­eg­ant ca­non­ic­al vari­able treat­ment of the Bo­hr the­ory. While that was go­ing on, Som­mer­feld’s Wel­len­mech­an­is­che Er­gän­zungs­band to his Atombau und Spek­trallini­en (Vieweg, Braun­sch­weig, 1929) came out. It was the first con­nec­ted treat­ment of the new wave mech­an­ics for­mu­la­tion of quantum mech­an­ics due to de Broglie and Schrödinger. We dropped everything to study wave mech­an­ics. Bliss was a re­mark­ably know­ledge­able math­em­at­ic­al phys­i­cist and quite ex­pert in the bound­ary value prob­lems of par­tial dif­fer­en­tial equa­tions. That was not so re­mark­able in a math­em­atician of his gen­er­a­tion. The nar­row­ing of the defin­i­tion of a math­em­atician and with­draw­al in­to ab­stract spe­cial­iz­a­tions was just be­gin­ning. In fact Bliss had been chief of math­em­at­ic­al bal­list­ics for the US Gov­ern­ment in World War I, and later was com­mis­sioned to do a math­em­at­ic­al study of pro­por­tion­ate rep­res­ent­a­tion for pur­poses of re­as­sign­ing Con­gres­sion­al dis­tricts. Bliss did not fol­low up his move in­to quantum mech­an­ics but re­turned to the clas­sic­al cal­cu­lus of vari­ations.

There were al­ways more stu­dents in sum­mers with all the teach­ers who came. Vis­it­ing pro­fess­ors like War­ren Weaver, E. T. Bell, C. C. Mac Duffee and Dun­ham Jack­son came to teach. And there was the mem­or­able vis­it of G. H. Hardy which was sup­posed to provide a unit­ing of Hardy’s ana­lyt­ic ap­proach to War­ing’s the­or­em with Dick­son’s al­geb­ra­ic ap­proach. Even with this in­fu­sion of tal­ent, the of­fer­ings of the de­part­ment were rather nar­row. Be­sides hav­ing no to­po­logy as such, more sur­pris­ingly, there was little in com­plex func­tion the­ory. And I do not re­call be­ing in a sem­in­ar, either a re­search or journ­al sem­in­ar. Es­sen­tially all teach­ing was done in lec­tures. Yet the only one of the abler stu­dents who I re­mem­ber tak­ing the ini­ti­at­ive to go else­where was Saun­ders Mac Lane, when he did not find at Chica­go what he was look­ing for.

I once asked Ed­win B. Wilson, a famed uni­ver­sal­ist among math­em­aticians, how he came to switch from ana­lys­is to stat­ist­ics at Yale. With a hu­mor­ous twinkle he said: “An im­mut­able law of aca­demia is that the course must go on, no mat­ter if all of the sub­stance and spir­it has gone out of it with the passing of the ori­gin­al teach­er. So when (Jo­si­ah Wil­lard) Gibbs re­tired, his courses had to go on. And the de­part­ment said: ‘Wilson, you are it’.” A gradu­ate stu­dent at Chica­go in the late twen­ties could see this im­mut­able aca­dem­ic law in ef­fect. In each line of study of the, then passing, old Chica­go de­part­ment, a young­er Chica­go PhD had been des­ig­nated to carry on the work. If, in one’s im­ma­tur­ity, this was not ap­par­ent, the point was made loud and clear in a blast from Dick­son dur­ing a col­loqui­um with gradu­ate stu­dents present. Dick­son charged the chair­man with per­mit­ting the de­part­ment to slide in­to second rate status. It was true that the spir­it of ori­gin­al in­vest­ig­a­tion giv­en way to di­li­gent ex­pos­i­tion in some of these fields. In some cases the fields them­selves had gone sterile.

It was the lot of Bliss to preside over this ebb cycle of the de­part­ment. He did an im­press­ive best pos­sible with what he had, with high math­em­at­ic­al stand­ards, firmly, kindly and quietly. Most of the dif­fi­culties he had in­her­ited. Bliss was able to ap­point some out­stand­ing young men but, if he had asked for the massive fin­an­cial out­lay to bring in es­tab­lished lead­ing math­em­aticians to make a new start like the ori­gin­al one un­der Pres­id­ent Harp­er, the sup­port would not have been forth­com­ing, even with a math­em­atician, Max Ma­son, as pres­id­ent and cer­tainly not with the young Robert M. Hutchins, bent primar­ily on es­tab­lish­ing his new col­lege. It took the Man­hat­tan Pro­ject, the first nuc­le­ar pile un­der the Stagg Field bleach­ers and En­rico Fermi to con­vince Hutchins of the im­port­ance of phys­ic­al sci­ence and math­em­at­ics and to throw massive re­sources in­to the re­or­gan­iz­a­tion of the de­part­ment near the end of World War II. Such re­or­gan­iz­a­tions are ne­ces­sary from time to time in every gradu­ate de­part­ment. They can be ef­fect­ive only when the time is right. It is the mark of a great uni­versity to re­cog­nize the ne­ces­sity to break the im­mut­able law of aca­demia, and the op­por­tun­ity, and to do it when the time is right. However, there were deep hurts, sym­bol­ized by Bliss’s re­fus­al ever again to set foot in Eck­hart Hall to his death. But this is really get­ting ahead of my story.

It was no ebb cycle for the Uni­versity of Chica­go as a whole in the twen­ties. There was in­tel­lec­tu­al ex­cite­ment in many places in the uni­versity. I at­ten­ded the phys­ics col­loquia where the great in­nov­at­ors of the day came to talk. With Mr. Bliss’s grudging con­sent, I took Ar­thur Compton’s course in X-rays. He already had the No­bel Prize for his work on the phe­nom­ena of X-rays col­lid­ing with elec­trons. Yet he seemed so naïvely simple minded to me, far less ex­pert and men­tally pro­found than oth­er phys­i­cists in the de­part­ment. Some­where in here Ein­stein came for a brief vis­it. He per­mit­ted him­self to be es­cor­ted by the phys­ics gradu­ate stu­dents for a tour of their ex­per­i­ments. To one he offered a sug­ges­tion. The brash young man ex­plained im­me­di­ately why it could not work. Ein­stein shook his head sadly. “My ideas are nev­er good,” he said.

Michel­son, an­oth­er Noble Prize­man, was around, though re­tired. So was the great geo­lo­gist, Cham­ber­lin, with his plan­etes­im­al hy­po­thes­is in cos­mo­logy. In bio­logy and bio­chem­istry the great break­throughs on the chem­ic­al nature of the ster­oid hor­mones and their ef­fects on growth and de­vel­op­ment were ex­cit­ingly un­fold­ing. Young Se­wall Wright was at­tract­ing stu­dents to his math­em­at­ic­al ge­net­ics. Eco­nom­ics prom­ised a real break­through, though as it turned out, it was slow in com­ing. Lin­guist­ics was bur­geon­ing. An­thro­po­logy and ar­che­ology were still act­ively fol­low­ing up the res­ults of digs in Egypt, Tur­key and Meso­pot­amia. The great de­bates over the truth of the­or­ies of re­lativ­ity and quantum mech­an­ics were ra­ging. What was later to be plan­et Pluto had been ob­served as “Plan­et X” but heated ar­gu­ments per­sisted on what it really was. On Sundays the Uni­versity Chapel pro­duced a suc­ces­sion of the lead­ing Chris­ti­an and Jew­ish spokes­men of the day. The text­book, The Nature of the World and of Man, H. H. New­man ed., Uni­versity of Chica­go Press, 1926, by il­lus­tri­ous Chica­go fac­ulty mem­bers was the best sur­vey of phys­ic­al and bio­lo­gic­al know­ledge for col­lege stu­dents that I have ever seen, though now dated, of course.

And out­side the uni­versity the dan­ger­ous and ugly city of Chica­go nev­er­the­less had its charms, cul­tur­al and oth­er­wise, that could take up all the time (and money) of a coun­try boy. One could hear Mary Garden or Rosa Raisa at the Chica­go Op­era by get­ting a job as ush­er or su­per, or at­tend a fiesta in hon­or of the pat­ron saint of some Hal­stead Street com­munity that main­tained its iden­tity with the home vil­lage in the old coun­try. One could drink wine at Al­ex­an­der’s clandes­tine speak­easy. For re­call that it was Pro­hib­i­tion and the height of the boot­leg­ging days of Al Ca­pone and rival gangs. The fam­ous Valentine Day mas­sacre was just one of the lur­id stor­ies in the Chica­go Tribune. We stu­dents formed an in­form­al pro­tect­ive as­so­ci­ation to pro­mul­gate rules to op­tim­ize safety for one­self and date. One old boy from Geor­gia, a gradu­ate stu­dent in his­tory, was so im­pressed by our ad­mon­i­tion nev­er to ap­proach a car ask­ing him to get in, that, when a po­lice car chal­lenged him with or­der to stop, he just took off in a blaze of speed. Caught later, out of breath, his one phone call brought some of us to po­lice court to testi­fy to his char­ac­ter. The of­ficer who had made the ar­rest moved to dis­miss the charges on the con­di­tion that “the de­fend­ant ap­pear at Sol­diers Field next Sat­urday and run for our com­pany in the po­lice­men’s track meet.” But it was grim busi­ness. Po­lice, armed with ma­chine guns, in such a car once ar­res­ted me on sus­pi­cion of rape on the Mid­way (not guilty!). Oth­er stu­dents were mugged, raped, robbed and even killed.

Like today it was a time of in­fla­tion and most of us were poor. I had a full fel­low­ship of \$410, of which \$210 had to be re­turned in tu­ition for three quar­ters. A dorm­it­ory room cost \$135 out of what was left. We could get cheap meals at the Com­mons, and on Sundays one could go to the Mer­it Cafet­er­ia and splurge on a plate-sized slab of roast beef. It cost 28¢ but it was worth it. We all looked for­ward to a teach­ing job, I think. Those jobs re­quired 15 hours of teach­ing for about \$2700. Soon the de­pres­sion hit and, if we were lucky, we kept our jobs with salary cut to \$2400. Some be­gin­ning salar­ies for Chica­go PhD’s were as low as \$1800 in the early thirties.

Be­fore clos­ing these re­col­lec­tions I must write something about wo­men as gradu­ate stu­dents in those times, not long after the vic­tory of wo­men’s suf­frage. Only years later did I learn that it was con­sidered un­lady­like to study math­em­at­ics. Many of the gradu­ate stu­dents in math­em­at­ics were wo­men. In fact there were 26 wo­men PhD’s in math­em­at­ics at Chica­go between 1920 and 1935. I shall men­tion only a few by name. May­me I. Logs­don (1921) was in the fac­ulty of the de­part­ment. Mina Rees (1931) was already show­ing the kind of abil­ity that led her to a dis­tin­guished ad­min­is­trat­ive ca­reer at Hunter Col­lege and CUNY. She did more than any oth­er per­son to gain fed­er­al sup­port for math­em­at­ics through her po­s­i­tion as chief, Math­em­at­ics Branch ONR, when the Na­tion­al Sci­ence Found­a­tion was es­tab­lished. Oth­ers in­cluded Abba New­ton (1933), chair­man at Vas­sar, and Frances Baker (1934) also of Vas­sar, Ju­lia Wells Bower (1933), chair­man at Con­necti­c­ut Col­lege, Mar­ie Litzinger (1934), chair­man, Mt. Holy­oke, Lois Grif­fiths (1927) North­west­ern, Be­atrice Ha­gen (1930) Penn State, and Gwen­eth Humphreys (1935) Ran­dolph Ma­con. Gradu­ate stu­dents mar­ried gradu­ate stu­dents, though of ne­ces­sity only after the man had his de­gree. In the de­part­ment Vir­gin­ia Haun mar­ried E. J. Mc­Shane. Emily Chand­ler, stu­dent of Dick­son, mar­ried Henry Pix­ley and con­tin­ued her pub­lish­ing and teach­ing ca­reer at the Uni­versity of De­troit. Ant­oinette Kil­len mar­ried Ral­ph Hu­s­ton. They both later taught at Rens­selaer Poly­tech. Aline Huke mar­ried a non-Chica­go math­em­atician, Or­rin Frink, and con­tin­ued her teach­ing at Penn State. Jew­el Hughes Bushey was in the de­part­ment of Hunter Col­lege. These, and a num­ber of oth­ers, were able to con­tin­ue their pro­fes­sion­al work in spite of fam­ily ob­lig­a­tions. Even in­ter­mar­riage between de­part­ments was per­mit­ted! My wife to be, Mary Hardesty, was in zo­ology. We got our PhD de­grees in the same com­mence­ment.

Look­ing back on those days, I won­der if the cur­rent wo­men’s lib­er­a­tion has even yet suc­ceeded in push­ing the pro­fes­sion­al status of wo­men to the level already reached in the twen­ties. Maybe this time wo­men can hold their gains in uni­versit­ies.