Celebratio Mathematica

I am sorry that I can­not be there, but pleased that I may share a few of my thoughts.

I ar­rived at Berke­ley in 1983, already a ded­ic­ated and quite ex­per­i­enced teach­er, de­term­ined to find a Ph.D. ad­viser whom I could re­spect both as a re­search­er and as an edu­cat­or. In Emery I found this, as well as an in­cred­ible ment­or and sup­port­er.

I am par­tic­u­larly thank­ful that I was able to vis­it with Emery last year. He gave me a copy of his last pa­per, and ex­plained to me how we, as math­em­aticians, have a re­spons­ib­il­ity as we grow older to look at and write pa­pers on the “big pic­ture” in­stead of on small, spe­cif­ic prob­lems. He told me what was in his pa­per as an ex­ample of this. We then chat­ted about my frus­tra­tions with serving as De­part­ment Chair. When I men­tioned that I was be­ing pres­sured to ex­tend my term by one year, he quite force­fully in­formed me that I had to say no; that I had done my full term and that I needed the time for my re­search. I smiled at the thought of telling the col­lege ad­min­is­tra­tion that I couldn't be Chair be­cause my ad­viser said so. But, of course, Emery was cor­rect and, of course, I fol­lowed his ad­vice and am very glad of it!

I re­mem­ber that vis­it with great fond­ness and am com­for­ted by the know­ledge that Emery had nev­er stopped be­ing my ad­visor. I con­sider my­self to be very lucky.

I am very sorry I am not able to be in Berke­ley for Emery’s me­mori­al. I have al­ways thought that one of the high points in my ca­reer was to have Emery as my ad­viser and sub­sequently Emery and Jean as my friends.

I would like to re­late two stor­ies about Emery. None of them say much about Emery, the su­perb math­em­atician who made ma­jor con­tri­bu­tions to ho­mo­topy the­ory and the geo­metry of vec­tor fields, but rather say something about Emery’s hu­man side.

The first story has to do with my de­fer­ment from the draft. These were the Vi­et­nam War years, and I had been for­tu­nate to be one of the last classes to enter gradu­ate school with 5 years de­fer­ment. I ex­plained to Emery that I would like to work at, shall we say, a leis­urely pace. Emery was sym­path­et­ic to the idea. Un­for­tu­nately, not be­ing very dis­cip­lined, I took ad­vant­age of Cali­for­nia (and Berke­ley in the ’60s) and did not spend as much time as I should have on my schol­arly pur­suits. Then came the lot­tery! I did quite well, and was no longer threatened by the draft. I was not aware that Emery knew more about his stu­dents than just their math­em­at­ics. He knew my birth­day! A few weeks after the lot­tery I got one of those phone calls that are nev­er for­got­ten. Emery asked: “How is that thes­is go­ing?” After I got over my shock, with Emery’s won­der­ful guid­ance, I did fi­nally fin­ish up.

The oth­er story is also re­lated to the war. Uni­versit­ies around the coun­try were re­dir­ect­ing their en­er­gies to protest the war after Nix­on ini­ti­ated the bomb­ing of Cam­bod­ia. Not to be out­done, some mem­bers of the math de­part­ment held lengthy meet­ings dis­cuss­ing pos­sible protests. After many hours dis­cuss­ing many pro­pos­als, not all real­ist­ic, Emery, with a twinkle in his eye (at least in my memory), sug­ges­ted the math­em­aticians go on strike and re­fuse to prove the­or­ems! Some­how this en­cap­su­lated the im­prac­tic­al­ity of the pre­vi­ous hours of dis­cus­sion. The de­bate be­came more reas­on­able there­after. I do not re­call the form of protest en­dorsed by the group, but still re­call Emery’s sug­ges­tion.

I guess the point of these stor­ies is to show that Emery was more than a math­em­atician. He un­der­stood his role as a ment­or dur­ing dif­fi­cult polit­ic­al times. This be­came es­pe­cially true as his ill­ness pro­gressed. He was still a ment­or, but now teach­ing us the mean­ing of cour­age.

I am writ­ing in ap­pre­ci­ation of Emery’s work.

He was a main­stay of re­search in ho­mo­topy the­ory for many years, and his in­flu­ence, par­tic­u­larly through his su­per­vi­sion of gradu­ate stu­dents on math­em­at­ics in Berke­ley, was con­sid­er­able. I got to know him well through my vis­its to Berke­ley and his re­cip­roc­al vis­its to the UK. Over six or sev­en years in the 1970s we were in­volved in a very act­ive col­lab­or­a­tion, ap­ply­ing cobor­d­ism the­ory to prove the ri­gid­ity of cer­tain sin­gu­lar­it­ies in com­plex al­geb­ra­ic geo­metry. Throughout this work I was greatly im­pressed by his en­thu­si­asm, en­ergy and pro­fes­sion­al­ism, and so he kept the pro­ject mov­ing for­ward. He be­came a friend as well as a col­lab­or­at­or, and gave me valu­able ad­vice on a num­ber of is­sues.

Emery un­selfishly shared his love of math­em­at­ics. He was un­stint­ing with his at­ten­tion and his guid­ance. He al­ways knew the right ques­tions to ask: where fur­ther pro­gress could be made, and also where something was not quite right. The way Emery con­tin­ued to do math­em­at­ics even after be­ing struck by Par­kin­son’s syn­drome will al­ways be an in­spir­a­tion to me.

I had the priv­ilege of tak­ing gradu­ate courses from Emery Thomas, and be­ing a Ph.D. stu­dent of his. At that time he was about to start a new epis­ode of his math­em­at­ic­al life: he was switch­ing to num­ber the­ory. He was think­ing of ap­ply­ing to­po­lo­gic­al tech­niques to num­ber the­ory. Per­haps I was his last to­po­logy stu­dent. Only after I re­turned to my coun­try, my real in­volve­ment with his earli­er pa­pers star­ted, and I have re­gret­ted that I had in­sisted on do­ing what I had in mind dur­ing my Ph.D. stud­ies, in­stead of work­ing on his stuff. The fla­vor of his charm­ing pa­pers on vec­tor fields, and his beau­ti­ful work on top­ics like the span of man­i­folds, Post­nikov towers, and co­homo­logy op­er­a­tions, af­fected my math­em­at­ic­al taste deeply. Af­ter­ward I have al­ways sought this fla­vor, strength, rich­ness in all the pa­pers I read. It was an amaz­ing co­in­cid­ence that only one day be­fore I heard the sad news of his passing away, he was the sub­ject of a math­em­at­ic­al talk between me and Sel­man Ak­bu­lut on the phone. A the­or­em of Emery Thomas on the span of man­i­folds, that I could luck­ily re­mem­ber, had greatly im­proved Sel­man’s res­ults in his latest pa­per, and saved him from months of ex­tra work. Two days later I talked about this irony of fate with Sel­man; “it must be his kind spir­it”, he said.

Emery Thomas was a great ad­visor and a kind per­son. I will al­ways re­mem­ber our vis­its at Stan­ford for sem­inars in his car, his kind, fath­erly ges­tures like in­vit­ing me to lunch at un­ex­pec­ted times.

I would like to send my con­dol­ences to his fam­ily and to the whole math­em­at­ic­al com­munity.

I con­sider my­self very for­tu­nate to have been a doc­tor­al stu­dent of Emery Thomas. At that time, Emery was pub­lish­ing the­or­ems on the span of man­i­folds, on the ex­ist­ence of im­mer­sions, sub­mer­sions, em­bed­dings, etc., util­iz­ing the ob­struc­tion the­ory of mod­i­fied Post­nikov res­ol­u­tions. His re­search showed his stu­dents the im­port­ance of ap­ply­ing al­geb­ra­ic to­po­logy to geo­met­ric prob­lems. He was a great ad­visor and an ex­cel­lent lec­turer. Par­tic­u­larly mem­or­able was a party at his res­id­ence for Beno Eck­mann in 1967.

I send my con­dol­ences to his fam­ily.