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Celebratio Mathematica

P. Emery Thomas

Topology; number theory

Paul Emery Thomas

by Rob Kirby, Calvin C. Moore and Kenneth Ribet

Paul Emery Thomas (known to every­one as Emery) was born on 15 Feb­ru­ary 1927 in Phoenix, Ari­zona. His fath­er had been born in North Dakota, and his moth­er in South Dakota. The fam­ily re­turned to North Dakota, where Emery gradu­ated from Cent­ral High School in Fargo, North Dakota, in 1945. He served a year in the Navy, re­pair­ing radar sets in Monterey, be­fore en­ter­ing Ober­lin Col­lege in 1946. Emery gradu­ated with a bac­ca­laur­eate de­gree in math­em­at­ics in 1950. He sang in the Ober­lin Con­ser­vat­ory chor­us, and spent sum­mers work­ing in Estes Park, Col­or­ado.

Next came a Rhodes Schol­ar­ship to Ox­ford Uni­versity (Hert­ford Col­lege), where he earned a first class de­gree and an MA. At Ox­ford, Emery de­veloped a strong in­terest in al­geb­ra­ic to­po­logy un­der the in­flu­ence of J. H. C. White­head and ini­ti­ated a long time friend­ship and col­lab­or­a­tion with Ioan James. Re­turn­ing to the US in 1953, he entered gradu­ate school at Prin­ceton Uni­versity and quickly com­pleted his doc­tor­al de­gree un­der Nor­man Steen­rod in 1955. His dis­ser­ta­tion, “A Gen­er­al­iz­a­tion of the Pon­trja­gin Square Co­homo­logy Op­er­a­tion,‘ was a sig­ni­fic­ant piece of work that in­tro­duced new co­homo­logy op­er­a­tions. An an­nounce­ment of it was pub­lished in the Pro­ceed­ings of the Na­tion­al Academy of Sci­ences, and the full ver­sion ap­peared in 1958 as a Mem­oir of the Amer­ic­an Math­em­at­ic­al So­ci­ety.

After ob­tain­ing his de­gree Emery served as a re­search as­so­ci­ate at Columbia Uni­versity for the 1955–56 aca­dem­ic year, and then he was ap­poin­ted as an as­sist­ant pro­fess­or at the Uni­versity of Cali­for­nia, Berke­ley, start­ing in 1956. His work branched out in­to oth­er areas of to­po­logy, in­clud­ing char­ac­ter­ist­ic classes, fiber bundles, the struc­ture of clas­si­fy­ing spaces, and vec­tor fields on man­i­folds. Emery mar­ried Jean Chan, a pot­ter and teach­er, in 1958, and they spent their first year to­geth­er at Ox­ford. Back at Berke­ley, he won rap­id pro­mo­tion, first to as­so­ci­ate pro­fess­or in 1960, and then to full pro­fess­or in 1963.

Emery’s work fur­ther broadened to in­clude prob­lems of ob­struc­tions to smooth­ing sin­gu­lar­it­ies and em­bed­ding prob­lems, but co­homo­logy the­ory (in­clud­ing co­homo­logy op­er­a­tions) re­mained a cent­ral tool in his work. Al­though he began his ca­reer as a to­po­lo­gist, he be­came in­ter­ested in num­ber the­ory and al­geb­ra­ic geo­metry by the late 1970s. He stud­ied Hil­bert mod­u­lar vari­et­ies and re­lated arith­met­ic ques­tions about real cu­bic fields. Emery car­ried out a re­search pro­gram centered around these ideas, of­ten in col­lab­or­a­tion with A. T. Vasquez of the City Uni­versity of New York.

After his work on Hil­bert mod­u­lar vari­et­ies was com­pleted, Emery real­ized that he had been trans­formed in­to a num­ber the­or­ist! From 1990 on, his pub­lished art­icles fall squarely in­to num­ber the­ory, and sev­er­al of them treat ques­tions in­volving Di­o­phant­ine equa­tions. His last pub­lished art­icle, pub­lished in 2000, deals with subtle ques­tions about the num­ber of solu­tions of cer­tain equa­tions that had been stud­ied pre­vi­ously by some of the gi­ants of twen­ti­eth cen­tury arith­met­ic. The re­view of the art­icle, writ­ten by the Stras­bourg num­ber the­or­ist Yann Bugeaud, con­cludes as fol­lows: “I would like to point out that this pa­per is writ­ten in a very clear and read­able style. Moreover, it con­tains sev­er­al im­port­ant new ideas, which will cer­tainly have fur­ther ap­plic­a­tions.”

Emery su­per­vised the doc­tor­al work of 31 stu­dents, many of whom also had suc­cess­ful ca­reers in math­em­at­ics. He served as vice chair of the De­part­ment of Math­em­at­ics and also as the de facto chair in 1967 dur­ing a dif­fi­cult time when the dean and de­part­ment could not agree on a chair. Emery be­came chair in 1972–73 and led the De­part­ment of Math­em­at­ics in design­ing a sys­tem of elect­ing the chair which has worked well ever since.

Emery was a Gug­gen­heim Fel­low at the In­sti­tute for Ad­vanced Study in 1961. He was a Miller Pro­fess­or in 1966–67, and then served on the ex­ec­ut­ive com­mit­tee of the Miller In­sti­tute dur­ing 1983–89 and was ex­ec­ut­ive dir­ect­or from Ju­ly 1987 through June 1989. He was a trust­ee of the Amer­ic­an Math­em­at­ics So­ci­ety dur­ing 1980-85 and served on nu­mer­ous com­mit­tees of the AMS. He was also deputy dir­ect­or of the Math­em­at­ic­al Sci­ences Re­search In­sti­tute from 1987 to 1990.

Emery was the first real to­po­lo­gist to come to Berke­ley, so he was a pi­on­eer in that sense. He was a warm, good-natured per­son — cheer­ful and pub­lic-spir­ited. One al­ways felt up­lif­ted after talk­ing to him. He was a val­ued cit­izen of the de­part­ment and the cam­pus. He re­tired in 1991 un­der the Uni­versity’s Vol­un­tary Early Re­tire­ment Pro­gram but re­mained act­ive in re­search. His last math­em­at­ics pa­per was fin­ished in 2003 and in gal­ley proofs when he died 13 June 2005, of com­plic­a­tions of Par­kin­son’s dis­ease.

Emery is sur­vived by his wife of 47 years, Jean, daugh­ters Jenny Thomas of Her­cules, Cali­for­nia, and Valer­ie Thomas of Montclair, New Jer­sey, and two grand­chil­dren.