Celebratio Mathematica

I knew and re­spec­ted Andy Gleason as a math­em­atician for most of my ca­reer and most of his. His con­tri­bu­tions to math­em­at­ics are well known and worthy of re­spect, but his over­all con­tri­bu­tion to the math­em­at­ics pro­fes­sion goes far bey­ond the math­em­at­ics he did, the courses he taught, the stu­dents he in­flu­enced, his role on the Har­vard cam­pus, and his ex­tens­ive com­mit­ment to math­em­at­ics edu­ca­tion. For many years Andy was the con­sum­mate per­son to call upon to rep­res­ent the pro­fes­sion in a vari­ety of set­tings. His cre­den­tials were im­pec­cable: a Yale gradu­ate, a Har­vard pro­fess­or with a chair in math­em­aticks (with a “ck”) and nat­ur­al philo­sophy. What bet­ter per­son to send to Wash­ing­ton to testi­fy be­fore a con­gres­sion­al com­mit­tee or to add to the Math­em­at­ic­al Sci­ence Edu­ca­tion Board of the Na­tion­al Academy of Sci­ences or to have as a spokes­per­son at the Coun­cil of Sci­entif­ic So­ci­ety Pres­id­ents? Not only did he have the cre­den­tials, but when he spoke, he had something to say: thought­ful, well con­ceived, suit­able to the audi­ence, com­pre­hens­ive, to the point, and, most likely, brief. His man­ner was gra­cious and his de­mean­or mod­est. Raoul Bott said it well at Andy’s re­tire­ment party:

The straight­ness Andy brings to his math­em­at­ics he ex­tends to all that have deal­ings with him. In these many years to­geth­er I have nev­er heard a word that seemed false in what he had to say. Nor have I seen him hes­it­ate to take on any task, however oner­ous, for the wel­fare of the De­part­ment or the Uni­versity. Need­less to say, the rest of us are mas­ters of this art. For, of course, the best way to avoid a chore is to be out of earshot when it is as­signed. Hun­gari­ans im­bibe this prin­ciple with their moth­er’s milk, but Andy, for all his bril­liance, nev­er seems to have learned it [3].

With­in the pro­fes­sion Andy served in many ways. He was pres­id­ent of the Amer­ic­an Math­em­at­ic­al So­ci­ety in 1981 and 1982. At the Math­em­at­ic­al As­so­ci­ation of Amer­ica he served on the com­mit­tee on the Put­nam Prize Com­pet­i­tion (he placed in the top five three years in a row dur­ing his years as an un­der­gradu­ate) and the Sci­ence Policy Com­mit­tee. In 1996 the MAA honored him with its Yueh-Gin Gung and Dr. Charles Y. Hu Award for Dis­tin­guished Ser­vice [e1].

Andy chaired the com­mit­tee in charge of the 1986 In­ter­na­tion­al Con­gress of Math­em­aticians in Berke­ley, Cali­for­nia. Hope Daly, the staff per­son from the AMS who handled the op­er­a­tion, says of him, “He was won­der­ful, a great lead­er. He quickly un­der­stood prob­lems when they arose and had im­me­di­ate an­swers. And he was really won­der­ful to work with, humble, pleas­ant.” She of­fers as an ex­ample of the many ways in which he could help his ac­tion on the morn­ing of the meet­ing when he saw the staff mak­ing dir­ec­tion signs for the some­what con­fus­ing Berke­ley cam­pus to re­place those the stu­dents had taken down the night be­fore. Ask­ing what needed to be done, he was told the signs had to be tacked up. So he took a stack and a ham­mer and went out and did just that. After the suc­cess­ful con­gress he ed­ited the pro­ceed­ings; see [2].

He was a mas­ter of ex­pos­i­tion for audi­ences at any level. His 1962 Earle Ray­mond Hedrick Lec­tures for the MAA on “The Co­ordin­ate Prob­lem” ad­dressed the need for good names. The ab­stract1 reads:

In the study of math­em­at­ic­al struc­tures, es­pe­cially when com­pu­ta­tions are to be made, it is im­port­ant to have a sys­tem for nam­ing all of the ele­ments. Moreover, it is es­sen­tial that the names be so chosen that the struc­tur­al re­la­tions between the vari­ous ele­ments can be ex­pressed by re­la­tions between their names. When the struc­ture has car­din­al \( \aleph_0 \) it is nat­ur­al to take in­tegers or fi­nite se­quences of in­tegers as names. When the car­din­al is \( c \), it is ap­pro­pri­ate to take real num­bers or se­quences of real num­bers as names. Most math­em­at­ic­al sys­tems are de­scribed ini­tially in terms of purely syn­thet­ic ideas with no ref­er­ence to the real num­ber sys­tem. The­or­ems con­cern­ing the ex­ist­ence of ana­lyt­ic rep­res­ent­a­tions for dif­fer­ent types of struc­tures [are] dis­cussed.

He also wrote for the gen­er­al read­er. In Sci­ence in 1964 he ex­plained the re­la­tion­ship between to­po­logy and dif­fer­en­tial equa­tions [1]. His first para­graph sets the tone for that hard task:

It is no­tori­ously dif­fi­cult to con­vey the prop­er im­pres­sion of the fron­ti­ers of math­em­at­ics to non­spe­cial­ists. Ul­ti­mately the dif­fi­culty stems from the fact that math­em­at­ics is an easi­er sub­ject than the oth­er sci­ences. Con­sequently, many of the im­port­ant primary prob­lems of the sub­ject — that is, prob­lems which can be un­der­stood by an in­tel­li­gent out­sider — have either been solved or car­ried to a point where an in­dir­ect ap­proach is clearly re­quired. The great bulk of pure math­em­at­ic­al re­search is con­cerned with sec­ond­ary, ter­tiary, or high­er-or­der prob­lems, the very state­ment of which can hardly be un­der­stood un­til one has mastered a great deal of tech­nic­al math­em­at­ics.

In spite of these for­mid­able dif­fi­culties, he con­cludes his in­tro­duc­tion:

I should like to give you a brief look at one of the most fam­ous prob­lems of math­em­at­ics, the n-body prob­lem, to sketch how some im­port­ant prob­lems of to­po­logy are re­lated to it, and fi­nally to tell you about two im­port­ant re­cent dis­cov­er­ies in to­po­logy whose sig­ni­fic­ance is only be­gin­ning to be ap­pre­ci­ated.

Need­less to say, he suc­ceeds.

The oth­er es­says in this col­lec­tion de­tail the depth and sig­ni­fic­ance of his work in math­em­at­ics and math­em­at­ics edu­ca­tion. Here I have sought to ac­know­ledge how he has con­trib­uted both to our pro­fes­sion and far bey­ond it, to the un­der­stand­ing of the role of math­em­at­ics in today’s world.

On a per­son­al note, I found Andy the source of ex­traordin­ar­ily use­ful non­mathem­at­ic­al in­form­a­tion. I have cap­it­al­ized per­son­ally on his know­ledge of in­ter­est­ing books, speeches, and oth­er activ­it­ies na­tion­wide, and the latest scoop on res­taur­ants and auto mech­an­ics in the Cam­bridge area. It was fun, re­ward­ing, and chal­len­ging to work with him. I will miss his pres­ence in the math­em­at­ics com­munity.