Celebratio Mathematica

Andrew Mattei Gleason

Andrew Gleason — a remembrance.
Remarks delivered at the memorial service, Memorial Church, Harvard University,
November 14, 2008

by Leslie Dunton-Downer

I was a Ju­ni­or Fel­low in Com­par­at­ive Lit­er­at­ure at the Har­vard So­ci­ety of Fel­lows dur­ing the fi­nal years that Pro­fess­or An­drew Gleason served as its chair, from 1993 to 1996. The so­ci­ety gath­ers re­search­ers from all fields: from as­tro­phys­ics, clas­sics, eco­nom­ics, and oth­ers, clear through to zo­ology. Fel­lows at the so­ci­ety spend three years free from any re­quire­ment or ex­am­in­a­tion, pur­su­ing, and I now quote from the vows that all new Fel­lows take: “a frag­ment of the truth, which from the sep­ar­ate ap­proaches every true schol­ar is striv­ing to descry.” On Monday nights in aca­dem­ic term-time, Ju­ni­or Fel­lows con­verse with a dozen or so Seni­or Fel­lows, pro­fess­ors who not only elect Ju­ni­or Fel­lows but also en­gage them in mind-open­ing con­ver­sa­tions over sup­pers in a din­ing hall fur­nished to nour­ish these ex­changes. Pro­fess­or Gleason, who had him­self been a Ju­ni­or Fel­low, of­fi­ci­ated when I took my vows at the so­ci­ety, and as chair he presided over Monday night din­ners dur­ing my three years in his fel­low­ship. This is how I knew him, and my fond­ness for him grew ex­po­nen­tially with each passing sea­son at the so­ci­ety.

The first time I be­held Pro­fess­or Gleason, here was the situ­ation: It was a Monday morn­ing at the so-called Yel­low House, at 78 Mount Au­burn Street here in Cam­bridge, the so­ci­ety’s ad­min­is­trat­ive base camp. I was surely ex­tremely nervous, be­cause I was to be in­ter­viewed that very af­ter­noon by the full as­semblage of Seni­or Fel­lows, a ter­ri­fy­ing pro­spect — each Seni­or Fel­low was an aca­dem­ic star in his re­spect­ive field, and many were re­puted to be in­tim­id­at­ing. A Ju­ni­or Fel­low had been as­signed the task of show­ing me about the build­ing. At one point, nois­ily chat­ter­ing, we made our way down a cor­ridor, where an of­fice door was opened widely. We paused there to look through the door­way. In­side the room, there was a man lean­ing back on his chair be­fore an empty desk. His head was tilted sky­ward, and his eyes fo­cused on a point that ap­peared to be on the ceil­ing, but may have been fur­ther off. We stood there for an awk­ward few beats. I be­lieve that we were to­geth­er un­sure if the man was about to greet us or if we ought to take the ini­ti­at­ive to greet him. But he re­mained still, ab­sorbed in his own world. The Ju­ni­or Fel­low and I shrugged at each oth­er and con­tin­ued on our way un­til we reached a com­mon room out of earshot. I turned to her, made a quiz­zical face, and asked, “What was that man do­ing?” “Math,” she said.

I had nev­er be­fore seen a real math­em­atician in the act of do­ing math. I was mys­ti­fied by the ab­sence of any tools in his of­fice. Wouldn’t he re­quire a cal­cu­lat­or or a slide rule or something to in­spire him­self to be math­em­at­ic­al — maybe a chess­board or a Ru­bik’s Cube? At the very least, what about a pen­cil and pa­per? She shook her head: “That math­em­atician is An­drew Gleason. He works in his head.”

Pro­fess­or Gleason was, I think by dis­pos­i­tion, a de­cipher­er. He had de­ciphered codes and math­em­at­ic­al prob­lems and as a hobby took de­light in de­ci­pher­ing the move­ments of ce­les­ti­al bod­ies. On Monday nights Pro­fess­or Gleason sat at the head of a horse­shoe-shaped table in the so­ci­ety’s din­ing room. Like all chairs at the so­ci­ety, he would guide his flocks of Ju­ni­or Fel­lows in his own way, leav­ing his own sig­na­ture on the in­sti­tu­tion. He was not a gar­rulous chair — “Oscar Wildean” is not the first ad­jectiv­al phrase that comes leap­ing to mind to de­scribe his con­ver­sa­tion­al style — but he could be­come an­im­ated sud­denly, and with deep sin­cer­ity, when con­ver­sa­tion turned to sub­jects close to his heart: as­tro­nomy, clas­sic­al mu­sic, and, among so many oth­ers, of course, math.

Much of the time he would listen or ob­serve with his ex­traordin­ary Gleaso­ni­an powers of con­cen­tra­tion. Many of us wondered what he was think­ing on those oc­ca­sions when he was so sharply present yet en­ig­mat­ic­ally si­lent. Per­haps he was de­ci­pher­ing us. He nev­er made a single judg­ment­al re­mark; his lead­er­ship was del­ic­ate, trust­ing, and sure­footed. He put out a strong aura of prin­cipled tran­quil­ity, as if his Ju­ni­or Fel­lows’ paths, and in­deed the paths of all people and ob­jects and ideas in his midst, no mat­ter how rough, were part of a lar­ger pat­tern that would even­tu­ally be­come clear­er to him. I found a poem that cap­tures this Pro­fess­or Gleason, the one whom I and oth­ers came to know in a quiet way and to love with great re­spect, a man whose pres­ence we now be­gin to sense ex­pand­ing through all that he dis­cerned. He seems to be present in these lines by Robin­son Jef­fers:

I ad­mired the beauty
While I was hu­man, now I am part of the beauty.
I wander in the air,
Be­ing mostly gas and wa­ter, and flow in the ocean;
Touch you and Asia
At the same mo­ment; have a hand in the sun­rises
And the glow of this grass.

The last time that I saw An­drew Gleason was at the an­nu­al din­ner held by the so­ci­ety in May of this year. The gath­er­ing took place at the Fogg Mu­seum, a few meters to the east of here. On that oc­ca­sion, many Ju­ni­or Fel­lows from Pro­fess­or Gleason’s time as chair gathered to catch up with one an­oth­er and with him. He had led us through our fel­low­ship years with a light touch, a seem­ingly in­vis­ible touch. He al­ways en­cour­aged each fel­low to wrestle with those daunt­ing “frag­ments of truth” on his or her own terms, come what may. It had only been with hind­sight, after leav­ing the so­ci­ety, that many of us came to ap­pre­ci­ate the subtle qual­it­ies of his lead­er­ship, how he shaped our lives, both in­wardly and in ac­tion, even as he had of­ten seemed chiefly to be de­ci­pher­ing the world, work­ing things out in his head.

Steph­en Hawk­ing pub­lished this ob­ser­va­tion twenty years ago, by chance on the eve of Pro­fess­or Gleason’s be­com­ing chair at the so­ci­ety: “We do not know what is hap­pen­ing at the mo­ment farther away in the uni­verse: the light that we see from dis­tant galax­ies left them mil­lions of years ago, and in the case of the most dis­tant ob­ject that we have seen, the light left some eight thou­sand mil­lion years ago. Thus, when we look at the uni­verse, we are see­ing it as it was in the past.”

Per­haps we are only now be­gin­ning to see An­drew Gleason. Those of us who had the priv­ilege to know him will cher­ish the light that he casts out to us, even in his ab­sence — per­haps all the more force­fully be­cause of his ab­sence or, rather, be­cause he has now be­come a beau­ti­ful part of the beauty that he once ad­mired.