Celebratio Mathematica

Benedict H. Gross

Benedict H. Gross: Becoming a mathematician

by Rob Kirby

Family background and first steps toward becoming a mathematician

Be­ne­dict (Dick) Hy­man Gross is a dis­tin­guished num­ber the­or­ist, best known for the Gross–Za­gi­er the­or­em on the \( L \)-func­tions of el­lipt­ic curves. His many hon­ors in­clude a Ma­cAr­thur Fel­low­ship (1986); the Cole Prize in Al­gebra (1987); elec­tion to the Amer­ic­an Academy of Arts and Sci­ence (1992); and elec­tion to the Na­tion­al Academy of Sci­ences in 2004. Dick spent most of his math­em­at­ic­al life as a pro­fess­or at Har­vard (1985–2015), and, after his re­tire­ment, has sub­sequently taught at the Uni­versity of Cali­for­nia, San Diego.

Dick’s four grand­par­ents all came to the US as teen­agers, fu­git­ives from the anti-Semit­ism of Old Europe. His pa­ternal grand­par­ents (Aus­tri­an) ran an in­de­pend­ent busi­ness selling steam­ship tick­ets to im­mig­rants bring­ing their fam­il­ies from Europe. They had 11 chil­dren — each child re­quired to learn a dif­fer­ent European lan­guage so they could sell tick­ets ef­fect­ively in Pol­ish, Rus­si­an, Hun­gari­an, etc. His ma­ter­nal grand­par­ents emig­rated from Po­land. His grand­fath­er, Samuel Stav­isky, went in­to the gar­ment busi­ness, mak­ing liners for jack­ets.

Dick’s fath­er, Joel, was born on a farm in Jer­sey City, New Jer­sey. His older broth­ers, who had be­come law­yers, had skipped col­lege and law school and had just read for the bar. But Joel was ad­mit­ted to and at­ten­ded Columbia Col­lege and then Columbia Law School, even­tu­ally join­ing his broth­ers’ law firm be­fore set­ting out on his own. One of six chil­dren, Dick’s moth­er, Terry, was born in New York City and went to Hunter Col­lege. She be­came a sub­sti­tute teach­er after rais­ing her chil­dren.

Dick was born in South Or­ange, New Jer­sey on June 22, 1950, the day his sis­ter Ruth gradu­ated from high school and his broth­er Av gradu­ated from ju­ni­or high. One dis­ad­vant­age of com­ing late in his par­ents’ life was that dur­ing this last preg­nancy, his moth­er was pre­scribed the drug Di­ethyl­stil­bestrol (DES) to pre­vent mis­car­riage. Twenty years later, the FDA ad­vised doc­tors to stop pre­scrib­ing DES, be­cause by then it was known that the chil­dren of moth­ers who had taken this drug in early preg­nancy were more likely to de­vel­op prob­lems in their re­pro­duct­ive sys­tems. Dick de­veloped testic­u­lar can­cer when he was in col­lege, and re­ceived ra­di­ation ther­apy to pre­vent re­cur­rence. Over his life­time he had five ma­jor ab­dom­in­al sur­ger­ies to deal with is­sues caused by this ra­di­ation.

When Dick was five the fam­ily moved to Santa Mon­ica, Cali­for­nia, for a brief peri­od where he was en­rolled in a school that lacked a kinder­garten and com­bined chil­dren of the first and second grades in­to a single class. The fam­ily re­turned to New Jer­sey not long after, at which point Dick re­sumed school at the second-grade level. From then on Dick was young­er than his class­mates. Even so, by his tenth grade year, Dick had ex­hausted the of­fer­ings at West Or­ange High School so he trans­ferred to the Pingry School, a private school about ten miles from home.

Dick en­rolled at Har­vard in the fall of 1967, ex­pect­ing to be a math ma­jor. He tried to take the hon­ors fresh­man course Math 55, which was taught that year by Loomis and Stern­berg out of their book. His room­mate loved the text, where he said that the only num­bers in it were sub­scripts. But Dick found the course way above his level.

I didn’t know the the­ory of fi­nite di­men­sion­al vec­tor spaces and the book star­ted with to­po­lo­gic­al vec­tor spaces! So I dropped the course, took mul­tivari­able cal­cu­lus, and de­cided to be­come a phys­ics ma­jor. In my sopho­more year I was look­ing for an ex­tra course and wandered in­to a room where An­drew Gleason was teach­ing Math 55. His style of lec­tur­ing was just en­tran­cing and I en­rolled in his course. Many times in my re­search ca­reer when I un­der­stood something fun­da­ment­al, like ex­ter­i­or powers as func­tors on the cat­egory of fi­nite di­men­sion­al vec­tor spaces, I real­ized that it was something Andy was try­ing to teach us in Math 55.

In col­lege I took real ana­lys­is and com­plex ana­lys­is and al­gebra, but I nev­er un­der­stood how they were linked to­geth­er, what the sub­ject was really about. When I gradu­ated in 1971 I was still very con­fused. So I de­cided to take some time off to travel and get my head screwed around right. For­tu­nately I won a Shel­don Trav­el­ing Fel­low­ship from Har­vard. This gave me $3500, and the only stip­u­la­tion of the award was that you couldn’t stay in one place too long. I thought I would have the chance to travel in Europe in the fu­ture, so I went to Africa and Asia, fo­cus­ing on mu­sic. I took Emil Artin’s Geo­met­ric Al­gebra to read on the trip. It was an in­spired choice — what an el­eg­ant treat­ment of the clas­sic­al groups!

Dick sub­sequently won a Mar­shall Fel­low­ship to study at Ox­ford Uni­versity (1972–74), where he ini­tially de­par­ted from his math­em­at­ic­al fo­cus: I star­ted read­ing his­tory and so­ci­ology, but it was a com­plete dis­aster. I had no tal­ent in the sub­ject at all. So I switched to an MSc in math­em­at­ics. For­tu­nately, Mi­chael Atiyah had just re­turned from the In­sti­tute for Ad­vanced Study and gave a course on Hil­bert mod­u­lar forms. I had tried to read Serre’s Course in Arith­met­ic and found the last chapter on mod­u­lar forms im­pen­et­rable. Atiyah star­ted with that chapter in his breezy way and everything was beau­ti­ful. So I de­cided to learn more about it. I found one oth­er per­son at Ox­ford, who was in­ter­ested in num­ber the­ory at the time. That was An­drew Wiles, who was fin­ish­ing up as an un­der­gradu­ate. We some­how got a copy of John Tate’s lec­ture notes on el­lipt­ic curves. We tried to read our way through these notes and got stuck pretty quickly, but we had a lot of fun talk­ing about it. When we fin­ished our de­grees An­drew went off to Cam­bridge and I went off to Har­vard, hop­ing to work with John Tate.

When I got there Tate already had five PhD stu­dents. He gave me his great pa­per on \( p \)-di­vis­ible groups, ask­ing if I could gen­er­al­ize his Hodge de­com­pos­i­tion for the \( p \)-ad­ic étale co­homo­logy of an abeli­an vari­ety to the high­er co­homo­logy of an ar­bit­rary vari­ety. I was ini­tially ex­cited to have been giv­en a prob­lem, but came back a month later and said, “Isn’t this the cent­ral un­solved prob­lem in the whole sub­ject? Why do you think I can do it?” And Tate replied, “Well, if you can’t do that, find an­oth­er prob­lem on your own.”

So I star­ted look­ing around. Dav­id Rohr­lich and Neil Kob­litz had ar­rived as as­sist­ant pro­fess­ors, and I star­ted talk­ing to them. We wrote some pa­pers to­geth­er, try­ing to gen­er­al­ize Barry Mazur’s great pa­per on the Ei­s­en­stein ideal, and I built up a little con­fid­ence. Serre was vis­it­ing Har­vard and giv­ing a course on ana­lyt­ic num­ber the­ory. He showed me a nice ex­ample of an al­geb­ra­ic Hecke char­ac­ter of \( \mathbb Q(\sqrt{-7}) \). I found a gen­er­al­iz­a­tion to ima­gin­ary quad­rat­ic fields of prime dis­crim­in­ant and a con­nec­tion with el­lipt­ic curves with com­plex mul­ti­plic­a­tion, and that be­came my thes­is. Once I star­ted work­ing on it, Tate was very help­ful. He could take a half-baked idea and turn it in­to something beau­ti­ful. I re­main in awe of the clear way he thought about math­em­at­ics. He was also my mod­el for thes­is ad­vising. When I came back to Har­vard as a pro­fess­or I had won­der­ful stu­dents. I just felt that the best thing I could do is get out of their way, to talk to them and try to un­der­stand what they were do­ing.

From early career decisions to the present

Rob: I’d like to pick up where we left off in the first part of this pro­ject, where we learned about your early life and your fam­ily. Let’s talk about the early years of your ca­reer — about the de­cision-mak­ing that got your ca­reer star­ted.

Dick: The first part got me through gradu­ate school, and everything after that was down­hill.

I fin­ished at 28 be­cause I star­ted at 24 after tak­ing time off. My 30th birth­day was a time of great con­cern be­cause I felt that I hadn’t done any­thing. I wasn’t mar­ried, I didn’t have kids, I hadn’t ac­com­plished any­thing in math, etc., etc. But two years later I was mar­ried, 3 years later I had kids and 5 years later I was at Har­vard, so it all worked out.1 I was mar­ried in 1982, to Jill Mesirov, whom I met at a party at the Lang­lands’s house. We had both been in Prin­ceton for 4 years, both in math, both in­ter­ested in disco dan­cing, and we had nev­er bumped in­to each oth­er. She had a job in Prin­ceton at IDA. At the time of the party, I was con­sult­ing for a movie (It’s My Turn) with Jill Clay­burgh who plays a math pro­fess­or (and gives a talk in which the “Snake Lemma” ap­pears). I had sent Jill C. in­to New York to talk to Linda Keen and Linda Ness and Dusa Mc­Duff to get an idea of what it was like to be a wo­man in math. Jill C. said it was too de­press­ing talk­ing to those wo­men and it’s not who I want to be (in the movie).

But Jill M. had read about the mak­ing of the movie and she was roy­ally pissed off be­cause here was this act­ress play­ing a math­em­atician and be­ing coached by a man. So I was at the Lang­lands’s, in the kit­chen get­ting a beer, and here was this young wo­man. I said: “Hi, I’m Dick Gross”, and she im­me­di­ately says: “You’re the jerk who’s work­ing on that movie.” I don’t even know this wo­man’s name yet and she’s giv­ing me a hard time!

I didn’t get ten­ure at Prin­ceton, but then I got an of­fer from Brown Uni­versity and Jill was will­ing to leave IDA and be­came As­so­ci­ate Ex­ec­ut­ive Dir­ect­or at the AMS. We stayed at Brown for three years and then I got the of­fer from Har­vard and Jill moved to the Think­ing Ma­chines com­pany, which went belly up after 10 years. Jill was re­cruited by Eric Lander to work on the gen­ome pro­ject. Jill has had a tre­mend­ous sci­entif­ic ca­reer; she has tons more cita­tions than J. P. Serre has. If you work in com­pu­ta­tion­al bio­logy, a lot of people read your pa­pers.

But as I said, after I got out of grad school I went to Prin­ceton. It was great. I got to speak to the greats at IAS; An­dré Weil was hold­ing forth; I’d go for walks with him near IAS and not say a word, just listen, listen, listen. And Lang­lands was there and of course I was in­ter­ested in his work. Prin­ceton offered to ex­tend my po­s­i­tion but it wasn’t go­ing any­where so I de­cided to take the ten­ure of­fer at Brown.

And when I went to Brown, it was just ma­gic­al. When I went to Brown the de­part­ment had Bob MacPh­er­son, Bill Fulton, Joe Har­ris, Jean-Luc Bryl­in­ski, and the de­part­ment was small enough that we were all talk­ing to one an­oth­er, pol­lin­at­ing each oth­er, and then we all left. I was the first, and then Bob went to MIT and Bill went to Chica­go and so on. But Bob said we’ll all have to ad­mit that we did our best work at Brown. It was really an amaz­ing de­part­ment for a couple of years.

Rob: Why did it fall apart?

Dick: Why? The first per­son to leave was me. After three years there I had done my work with Za­gi­er, I was get­ting of­fers from every­where. Chern tried to re­cruit me to Berke­ley, and then I got an of­fer from MIT and then IHES and Har­vard. I didn’t know what to do, so Bill said let’s go in and see the Prov­ost and see if he can counter all these of­fers. We went in and the Prov­ost said: “Are you the young man with an of­fer from Har­vard? Well, con­grat­u­la­tions. My very best wishes.” Bill al­most killed him on the spot. There was no one in the ad­min­is­tra­tion that ap­pre­ci­ated what they had in the math de­part­ment at that time. All they wanted us to do was teach cal­cu­lus. And we wanted some money for vis­it­ors, we wanted to run a de­part­ment like Har­vard or Berke­ley or MIT. And two years after I left, Fulton and MacPh­er­son and Har­ris and Bryl­in­ski all left, and so it all went away.

Rob: So Chern tried to re­cruit you to Berke­ley? It must have rained all the time?

Dick: I didn’t meet Chern in Berke­ley, but at the Arbeit­sta­gung in Bonn. In the most Chern-ish way, he said: “Young man, let’s go out to lunch, I need to talk to you.” He said Berke­ley was go­ing to try to cre­ate a num­ber the­ory group and I could have a num­ber of ap­point­ments, and the whole ap­par­at­us. I said that I ap­pre­ci­ate that but if I go to Har­vard, Tate and Mazur are there and Stark at MIT and I already have the group right there. And Tate was my ad­visor and it was sort of like be­ing “called”. Of course as soon as I went to Har­vard, Tate went to Texas! But I think it was the right de­cision. I had won­der­ful col­leagues and I could work with Mike Hop­kins and Curt McMul­len as well as num­ber the­or­ists. So I’m glad I made that move, but it was hard leav­ing Brown be­cause Brown had been so good to me and it was a great place to meet with the people who didn’t do num­ber the­ory.

McMul­len and I be­came great friends. We had a lot of com­mon in­terests, like ski­ing. We used to drive up to his Mom’s house in Ver­mont and go ski­ing at Stowe. And the whole time we’d be talk­ing about math; he wanted to know as much as pos­sible about num­ber the­ory, and I thought, you’re com­ing to Har­vard, you have to know num­ber the­ory. So he, and Joe Har­ris whom I met as a fresh­man in col­lege, be­came my best friends at Har­vard.

Rob: Curt stores a bi­cycle in my back yard for when he vis­its.

Dick: I think one reas­on he vis­its is that no one cares if he wears shorts in Berke­ley. At Har­vard he wears shorts in the dead of winter.

I was really blessed with great col­leagues at Brown and at Har­vard. And I’m sure I would have en­joyed Berke­ley. But that lunch with Chern — it was like the per­fect re­cruit­ment — that guy was so won­der­ful!

Rob: You know I got my job at Berke­ley at the Arbeit­sta­gung in 1971. On the tra­di­tion­al boat trip on the Rhine, I found my­self stand­ing at the rail­ing next to Steve Smale, and some­how he dis­covered I’d be in­ter­ested in a job at Berke­ley, so he made it hap­pen.

Dick: Those were the days, Rob, those were the days. A couple of phone calls and it was done. I’ll tell you how I got the in­struct­or­ship at Prin­ceton. I walked in­to Tate’s of­fice, I had fin­ished my thes­is and I was go­ing to ask him where I should ap­ply for jobs. He said: “Dick, I’m so glad to see you. I just got a tele­phone call from Nick Katz. It seems Ken Ribet is go­ing to leave Prin­ceton and go out to Berke­ley. They need an­oth­er young num­ber the­or­ist. Would you go?” I said: “Do I have to ap­ply?” He said: “No, no, no, just call Nick back. And, oh, do you want Ken’s apart­ment too?” I nev­er ap­plied for that job. And the jobs at Brown and Har­vard, they just called you and made an of­fer. They don’t do that any­more. You can see what they go through at the Uni­versity of Cali­for­nia; it’s just pain­ful to watch.

Rob: Things went wrong oc­ca­sion­ally, but it was much more ef­fi­cient.

Dick: You called people you trus­ted and you re­lied on their judge­ment. They didn’t have to put it in a let­ter with all kinds of bull­shit. They told you what they thought.

Rob: I re­mem­ber read­ing Raoul Bott’s let­ter for Thur­ston. He wrote: “ Bill Thur­ston is the next Hassler Whit­ney. Hire him.” Of course with the Thur­stons, it’s easy.

Dick: My fa­vor­ite is when De­ligne moved from IHES to IAS, they asked for let­ters be­cause they had to have let­ters, even though it’s com­pletely ri­dicu­lous. He’s so far above every­body. I was speak­ing to Nick Katz and said what are you go­ing to write? He said that he’d already writ­ten his let­ter. What did you say? He said that ask­ing him his opin­ion of De­ligne was like ask­ing the guy who washes lettuce in a 3-star French res­taur­ant what he thinks of the chef. That’s what he said. It’s bril­liant. Who are we to even com­ment about such a math­em­atician.

But Bott had two opin­ions about Thur­ston. He felt that Bill had com­pletely wiped out the field of fo­li­ations. But he felt that Bill’s mind was un­fathom­able.

Rob: Cliff Taubes some­times uses the phrase, “He’s from a dif­fer­ent plan­et,” as with Kont­sevich.

Dick: He feels that way about Wit­ten too. They’ve come down to Earth to com­mu­nic­ate some bits of wis­dom to us earth­lings.

You’ve been lucky Rob, but I too have been very lucky; I went in­to something I love, I was able to do it with in­cred­ible stu­dents and in­cred­ible col­leagues, very lucky.

I’ll send you a little thing about work­ing with Za­gi­er, which was the best thing I ever did. It was for­tu­nate he was in the States. He’d got­ten this job at Mary­land (1982) and I de­scribe the one week when I went down to vis­it him. He star­ted as a to­po­lo­gist. First as a stu­dent of Atiyah, and then Hirzebruch, char­ac­ter­ist­ic classes, etc., but he was nev­er really a to­po­lo­gist. I met him when I was a grad stu­dent and he came to Har­vard as a dis­tin­guished vis­it­ing Pro­fess­or, yet I was a year older. So if you work in math, you have to get used to the fact that there are people who are a lot smarter than you are.

You know, one of the bless­ings of my life is that I got to un­der­stand the work of people like Serre and De­ligne and Tate. I was at a level where I could ap­pre­ci­ate what they had done. That really meant a lot to me.

Not only did I col­lab­or­ate with Za­gi­er, but I also col­lab­or­ated with my stu­dents, Noam Elkies and Man­jul Bhar­gava, and those three guys have a mind — it’s un­fathom­able how they do things. With Noam it was very fun; he was my doc­tor­al stu­dent so he looked up to me as a great pro­fess­or, and I’d ask him something about our joint pa­per and how do we know this, and he’d say, “I’ve ex­plained this to you three times already, but since you are my dis­tin­guished pro­fess­or, I must not have ex­plained it cor­rectly!” Where­as Za­gi­er didn’t pay me any of that kind of re­spect. And Man­jul is just very nice.

I was Dean at Har­vard from 2004 to 2007. That was enough, Rob, that was enough, be­lieve me!

Our move out to San Diego was really funny. After be­ing Dean I got all these of­fers. They wer­en’t really hir­ing me, they wanted to hire the Dean of Har­vard Col­lege. I turned them all down, but the only thing I ex­plored was the Dean at UC San Diego. I went out and was in­ter­viewed by the Vice Chan­cel­lor. I said I can’t come un­less there is a job for my wife. She (the VC) rolled her eyes and said “An­oth­er spous­al ap­point­ment! Send her re­sume and I’ll see what I can do.”

I sent the re­sume; Jill was work­ing at the Broad In­sti­tute, had been in­volved with the hu­man gen­ome pro­ject, etc. I got a call from the Vice Chan­cel­lor that even­ing. She said “I’ve got three po­s­i­tions, one in com­puter sci­ence, one in bio­logy, and one in the med­ic­al school. And if you still want to come out and be Prov­ost, that’s ok too.” They really wanted Jill, and I was go­ing to be the spous­al ap­point­ment!

I didn’t really want the Prov­ost job, and we wer­en’t quite ready to move. But the head of the med­ic­al school wanted to get more in­to com­pu­ta­tion and kept in­vit­ing Jill out for con­sult­ing, and we fi­nally ac­cep­ted their of­fers. I re­tired from Har­vard and joined the UC­SD math de­part­ment, taught some courses and then re­tired again. It was all for­tu­it­ous, for as you know Rob, it is para­dise out here.