Celebratio Mathematica

Shiing-Shen Chern

Remarks at the Banquet, Chern Centennial Conference, MSRI, 1 November 2011

by Hung-Hsi Wu

I first got to meet Pro­fess­or Chern as a stu­dent in 1962, in an AMS Sum­mer In­sti­tute in Santa Bar­bara. Con­trary to all the stor­ies you have heard in the last two days, he did not take me out to lunch that day. I came to Berke­ley as an As­sist­ant Pro­fess­or in 1965, and for the next thirty-five years I saw him of­ten. It may be that I saw him even more after he really re­tired from the de­part­ment and MSRI around 1985.

Our ca­non­ic­al im­age of Pro­fess­or Chern is someone with im­pec­cable judg­ment, so I’d like to share three stor­ies with you about the few oc­ca­sions when he was wrong. The first took place in 1949, between his de­par­ture from China and his ar­rival in Chica­go. It may be re­called that he proved the Gauss–Bon­net the­or­em in late 1943, and fin­ished his manuscript on Chern classes in Ju­ly, 1945, in China. Soon after that he was called upon to cre­ate the In­sti­tute of Math­em­at­ics in China. For the next three years he had to be the all-in-one teach­er, care­taker, and ad­min­is­trat­or of the in­sti­tute, and these du­ties con­sumed him. He was then between 35 and 38 years old, and for a math­em­atician, these are the peak years of cre­ativ­ity. But he will­ingly sac­ri­ficed those years for the good of Chinese math­em­at­ics. Such oner­ous re­spons­ib­il­it­ies took their toll, however, and he paid the price in his own math­em­at­ic­al work. Al­though he tried to keep his re­search go­ing, it was not hu­manly pos­sible un­der the cir­cum­stance to sus­tain the same high level as in the earli­er years. Even­tu­ally, er­rors crept in­to his pa­pers. So it came to pass that when he ar­rived at the In­sti­tute for Ad­vanced Study in early 1949, he thought his ca­reer as a re­search math­em­atician was over; he did not be­lieve he was cap­able of do­ing cre­at­ive work any­more. Such self-doubt is in stark con­trast with our usu­al per­cep­tion of him as someone with un­lim­ited self-con­fid­ence about math­em­at­ics. It makes him more hu­man.

Of course he was wrong; he was com­pletely wrong this time. The rest, as they say, is his­tory.

A second story takes us to the early 1980s, when China was be­gin­ning to open up to the West after the long hi­berna­tion dur­ing the Cul­tur­al Re­volu­tion of 1966 to 1976. Pro­fess­or Chern, in con­cert with the Chinese gov­ern­ment, in­vited many math­em­aticians to vis­it China, in­clud­ing Weil, Bom­bieri, Lax, Niren­berg, Grif­fiths, Atiyah, Bott, and many oth­ers. He did all this with a def­in­ite goal in mind, and I got a glimpse of it when he ex­pressed frus­tra­tion that the young math­em­atician in China did not make good use of the op­por­tun­ity to talk to these dis­tin­guished guests and learn from them. We know how much he learned by talk­ing to Élie Cartan, and we also know that his con­ver­sa­tions with Weil in 1943 made him aware of the Gauss–Bon­net en­igma at the time. His own ex­per­i­ences no doubt colored his think­ing, and that was why he was frus­trated: why couldn’t they all be like me? This is the case of a great gen­er­al not be­ing in tune with the obstacles faced by his foot sol­diers. I think he was wrong to ex­pect so much from the young math­em­aticians of China be­cause it takes con­fid­ence and tal­ent to be­ne­fit from talk­ing to a dis­tin­guished col­league. For ex­ample, it is amus­ing to con­tem­plate how a young per­son, in­tel­lec­tu­ally not quite the equal of Pro­fess­or Chern him­self, could be­ne­fit from talk­ing to a cur­mudgeon like An­dré Weil.

The last story is not about math­em­at­ics at all but about Chinese polit­ics. After his vis­it to China in 1972 (right in the middle of the Cul­tur­al Re­volu­tion) Pro­fess­or Chern began to tell those around him that Ma­dame Mao would try to seize su­preme power. He prob­ably got some vibes to this ef­fect dur­ing his vis­it, but it was news to many of us. Then to­ward the end of Mao’s life in 1976, he pre­dicted that she would suc­ceed. I want to as­sure you that he did not want her to suc­ceed, but he had to call it like it is. He was not someone who would al­low sen­ti­ment­al­ity to cloud his judg­ment. The to­po­lo­gist Wu-yi Hsiang was hor­ri­fied by that pro­spect and he made a bet with Pro­fess­or Chern that she would fail. At stake was a fancy din­ner. I was wit­ness to the bet so I would get my din­ner either way, but I must say that, in all the years when I al­most al­ways agreed with Pro­fess­or Chern in and out of math­em­at­ics, that time I was root­ing against him like crazy. As we all know, Pro­fess­or Chern lost the bet and every­body was happy at the end.

I would add a few com­ments about the Chern per­sona. Many people have re­ferred to his charm and grace, but to my mind, those words do not be­gin to tell the story. His cha­risma had to be felt firsthand to be fully un­der­stood. I think Raoul Bott cap­tured its es­sence by not us­ing any stand­ard words or phrases to de­scribe what he saw. In 1979, there was a sym­posi­um at Berke­ley in hon­or of Pro­fess­or Chern’s re­tire­ment. On that oc­ca­sion, Bott began his lec­ture like this:

It is a great pleas­ure to ad­dress this sym­posi­um in hon­or of my dear friend, teach­er, and col­lab­or­at­or. I first met Chern in 1950, when he dropped in to vis­it Prin­ceton for just one day and I sat near him at lunch. I don’t sup­pose that you re­mem­ber this oc­ca­sion, my dear friend, though I am sure I con­trived to at­tract your at­ten­tion by some im­per­tin­ence or oth­er. For I was im­me­di­ately cap­tiv­ated by what you said and how you said it.

We are here this even­ing to hon­or Pro­fess­or Chern’s memory, sev­en years after he passed away. You just might be curi­ous, as one of my col­leagues is, as to why he is singled out among many dis­tin­guished math­em­aticians for such ad­u­la­tion. There is no lack of first rate math­em­aticians of today that can in­spire awe and ad­mir­a­tion with their in­tel­lec­tu­al prowess, but awe and ad­mir­a­tion do not dir­ectly trans­late in­to ad­u­la­tion. It may be that Hirzebruch got to the heart of the mat­ter when in 2001, in the pre­face to a volume of Res­ults in Math­em­at­ics ded­ic­ated to Pro­fess­or Chern, he said:

There have been many meet­ings and volumes ded­ic­ated to Chern, al­ways as a sym­bol of af­fec­tion and grat­it­ude.

No­tice that Hirzebruch did not even men­tion Chern class. Rather, he spoke of af­fec­tion for Pro­fess­or Chern. Now to win over our minds there is a simple al­gorithm: prove great the­or­ems. But to win over our hearts, there is no al­gorithm known to man. Per­haps we can gain an ap­pre­ci­ation of how Pro­fess­or Chern suc­ceeded in do­ing that by re­flect­ing on something he once said. In de­scrib­ing his ex­per­i­ences with Élie Cartan and Her­mann Weyl, per­haps the two most im­port­ant ment­ors of his life, he said they were both ex­tremely mod­est and per­son­able. But the dif­fer­ence to Pro­fess­or Chern was that where­as with Cartan, one could talk to him as a friend for hours without be­ing aware that he was a great math­em­atician, with Her­mann Weyl, one would know not only that he was a great math­em­atician but also that he knew he was great. Then he ad­ded that he pre­ferred Cartan’s way. It would seem that Pro­fess­or Chern man­aged to learn not only mov­ing frames from Cartan, but this per­son­al secret as well. He made us feel that he was one of us, and we sur­rendered our hearts to him without know­ing.

On this oc­ca­sion, I would like to close by re­mem­ber­ing Mrs. Chern, be­cause as Pro­fess­or Chern wrote so mov­ingly in the pre­face to his Se­lecta:

I would not con­clude this ac­count without men­tion­ing my wife’s role in my life and work. Through war and peace and through bad and good times we have shared a life for forty years, which is both simple and rich. If there is cred­it for my math­em­at­ic­al works, it will be hers as well as mine.