Died: 3 December 2004 in Tianjin Municipality, China

**Shiing-shen Chern**, whose name can also be written as **Chen Xingshen**, studied at Nankai University in Tientsin, China, then undertook graduate studies at Tsing Hua University, Peking. He was the only graduate student in mathematics to enter the university in 1930 but during his four years there he not only studied widely in projective differential geometry but he also began to publish his own papers on the topic.

He received a scholarship in 1934 to study in the United States, but he made a special request that he be allowed to go to the University of Hamburg. His reason was that he had met Blaschke when he visited Peking in 1932 and found his mathematics attractive. After working under Blaschke for only a little over a year Chern received his D.Sc. from Hamburg in 1936.

At this stage Chern was forced to choose between two attractive options, namely to stay in Hamburg and work on algebra under Artin or to go to Paris and study under Cartan. Although Chern knew Artin well and would have liked to have worked with him, the desire to continue work on differential geometry was the deciding factor and he went to Paris. His time in Paris was a very productive one and he learnt to approach mathematics, as Cartan did, see [2]:-

... from evidence and the phenomena which arise from special cases rather than from a general and abstract viewpoint.

In 1937 Chern left Paris to become professor of mathematics at Tsing Hua University. However the Chinese-Japanese war began while he was on the journey and the university moved twice to avoid the war. He worked at what was then named Southwest Associated University from 1938 until 1943. After spending 1943-1945 at Princeton where he impressed both Weyl and Veblen. He became friendly with Lefschetz who persuaded him to become an editor of the *Annals of Mathematics.*

At the end of World War II, Chern returned to China to the Institute of Mathematics at the Academia Sinica in Nanking. However this time a civil war in China began to make life difficult and he was pleased to accept an invitation in 1948 from Weyl and Veblen to return to Princeton.

From 1949 Chern worked in the USA accepting the chair of geometry at the University of Chicago after first making a short visit to Princeton. He remained at Chicago until 1960 when he went to the University of California, Berkeley.

He was awarded the National Medal of Science in 1975 and the Wolf Prize in 1983/84. In 1985 he was elected a Fellow of the Royal Society of London and the following year he was made an honorary member of the London Mathematical Society.

His area of research was differential geometry where he studied the (now named) Chern characteristic classes in fibre spaces. These are important not only in mathematics but also in mathematical physics. He worked on characteristic classes during his 1943-45 visit to Princeton and, also at this time, he gave a now famous proof of the Gauss-Bonnet formula.

His work is summed up in [17] as follows:-

When Chern was working on differential geometry in the1940s, this area of mathematics was at a low point. Global differential geometry was only beginning, even Morse theory was understood and used by a very small number of people. Today, differential geometry is a major subject in mathematics and a large share of the credit for this transformation goes to Professor Chern.

In 1979 a Chern Symposium held in his honour offered him this tribute in song:-

Hail to Chern! Mathematics Greatest!

He made Gauss-Bonnet a household word,

Intrinsic proofs he found,

Throughout the World his truths abound,

Chern classes he gave us,

and Secondary Invariants,

Fibre Bundles and Sheaves,

Distributions and Foliated Leaves!

All Hail All Hail to CHERN.

**Article by:** *J J O'Connor* and *E F Robertson*

**November 1997**

[http://www-history.mcs.st-andrews.ac.uk/Biographies/Chern.html]