IN THE international world of pure mathematics, Shiing-Shen Chern was a towering figure. From the 1940s onwards he redefined the subject of geometry, combining the global viewpoint of topology with the type of detailed calculations that used to drive Einstein to despair. Beyond that, he was also a source of inspiration for all Chinese mathematicians. Born in the final year of the Qing dynasty, and educated at a time when China was only beginning to set up Western-style universities, he spent a lifetime going back and forth from East to West carrying news of the latest developments and encouraging young mathematicians. Of those he taught, C-N. Yang won a Nobel Prize in Physics and S-T.Yau the Fields medal, its mathematical equivalent.

Perhaps the ultimate measure of his achievement was his presiding, next to President Jiang Zemin, over the opening of the 2002 International Congress of Mathematicians, with 1,700 Chinese mathematicians in active discussion with 2,500 from the rest of the world.

Shiing-Shen Chern was born in 1911 in Jia Xin. At Fulun Middle School in Tsientsin he cut his mathematical teeth on classical textbooks and Cambridge Tripos questions, and at 15 went to Nankai University. As a postgraduate at Tsinghua University in 1930 he came under the influence of Dan Sun, the only mathematician in China at the time publishing research papers. During this period he became seriously interested in differential geometry, Sun’s subject, and studied in detail the works of Wilhelm Blaschke. After Blaschke paid a visit to Tsinghua in 1932, Chern won a fellowship to study with him in Hamburg in 1934-36. That experience, and a year in Paris working with Elie Cartan, defined the area of his future work. Cartan was the dominant figure in geometry at the time, introducing new techniques which few people understood. Blaschke had links to the 19th-century Göttingen school but also appreciated the more modern role of differential equations.

When Chern returned to China in 1937, the Sino-Japanese war had broken out and his university had moved, to Kunming. There, despite the deprivations of war and the lack of communication with the outside world, he found the time to pore over Cartan’s work and form his own vision of geometry. He also taught many students who later made substantial contributions in mathematics and physics. He was already known internationally when in 1943 he was able, via a chain of military flights through India, Africa, Brazil and Central America, to make his way to the Institute for Advanced Study in Princeton where he proved the first of his many results in global differential geometry — the general Gauss-Bonnet theorem.

Going back to China after the war, Chern was given the task of setting up an Institute of Mathematics as part of the Academia Sinica. He did this very successfully, but Nanjing, where the institute was located, was getting more dangerous in the turmoil of the civil war. Robert Oppenheimer, the Director of the Princeton Institute, was perhaps more aware of this than Chern, and finally persuaded him to return to the USA in 1948. The following year he took a permanent position in Chicago. In 1960 he moved to Berkeley where he stayed until his retirement in 1979.

Chern’s mathematical work is characterized by his absolute mastery of the techniques he learnt from Cartan and their application to a vast number of global problems in geometry, topology and complex analysis. One of the areas he studied most was the theory of fibre bundles, and it was somewhat ironic that his former student and friend Chen Ning Yang developed this in another direction — the Yang-Mills gauge theory in theoretical physics. Nowadays string theorists are also perfectly at home with Chern classes and Chern-Simons theory. These were not invented by Chern for that specific purpose — he was a problem solver rather than a generalist — but they demonstrate the scope of his contributions.

Retirement did not stop Chern from engaging fully with the mathematical world. He was a founder of the national Mathematical Sciences Research Institute in Berkeley and its first director from 1981-84. In China he set up the Nankai Institute for Mathematics in 1985. He received many awards for his work including the US National Medal of Science in 1975 and the Wolf Prize in Mathematics in 1983. He was elected a Foreign Member of the Royal Society in 1985.

Those who met Chern were always struck by his approachability. He felt that modern science was too competitive and, in a Confucian spirit, looked forward to the “injection of the human element” into mathematics. His relaxed style and willingness to encourage young researchers earned him a loyalty from generations of mathematicians. One such appreciative student bought his weekly California State Lottery tickets with the single thought: “If I win, I will endow a professorship to honour Professor Chern”. In 1995 he won $22 million and the Chern Visiting Professors are now a regular feature on the Berkeley campus.

He is survived by a son and a daughter. His wife of 61 years, Shih-ning, predeceased him.

Shiing-Shen Chern, mathematician, was born on October 28, 1911. He died on December 3, 2004, aged 93.