Noted French mathematician and teacher

Henri Cartan, one of the world’s foremost mathematicians in the last half of the 20th century, died Aug. 13 in Paris. He was 104. The cause of death was not reported.

Almost all of Cartan’s career was spent in France, and he was acclaimed for his research in pure mathematics, including algebra, topology and the analytic functions of complex variables. He was also an influential writer and teacher.

At least two of his students won Nobel Prizes, one in economics and one in physics. Two others received the Fields Medal, which is awarded for accomplishment in mathematics and is regarded as the mathematics equivalent of the Nobel Prize. In 1980, Cartan received the Wolf Prize, also one of the highest honors in mathematics.

Among mathematicians, Cartan was remembered as the last survivor of the Bourbaki group, a kind of cabal of younger, rebellious French mathematicians who in the 1930s essentially rewrote the book on their subject. Their work extended to 36 volumes, which were carefully studied for years.

In the United States, he worked with Samuel Eilenberg, another important 20th century mathematician. Their 1956 book, “Homological Algebra,” was regarded as a classic of mathematics and a reference for many researchers.

During World War II, one of Cartan’s two brothers was executed by the Nazis for his connections to the French Resistance. After the war, Cartan was known as a leading champion of European unity.

In applying reason and logic to politics, he said, he became a European federalist, recognizing that “there is no other way” than unity.

He was also known for advocacy on behalf of mathematicians, including some in the Soviet Union who were persecuted for their politics.

Cartan was born in Nancy, France, on July 8, 1904. His father, Elie, was also a renowned mathematician.

The younger Cartan told the American Mathematical Society in a 1999 interview that he had always been interested in mathematics and “had no doubt” he could become a mathematician. But he did not think he entered mathematics because of his father.

“He never tried to influence me,” Cartan said. “In general,” he added, summarizing their mathematical relationship, “my father worked in his corner, and I worked in mine.”

Cartan earned his doctorate in 1928 at the Ecole Normale Superieure in Paris, where he taught for much of the time from 1940 to 1965.

He said he “learned a lot from my students.”

A number of them, Cartan said, wrote their theses under his direction. But, he added, his “direction” amounted to “understanding what they had in mind.” In that way, he said, “I learned very much.”