Henri Cartan; Researcher Helped Revolutionize Math

Henri Cartan, 104, who was known as one of the foremost mathematicians of the last half of the 20th century, died Aug. 13 in Paris. No cause of death was reported.

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

At least two of his pupils 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, Dr. Cartan received the Wolf Prize, one of the highest honors in mathematics.

Among mathematicians, Dr. 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, one of the most important mathematicians of the 20th century. Their 1956 book, "Homological Algebra," was regarded as a classic of mathematics and a reference for many researchers.

In an extended 1999 interview published by the American Mathematical Society, Dr. Cartan referred to his work on that treatise with wit and modesty.

"All of it was written by Sammy," Dr. Cartan said. "I wrote nothing.

"Of course we had discussions, but after that, Sammy wrote. I was in charge of correcting the spelling mistakes -- in English! I don't know much English, but I can spell."

During World War II, one of Dr. Cartan's two brothers was executed by the Nazis for his connections to the French Resistance. After the war, Dr. 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 his advocacy on behalf of mathematicians, including some in the Soviet Union, who were persecuted for their politics.

He was married for many years and had at least two children, but details about survivors could not be learned

Dr. Cartan was born in Nancy, France, on July 8, 1904. His father, Elie Cartan, was an equally renowned mathematician.

The younger Dr. Cartan told his American Mathematical Society interviewer that he was always interested in mathematics and "had no doubt" that he could become a mathematician. But he did not think he entered mathematics because of his father.

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

Dr. Cartan received his doctorate in 1928 from the Ecole Normale Superieure in Paris. He taught there for much of the time from 1940 to 1965.

He said he "learned a lot from my students." A number of them, he 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."