#### Henri Cartan: mathematician

Henri Cartan was one of the most influential, versatile and distinguished pure mathematicians of the past century.

He was born in Nancy in 1904. His father, Élie, was a great mathematician, and father and son were later to collaborate. He was a professor of mathematics at Nancy until he moved in 1909 to Paris, where Henri grew up. A brother, Jean, a composer, died young of tuberculosis; another, Louis, a physicist, was executed by the Nazis for resistance activity in 1943.

Cartan studied mathematics at the École Normale Supérieure in Paris, where he was taught by Gaston Julia and by his father; André Weil, a lifelong friend and later collaborator, was one year ahead. Cartan's doctoral thesis of 1928 was written under the supervision of Paul Montel, whose field was complex analysis. After teaching for a year at the Lycée Caen, Cartan moved to the University of Lille (1929-31), and then to the University of Strasbourg (1931-40). He married Nicole Antoinette Weiss in 1935; the marriage produced two sons and three daughters. Cartan moved to Paris in 1940, to the Sorbonne till 1969, then to the Université de Paris-Sud at Orsay until his retirement in 1975.

French scientists were given no special treatment in the First World War, and many promising scientists and mathematicians were killed in the trenches. In an effort to redress this loss, and to meet the needs of the time for proper textbooks, a group of promising young mathematicians met in 1935. Their intention was to write a comprehensive treatment of mathematics from first principles that was modern and definitive, with much emphasis on a systematic development, with each theorem given a rigorous proof. The founding group of around ten, which included Cartan and Weil as well as Jean Dieudonné and Claude Chevalley, chose to write collectively under the pseudonym of Nicholas Bourbaki (the name was chosen in honour of a French general from the Franco-Prussian War). Their work was published over many years as a series of books under the title

*Eléments de mathématiques*, a conscious echo of Euclid's

*Elements*. While the coverage was never complete, "Bourbaki" was in its time very influential on a generation of mathematicians in the areas of mathematics that it covered. His great input into the Bourbaki project was one of Cartan's main achievements.

At Weil's invitation, he visited the US in 1947-48, where he met the mathematician Samuel Eilenberg. This contact resulted in their book

*Homological Algebra*(1956). This now classic text has been highly influential for more than half a century. The fusion of topology (roughly, the study of invariance under continuous deformation) with modern algebra in the field of algebraic topology was a key development in pure mathematics in the second half of the last century. Homological algebra, while part of algebraic topology, has important implications in other branches of pure mathematics such as algebraic geometry and algebraic number theory, and now finds applications also in modern mathematical physics.

Cartan wrote extensively on analytic functions of several complex variables, differential calculus and differential forms, potential theory and the theory of sheaves (faisceaux in French), a field of which he was one of the principal creators. Cartan's collected works were published in three volumes in 1979, in addition to 15 volumes of the

*Séminaire Cartan*at the École Normale Supérieure, published during 1948-64.

Cartan was active as a supporter of human rights. In Soviet times one of the techniques for repression was the incarceration of dissenters in mental hospitals. At the International Congress of Mathematicians in Vancouver in 1974, Cartan was one of the prime movers in a campaign for the release of the mathematician Leonid Plyushch, who had been detained in this way; he was eventually released in 1976. Cartan continued to campaign on behalf of other mathematicians who were victims of political persecution, in the East or the West.

Cartan was widely honoured. Like his father, he was elected to membership of the French Academy of Sciences (in 1974), and, again like his father he was a foreign member of the Royal Society of London. Among other academies, he was elected an honorary member of the London Mathematical Society, and was awarded many honorary doctorates (including one from Oxford, 1980) and academic prizes.

**Henri Cartan. mathematician, was born on July 8, 1904. He died on August 13, 2008, aged 104**

The Times, September 10, 2008 © The Times, 2008