astronomy

Henri Cartan

Henri Cartan is a astronomy topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Henri Cartan rather than just read about it. In short: Henri Paul Cartan (French: [kaʁtɑ̃]; 8 July 1904 – 13 August 2008) was a French mathematician who made substantial contributions to algebraic topology. He was the son of the mathematician Élie Cartan, nephew of mathematician Anna Cartan, oldest brother of composer Jean Cartan, physicist Louis Cartan and mathematician Hélène Cartan, and the son-in-law of physicist Pierre Weiss.

Key takeaways

Henri Cartan belongs to astronomy; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Henri Cartan to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Henri Cartan from memory before moving on to harder problems.

Reference excerpt

Henri Paul Cartan (French: [kaʁtɑ̃]; 8 July 1904 – 13 August 2008) was a French mathematician who made substantial contributions to algebraic topology. He was the son of the mathematician Élie Cartan, nephew of mathematician Anna Cartan, oldest brother of composer Jean Cartan, physicist Louis Cartan and mathematician Hélène Cartan, and the son-in-law of physicist Pierre Weiss.

Life According to his own words, Henri Cartan was interested in mathematics at a very young age, without being influenced by his family. He moved to Paris with his family after his father's appointment at Sorbonne in 1909 and he attended secondary school at Lycée Hoche in Versailles. In 1923 he started studying mathematics at École Normale Supérieure, receiving an agrégation in 1926 and a doctorate in 1928. His PhD thesis, entitled Sur les systèmes de fonctions holomorphes à variétés linéaires lacunaires et leurs applications, was supervised by Paul Montel. Cartan taught at Lycée Malherbe in Caen from 1928 to 1929, at the University of Lille from 1929 to 1931 and at the University of Strasbourg from 1931 to 1939. After the German invasion of France the university staff was moved to Clermont Ferrand. He recommended the mathematicians Marie-Hélène Schwartz and Laurent Schwartz move to work at the University of Strasbourg in Clermont Ferrand for both their research and for their safety. In 1940 he returned to Paris to work at Université de Paris and École Normale Supérieure. From 1969 until his retirement in 1975 he was professor at Paris-Sud University. Cartan died on 13 August 2008 at the age of 104. His funeral took place the following Wednesday on 20 August in Die, Drome.

Honours and awards In 1932 Cartan was invited to give a Cours Peccot at the Collège de France. In 1950 he was elected president of the Société mathématique de France and from 1967 to 1970 he was president of the International Mathematics Union. He was awarded the Émile Picard Medal in 1959, the CNRS Gold Medal in 1976, and the Wolf Prize in 1980. He was an invited Speaker at the International Congress of Mathematics in 1932 in Zürich and a Plenary Speaker at the ICM in 1950 in Cambridge, Massachusetts and in 1958 in Edinburgh. From 1974 until his death he had been a member of the French Academy of Sciences. He was elected a foreign member of many academies and societies, including the American Academy of Arts and Sciences (1950), London Mathematical Society (1959), Royal Danish Academy of Sciences and Letters (1962), Palermo National Academy of Science, Letters and Arts (1967), Royal Society of London (1971), Göttingen Academy of Sciences and Humanities (1971), Spanish Royal Academy of Sciences (1971), United States National Academy of Sciences (1972), Bavarian Academy of Science (1974), Royal Academy of Belgium (1978), Japan Academy (1979), Finnish Academy of Science and Letters (1979), Royal Swedish Academy of Sciences (1981), Polish Academy of Sciences (1985) and Russian Academy of Sciences (1999). He was awarded Honorary Doctorates from Münster (1952), ETH Zürich (1955), Oslo (1961), Sussex (1969), Cambridge (1969), Stockholm (1978), Oxford University (1980), Zaragoza (1985) and Athens (1992). The French government named him Commandeur des Palmes Académiques in 1964, Officier de la Légion d'honneur in 1965 and Commandeur de l'Ordre du Mérite in 1971.

Political and social activities During the 70's and the 80's Cartan used his influence to help obtain the release of several dissident mathematicians, including Leonid Plyushch, imprisoned by the Soviet Union, Jose Luis Massera, imprisoned between 1975 and 1984 by the Uruguayan dictatorship, and Sion Assidon, imprisoned during the Moroccan Years of Lead. For his humanitarian efforts, he received in 1989 the Heinz R. Pagels Human Rights of Scientists Award from the New York Academy of Sciences. Since the 30's Cartan had tight collaborations with many German mathematicians, including Heinrich Behnke and Peter Thullen. Right after World War II he put many efforts to improve the cooperation between French and German mathematicians and restore the flow of exchanges of ideas and students. Cartan supported the idea of European Federalism and from 1974 to 1985 was president of the French section of the Union of European Federalists. At the 1984 European elections he was the leader of the Liste pour les États-Unis d'Europe, which obtained 0.4% of votes and did not elect any candidate. In 1992 he gave a speech at the first European Congress of Mathematics in Paris, remarking the common heritage and future of European countries and praising the first reunion between mathematicians from the two previously separated parts of Europe.

Research

… excerpt ends here. Continue reading the full article.

Illustrations

Henri Cartan: During the "Cartan celebration", at Orsay in 1975. — During the "Cartan celebration", at Orsay in 1975.

Worked examples

Example 1 — a first encounter with Henri Cartan

Start with the simplest possible case. Write down what Henri Cartan claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In astronomy, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Henri Cartan before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Henri Cartan ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Henri Cartan

In research: Henri Cartan appears in astronomy research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Henri Cartan in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Henri Cartan is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1904 births, 2008 deaths, 20th-century French mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Henri Cartan outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Henri Cartan” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Henri Cartan in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Henri Cartan means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Henri Cartan out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Henri Cartan in simple terms?

Why does Henri Cartan matter?

Because it connects several astronomy ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Henri Cartan?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Henri Cartan.