mathematics

Pierre Cartier (mathematician)

Pierre Cartier (mathematician) is a mathematics 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 Pierre Cartier (mathematician) rather than just read about it. In short: Pierre Émile Cartier (10 June 1932 – 17 August 2024) was a French mathematician. An associate of the Bourbaki group and at one time a colleague of Alexander Grothendieck, his interests have ranged over algebraic geometry, representation theory, mathematical physics, and category theory.

Key takeaways

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

Reference excerpt

Pierre Émile Cartier (10 June 1932 – 17 August 2024) was a French mathematician. An associate of the Bourbaki group and at one time a colleague of Alexander Grothendieck, his interests have ranged over algebraic geometry, representation theory, mathematical physics, and category theory.

Life and career Cartier was born on 10 June 1932. He studied at the École Normale Supérieure in Paris under Henri Cartan and André Weil. After his 1958 thesis on algebraic geometry, he worked in a number of fields. He is known for the introduction of the Cartier operator in algebraic geometry in characteristic p, and for work on duality of abelian varieties and on formal groups. He is the eponym of Cartier divisors and Cartier duality. From 1961 to 1971, he was a professor at the University of Strasbourg. In 1970 he was an Invited Speaker at the International Congress of Mathematicians in Nice. He was awarded the 1978 Prize Ampère of the French Academy of Sciences. In 2012 he became a fellow of the American Mathematical Society. Cartier died in Marcoussis on 17 August 2024, at the age of 92.

Publications Cartier, Pierre; Foata, Dominique (14 November 2006). Problèmes combinatoires de commutation et réarrangements. Springer. ISBN 9783540360940. (1st edition 1969) Waldschmidt, Michel; Moussa, Pierre; Luck, Jean-Marc; Itzykson, Claude, eds. (9 March 2013). "An introduction to zeta functions by Pierre Cartier". From Number Theory to Physics. Springer. pp. 1–63. ISBN 9783662028384. (1st edition 1992) "A primer of Hopf algebras" (PDF). Report Number IHES-M-2006-40: 1–74. September 2006. Freedom in Mathematics, Springer India, 2016 (with Cédric Villani, Jean Dhombres, Gerhard Heinzmann), ISBN 978-81-322-2786-1. Translation from the French language edition: Mathématiques en liberté, La Ville Brûle, Montreuil 2012, ISBN 978-23-601-2026-0. Pierre Cartier: Alexander Grothendieck. A country known only by name. Notices AMS, vol. 62, 2015, no. 4, pp. 373–382, PDF.

As editor Cartier, Pierre; Illusie, Luc; Katz, Nicholas M.; Laumon, Gérard; Manin, Yuri I.; Ribet, Kenneth A., eds. (23 October 2007). The Grothendieck Festschrift, Volume III: A Collection of Articles Written in Honor of the 60th Birthday of Alexander Grothendieck. Springer. ISBN 9780817645762. (1st edition 1990) Cartier, Pierre É.; Julia, Bernard; Moussa, Pierre; Vanhove, Pierre, eds. (18 July 2007). Frontiers in Number Theory, Physics, and Geometry II: On Conformal Field Theories, Discrete Groups and Renormalization. Springer. ISBN 9783540303084.

See also Cotangent complex Dieudonné module MacMahon's master theorem

References

External links

Cartier's website at the Institut des Hautes Études Scientifiques, with a photograph, CV, and list of publications Issue of Moscow Mathematical Journal dedicated to Pierre Cartier O'Connor, John J.; Robertson, Edmund F., "Pierre Émile Jean Cartier", MacTutor History of Mathematics Archive, University of St Andrews Javier Fresán The Castle of Groups, Interview with Pierre Cartier, EMS Newsletter 2009, pdf "Pierre Cartier: Logarithmic divergences, ..." YouTube. Hausdorff Center for Mathematics. December 4, 2014. "Pierre Cartier. Schemes". YouTube. ERC PhiloQuantumGravity. November 29, 2015. "Pierre Cartier - Conférence inaugurale". YouTube. Institut des Hautes Études Scientifiques (IHÉS). December 3, 2015. "Pierre Cartier: Is History of Mathematics a Part of General History". YouTube. Prague Axiomatic Circle. May 10, 2018. Connes, Alain; Kouneiher, Joseph (May 2025). "Pierre Cartier: A Visionary Mathematician" (PDF). Notices of the American Mathematical Society. 72 (5): 514–522. doi:10.1090/noti3140.

Illustrations

Worked examples

Example 1 — a first encounter with Pierre Cartier (mathematician)

Start with the simplest possible case. Write down what Pierre Cartier (mathematician) claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, 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 Pierre Cartier (mathematician) 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 Pierre Cartier (mathematician) 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 Pierre Cartier (mathematician)

In research: Pierre Cartier (mathematician) appears in mathematics 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 Pierre Cartier (mathematician) 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: Pierre Cartier (mathematician) is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1932 births, 2024 deaths, 20th-century French mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Pierre Cartier (mathematician) 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.

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How to study Pierre Cartier (mathematician) in 20 minutes

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Frequently asked questions

What is Pierre Cartier (mathematician) in simple terms?

Why does Pierre Cartier (mathematician) matter?

Because it connects several mathematics 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 Pierre Cartier (mathematician)?

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 Pierre Cartier (mathematician).