mathematics

Pierre Samuel

Pierre Samuel 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 Samuel rather than just read about it. In short: Pierre Samuel (12 September 1921 – 23 August 2009) was a French mathematician, known for his work in commutative algebra and its applications to algebraic geometry. The two-volume work Commutative Algebra that he wrote with Oscar Zariski is a classic.

Key takeaways

Pierre Samuel 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 Samuel to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Pierre Samuel from memory before moving on to harder problems.

Reference excerpt

Pierre Samuel (12 September 1921 – 23 August 2009) was a French mathematician, known for his work in commutative algebra and its applications to algebraic geometry. The two-volume work Commutative Algebra that he wrote with Oscar Zariski is a classic. Other books of his covered projective geometry and algebraic number theory.

Early life and education Samuel studied at the Lycée Janson-de-Sailly in Paris before attending the École Normale Supérieure where he studied for his Agrégé de mathematique. He received his Master of Arts and then a Ph.D. from Princeton University in 1947, under the supervision of Oscar Zariski, with a thesis "Ultrafilters and Compactification of Uniform Spaces".

Career Samuel ran a Paris seminar during the 1960s, and became Professeur émérite at the Université Paris-Sud (Orsay). His lectures on unique factorization domains published by the Tata Institute of Fundamental Research played a significant role in computing the Picard group of a Zariski surface via the work of Jeffrey Lang and collaborators. The method was inspired by earlier work of Nathan Jacobson and Pierre Cartier, another outstanding member of the Bourbaki group. Nicholas Katz related this to the concept of p-curvature of a connection introduced by Alexander Grothendieck. He was a member of the Bourbaki group, and filmed some of their meetings. A French television documentary on Bourbaki broadcast some of this footage in 2000. Samuel was also active in issues of social justice, including concerns about environmental degradation (where he was influenced by Grothendieck), and arms control. He died in Paris in August 2009. His doctoral students include Lucien Szpiro and Daniel Lazard.

Awards and honors In 1958 he was an invited speaker (Relations d'équivalence en géométrie algébrique) at the ICM in Edinburgh. In 1969 he won the Lester R. Ford Award.

Works Algèbre locale, Mémorial des Sciences Mathématiques, vol. 123, Paris: Gauthier-Villars, 1953 Méthodes d'algèbre abstraite en géométrie algébrique, Berlin: Springer, 1955 with Oscar Zariski: Commutative algebra I, Graduate Texts in Mathematics, vol. 28, Berlin, New York: Springer-Verlag, 1975 [1958], ISBN 978-0-387-90089-6, MR 0090581 with Oscar Zariski: Commutative algebra. Vol. II, Berlin, New York: Springer-Verlag, 1975 [1960], ISBN 978-0-387-90171-8, MR 0389876 Anneaux factoriels, Publicaçoes da Sociedade de Matematica de São Paulo, 1962 Théorie algébrique des nombres. Hermann. 1967. ISBN 2-7056-5589-1. Algebraic Theory of Numbers (English translation by Allan Silberger), Paris: Hermann & Boston: Houghton Mifflin Co., 1970, republished by Dover, 2008. Écologie: détente ou cycle infernal, Union générale d'éditions, Collection 10-18, 1973 Amazones, guerrières et gaillardes, éditions Complexe & Presses universitaires de Grenoble, 1975 Le nucléaire en question, 1980 Géométrie projective, Presses universitaires de France, 1986 Projective Geometry (English translation by Silvio Levy), Undergraduate Texts in Mathematics, Springer-Verlag, 1988. Colloque en l'honneur de Pierre Samuel, Mém. Société mathématique de France (1989)

References

Further reading Colloque en l'honneur de Pierre Samuel, Mem. Math. Soc. Fr. (1989) Tangente Magazine

External links Pierre Samuel at the Mathematics Genealogy Project O'Connor, John J.; Robertson, Edmund F., "Pierre Samuel", MacTutor History of Mathematics Archive, University of St Andrews

Worked examples

Example 1 — a first encounter with Pierre Samuel

Start with the simplest possible case. Write down what Pierre Samuel 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 Samuel 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 Samuel 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 Samuel

In research: Pierre Samuel 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 Samuel 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 Samuel is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1921 births, 2009 deaths, 20th-century French mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Pierre Samuel 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 Samuel in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Pierre Samuel 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 Pierre Samuel out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Pierre Samuel in simple terms?

Why does Pierre Samuel 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 Samuel?

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 Samuel.