mathematics

Pierre Boutroux

Pierre Boutroux 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 Boutroux rather than just read about it. In short: Pierre Léon Boutroux (French: [butʁu]; 6 December 1880 – 15 August 1922) was a French mathematician and historian of science. Boutroux is chiefly known for his work in the history and philosophy of mathematics.

Key takeaways

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

Reference excerpt

Pierre Léon Boutroux (French: [butʁu]; 6 December 1880 – 15 August 1922) was a French mathematician and historian of science. Boutroux is chiefly known for his work in the history and philosophy of mathematics.

Biography He was born in Paris on 6 December 1880 into a well connected family of the French intelligentsia. His father was the philosopher Émile Boutroux. His mother was Aline Catherine Eugénie Poincaré, sister of the scientist and mathematician Henri Poincaré. A cousin of Aline, Raymond Poincaré was to be President of France. He occupied the mathematics chair at Princeton University from 1913 until 1914. He occupied the History of sciences chair from 1920 to 1922. Boutroux published his major work Les principes de l'analyse mathématique in two volumes; Volume 1 in 1914 and Volume 2 in 1919. This is a comprehensive view of the whole field of mathematics at the time. He was an Invited Speaker of the ICM in 1904 at Heidelberg, in 1908 at Rome, and in 1920 at Strasbourg. He died on 15 August 1922, aged 41 years.

Works L'Imagination et les mathématiques selon Descartes (1900) Sur quelques propriétés des fonctions entières (1903) Œuvres de Blaise Pascal, publiées suivant l'ordre chronologique, avec documents complémentaires, introductions et notes, par Léon Brunschvicg et Pierre Boutroux (1908) Leçons sur les fonctions définies par les équations différentielles du premier ordre, professées au Collège de France (1908) Les Principes de l'analyse mathématique, exposé historique et critique (2 volumes, 1914-1919) Texte en ligne 1 2 Contient : (I) Les nombres, les grandeurs, les figures, le calcul combinatoire, le calcul algébrique, calcul des fonctions, l'algèbre géométrique. (2) La géométrie algébrique. Extensions de l'algèbre et constructions logiques. Extensions de l'algèbre; les développements en séries. La méthode analytique en mathématiques. Analyse infinitésimale. Analyse des principes mathématiques. Analyse de la notion de fonction. L'Idéal scientifique des mathématiciens dans l'antiquité et dans les temps modernes (1920) Texte en ligne Les Mathématiques (1922)

References

Further reading R S Calinger, Biography in Dictionary of Scientific Biography (New York 1970-1990). L Brunschvicg, L'oeuvre de Pierre Boutroux, Revue de métaphysique et de morale 29-30 (1922), 285-289. Lettre de M Pierre Boutroux a M Mittag-Leffler, in The mathematical heritage of Henri Poincaré 2 (Providence, R.I., 1983), 441-445.

External links Media related to Pierre Boutroux at Wikimedia Commons French Wikisource has original text related to this article: Auteur:Pierre Boutroux Works by or about Pierre Boutroux at the Internet Archive Boutroux summary at www-gap.dcs.st-and.ac.uk

Illustrations

Worked examples

Example 1 — a first encounter with Pierre Boutroux

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

In research: Pierre Boutroux 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 Boutroux 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 Boutroux is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1880 births, 1922 deaths, 19th-century French mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Pierre Boutroux 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 Boutroux in 20 minutes

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

Frequently asked questions

What is Pierre Boutroux in simple terms?

Why does Pierre Boutroux 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 Boutroux?

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 Boutroux.