mathematics

Maurice Kraitchik

Maurice Kraitchik 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 Maurice Kraitchik rather than just read about it. In short: Maurice Borisovich Kraitchik (21 April 1882 – 19 August 1957) was a Belgian mathematician and populariser. His main interests were the theory of numbers and recreational mathematics.

Key takeaways

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

Reference excerpt

Maurice Borisovich Kraitchik (21 April 1882 – 19 August 1957) was a Belgian mathematician and populariser. His main interests were the theory of numbers and recreational mathematics. He was born to a Jewish family in Minsk. He wrote several books on number theory during 1922–1930 and after the war, and from 1931 to 1939 edited Sphinx, a periodical devoted to recreational mathematics. During World War II, he emigrated to the United States, where he taught a course at the New School for Social Research in New York City on the general topic of "mathematical recreations." Kraïtchik was agrégé of the Free University of Brussels, engineer at the Société Financière de Transports et d'Entreprises Industrielles (Sofina), and director of the Institut des Hautes Études de Belgique. He died in Brussels. Kraïtchik is famous for having inspired the two envelopes problem in 1953, with the following puzzle in La mathématique des jeux:

Two people, equally rich, meet to compare the contents of their wallets. Each is ignorant of the contents of the two wallets. The game is as follows: whoever has the least money receives the contents of the wallet of the other (in the case where the amounts are equal, nothing happens). One of the two men can reason: "Suppose that I have the amount A in my wallet. That's the maximum that I could lose. If I win (probability 0.5), the amount that I'll have in my possession at the end of the game will be more than 2A. Therefore the game is favourable to me." The other man can reason in exactly the same way. In fact, by symmetry, the game is fair. Where is the mistake in the reasoning of each man? Among his publications were the following:

Théorie des Nombres, Paris: Gauthier-Villars, 1922 Recherches sur la théorie des nombres, Paris: Gauthier-Villars, 1924 La mathématique des jeux ou Récréations mathématiques, Paris: Vuibert, 1930, 566 pages Mathematical Recreations, New York: W. W. Norton, 1942 and London: George Allen & Unwin Ltd, 1943, 328 pages (revised edition New York: Dover, 1953) Alignment Charts, New York: Van Nostrand, 1944

References

Illustrations

Worked examples

Example 1 — a first encounter with Maurice Kraitchik

Start with the simplest possible case. Write down what Maurice Kraitchik 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 Maurice Kraitchik 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 Maurice Kraitchik 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 Maurice Kraitchik

In research: Maurice Kraitchik 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 Maurice Kraitchik 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: Maurice Kraitchik is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1882 births, 1957 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Maurice Kraitchik 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 Maurice Kraitchik in 20 minutes

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

Frequently asked questions

What is Maurice Kraitchik in simple terms?

Maurice Borisovich Kraitchik (21 April 1882 – 19 August 1957) was a Belgian mathematician and populariser. His main interests were the theory of numbers and recreational mathematics.

Why does Maurice Kraitchik 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 Maurice Kraitchik?

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 Maurice Kraitchik.