Maurice Kraitchik
Encyclopedia
Maurice Kraitchik was a Belgian mathematician
and populariser
born in Minsk
. His main interests were the theory of numbers and recreational mathematics
.
He is famous for having inspired the two envelopes problem
in 1953, with the following puzzle in
La mathématique des jeux:
Kraitchik 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, Kraïtchik 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 Etudes de Belgique”.
Among his publications were the following:
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and populariser
Popular science
Popular science, sometimes called literature of science, is interpretation of science intended for a general audience. While science journalism focuses on recent scientific developments, popular science is broad-ranging, often written by scientists as well as journalists, and is presented in many...
born in Minsk
Minsk
- Ecological situation :The ecological situation is monitored by Republican Center of Radioactive and Environmental Control .During 2003–2008 the overall weight of contaminants increased from 186,000 to 247,400 tons. The change of gas as industrial fuel to mazut for financial reasons has worsened...
. His main interests were the theory of numbers and recreational mathematics
Recreational mathematics
Recreational mathematics is an umbrella term, referring to mathematical puzzles and mathematical games.Not all problems in this field require a knowledge of advanced mathematics, and thus, recreational mathematics often attracts the curiosity of non-mathematicians, and inspires their further study...
.
He is famous for having inspired the two envelopes problem
Two envelopes problem
The two envelopes problem, also known as the exchange paradox, is a brain teaser, puzzle or paradox in logic, philosophy, probability and recreational mathematics, of special interest in decision theory and for the Bayesian interpretation of probability theory...
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?
Kraitchik wrote several books on number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
during 1922-1930 and after the war, and from 1931 to 1939 edited Sphinx, a periodical devoted to recreational mathematics
Recreational mathematics
Recreational mathematics is an umbrella term, referring to mathematical puzzles and mathematical games.Not all problems in this field require a knowledge of advanced mathematics, and thus, recreational mathematics often attracts the curiosity of non-mathematicians, and inspires their further study...
.
During World War II, Kraïtchik emigrated to the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
, where he taught a course at the New School for Social Research in New York City
New York City
New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and...
on the general topic of "mathematical recreations."
Kraïtchik was « agrégé » of the Free University of Brussels
Free University of Brussels
The Free University of Brussels was a university in Brussels, Belgium. In 1969, it split into the Université Libre de Bruxelles and the Dutch-speaking Vrije Universiteit Brussel....
, engineer
Engineer
An engineer is a professional practitioner of engineering, concerned with applying scientific knowledge, mathematics and ingenuity to develop solutions for technical problems. Engineers design materials, structures, machines and systems while considering the limitations imposed by practicality,...
at the “Société Financière de Transports et d'Entreprises Industrielles (Sofina)
Sofina
Sofina, Société Financière de Transports et d'Entreprises Industrielles, is a Belgian holding company, headquartered in Brussels, which invests in several industrial sectors such as Telecommunication , Portfolio companies, Banks and Insurance , Private Equity , Services within the Company ,...
”, and director of the “Institut des Hautes Etudes de Belgique”.
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