Cinq minutes de mathématiques.
English Title : Five minutes mathematics. Translated from the German by Yannis Haralambous. (ZDM/Mathdi)
Titre original : Fünf Minuten Mathematik.
Auteurs : Behrends Ehrhard ; Haralambous Yannis. Trad.
Résumé
Cet ouvrage contient cent textes parus sous la rubrique « Fünf Minuten Mathematik » (« Cinq minutes de mathématiques ») des journaux « Die Welt » et « Berliner Morgenpost » en 2003 et 2004, rubrique dans laquelle sont abordés des domaines variés des mathématiques, dans un langage compréhensible par des non-spécialistes. Quelques extraits de la table des matières : Abstract In recent years, a lowering of the level of scientific knowledge of average person has been reported in many countries. As a consequence of a series of wrong political decisions, the weights of mathematics, physics and chemistry in curricula decrease at all levels of education. The lack of interest of young people for technical studies is a sad reality and attains such a degree that questions that were unconceivable 20 years ago, say, are nowadays explicitly asked. Among them, a recurrent question is the relevance of mathematics for the post-industrial society. As outrageous as it may sound to cultivated people, such inquiries need be carefully considered. Unfortunately, it is highly difficult for a mathematician, be it a teacher or researcher, to find a pertinent justification for mathematics, convincing from the point of view of a layperson carrying a lot of apprehension, mistrust, misconceptions. Such endeavor requires not only good will and a lot of time but also proper acquaintance with the domain and remarkable communication skills. Without any doubt, the book under review is a success story for the defenders of mathematics in an increasingly hostile world. It contains the 100 articles published by Professor Ehrhard Behrends in the newspaper Die Welt and, after a lapse of several weeks, also in Berliner Morgenpost. Readers’ feed-back was so encouraging that the Vieweg publishing house decided in 2006 to print all articles in a book. With relaxed space limitations it was possible to add explanations (many times, at readers’ suggestion), graphics, pictures making the material even more attractive. Consequently, a second, revised and enlarged, German edition was put in circulation in 2008. Meanwhile, the book has been translated in English and Japanese. The present review refers to the French translation, due to Yannis Haralambous. The entire project relies on three guiding ideas: mathematics are useful; mathematics are fascinating; without mathematics, it is impossible to really understand the world. To knowledgeable persons, they sound like axioms – the hard task is to convince a large majority of their truth. The author has selected a diversity of subjects from several areas of mathematics, ranging from odds of lottery players to mysteries of DVD players, from prime numbers to Bayes theorem, from cryptography to computer tomography, from quantum computing to non-standard analysis, from knot theory to Galois theory, from five-dimensional graphics to queuing lines, from Pythagoras, Fermat, and Gauss to Bach and Xenakis. More important for the success of such an endeavor is the way of presenting the chosen subjects. The author succeeds to completely avoid the professionals’ jargon, replacing conventional proofs by sketches of explanations that, on the one hand, contain sufficient hints to put the initiated reader on the right track, and, on the other hand, are non-inhibitive for the reader whose contacts with mathematics ended during the high-school. Examples taken from every-day life (football championship, TV advertising, lottery drawings, stock markets, music) are both straightforward and striking (e.g., the odds to win the big prize at Euromillions lottery are about as slim as those to have a one-centimeter wide stick hit by a one-cent coin thrown by a blind person during a journey of 140 km). To fully understand and appreciate the non-mathematical « packaging » of the original text, a more than cursory familiarity with the German language, history, classical culture and day-to-day life is necessary. This feature makes it very difficult to translate the book without diminishing its impact force. Yannis Haralambous succeeds brilliantly to overcome all hurdles by finding analogies comprehensible by French readers and supplementing the text with footnotes containing additional, localized explanations, as well as anecdotes extracted from French mass-media, all expressed in a very elegant, enjoyable manner. The book under review is visually attractive, being carefully printed on high quality paper and lacking the usual amount of misprints (actually, I have spotted only one – on p. 214, instead of L_{k_1} one should have L_{k-1}). All in all, the book is a very effective pleading for mathematics, accessible to virtually every person on the street. It is a compulsory reading for any cultivated person, no matter what background, profession or previous relationships with mathematics. (ZDM/Mathdi)
Les chroniques touchent à tous les sujets liés aux mathématiques : hasard et combinatoire, nombres et arithmétique en général, logique et paradoxes, cryptographie, quatrième dimension et puis encore des sujets beaucoup plus « matheux » comme la transcendance, la conjecture de Goldbach, les problèmes P et NP ou la logique floue.
– On ne peut tromper le hasard
– Mathématiques enchanteresses : les nombres
– Quel est l’âge du capitaine ?
– Des nombres premiers de taille vertigineuse
– Perte plus perte égale bénéfice : le jeu de hasard paradoxal du physicien Juan Parrondo
– Les grands nombres défient la raison
– La clé de décryptage se trouve dans le bottin
– Cryptographie : une science secrète
– Du barbier de village qui se rase lui-même
– S’arrêter au meilleur moment
– etc.
Notes
Cet ouvrage est l’objet d’une présentation sous la rubrique « Notes de lecture » de la revue Tangente n° 145.
Données de publication
Éditeur Société Mathématique de France (SMF) Paris , 2011 Collection La Série T Format 16 cm x 24,5 cm, 387 p.
ISBN 2-85629-325-5 EAN 9782856293256 ISSN 2109-7186
Public visé chercheur, élève ou étudiant, enseignant, formateur, tout public Niveau 1re, 2de, licence, lycée, terminale Âge 15, 16, 17, 18, 19, 20
Type ouvrage (au sens classique de l’édition), vulgarisation, popularisation Langue français Langue d’origine allemand Support papier
Classification
Mots-clés