ALT Première de couverture des "Éléments de mathématiques pour le XXIe siècle", volume 4.

ALT Quatrième de couverture des "Éléments de mathématiques pour le XXIe siècle", volume 4.

ALT Quote from Morris Kline : "The history of arithmetic and algebra illustrates one of the striking and curious features of the history of mathematics. Ideas that seem remarkably simple once explained were thousands of years in the making."

ALT Citation de Morris Kline : "L'histoire de l'arithmétique et de l'algèbre illustre l'un des aspects marquants et curieux de l'histoire des mathématiques. Des idées qui semblent remarquablement simples une fois expliquées ont mis des milliers d'années à se développer."

ALT Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. The Piff-Welsh Theorem : If M is a transversal matroid and F is a field then M is representable over some finite extension of F. In particular, M is representable over fields of any characteristic.

ALT Portrait photographique de Victor Hugo, et une citation : "La géométrie est à perte de vue."

ALT Photographic portrait of Victor Hugo, and a quote : "Geometry stretches as far as the eye can see."

ALT Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. Lieb’s Square Ice Theorem : For the graph of the n × n toroidal lattice, let fn denote the number of Eulerian orientations. Then lim n→∞ f_n^(1/n^2) = (8 √3) / 9

ALT Photographic portrait of Antoine-Augustin Cournot, and a quote : "The employment of mathematical symbols is perfectly natural when the relations between magnitudes are under discussion ; and even if they are not rigorously necessary, it would hardly be reasonable to reject them, because they are not equally familiar to all readers and because they have sometimes been wrongly used, if they are able to facilitate the exposition of problems, to render it more concise, to open the way to more extended developments, and to avoid the digressions of vague argumentation."

ALT Portrait photographique d'Antoine-Augustin Cournot, et une citation : "L'emploi des signes mathématiques est chose naturelle toutes les fois qu'il s'agit de discuter des relations entre des grandeurs ; et lors même qu'ils ne seraient pas rigoureusement nécessaires, s'ils peuvent faciliter l'exposition, la rendre plus concise, mettre sur la voie de développements plus étendus, prévenir les écarts d'une vague argumentation, il serait peu philosophique de les rebuter parce qu'ils ne sont pas également familiers à tous les lecteurs et qu'on s'en est quelquefois servi à faux."

ALT Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. Kuratowski’s 14-Set Theorem : Let T = (S, T ) be a topological space and for any subset X of S, denote by C(X) the complement S\X of X, and by K(X) the topological closure of X. Starting with an arbitrary subset of S , apply C and K repeatedly in any order; then the number of different sets that may be produced is at most 14.

ALT Photographic portrait of Emmy Noether, and a quote : "My methods are working and conceptual methods and therefore have spread everywhere."