Images of Mathematics
The original French versions of these articles and many more can be found at Images des mathématiques.
A Bit of Geometric Group Theory
Gilbert Levitt: Discrete groups appear in every area of mathematics — and even in Escher’s art. Even if the y are defined algebraically, we often understand them better by their action on geometric objects. More and more often, they are viewed as geometric entities in their own right. Their properties are especially striking when the curvature is negative.
Triangles after Euclid, Gauss and Gromov
Etienne Ghys: For centuries, geometry was Euclid’s geometry — the one we learn in school, with its right, isosceles and equilateral triangles and its theorems of Pythagoras and Thales; the geometry of “the world in which we live.” Euclid established its foundations in the third century BCE in the book — a landmark for mathematicians, titled “The Elements”. For more than twenty centuries, this book stood at the heart of mathematics, so definitive did it seem.
Dimers
Adrien Kassel: This is an introductory text on the dimer model and its links to combinatorics, statistical physics, and geometry. This article is a translation of the French original published in 2016. In the meantime, the study of the dimer model has seen several interesting developments, reflected in the final section, which was added at the time of translation in October 2025.
AMR Images of Mathematics Editorial Committee
Olga Kravchenko (U Lyon), Christopher-Lloyd Simon (U Rennes), Rostislav Matveev (Max-Planck-Institute for Mathematics in the Sciences, Leipzig), Sergei Tabachnikov (Penn State University, University Park)