Images of Mathematics
The original French versions of these articles and many more can be found at Images des mathématiques.
Charting the Worlds
Etienne Ghys: Cartography has accompanied mathematics since its very beginnings and continually renews its set of problems. I would like to present a few selected pieces of this interaction between cartography and mathematics. I hope to show through these examples how the two disciplines mutually enrich one another.
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.
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.
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.
About Images des mathématiques
Images des mathématiques (IdM) is a French website published by the CNRS and dedicated to popularizing mathematics. It has a variety of engaging materials related to all aspects of mathematics. Its slogan is “Mathematical research in words and images”. Some articles are color-coded, according to their technical difficulty, similarly to downhill slopes (from green to black diamond). The site follows several print journals of the same name, published at different times by the CNRS. The editorial board was headed by Étienne Ghys from 2009 to 2014, by Fabrice Planchon from 2015 to 2018, and since 2019, by Aurélien Alvarez.
AMR will publish translation into English of selected pieces that appeared in IdM over the years. We shall select the ones that are most suitable for our audience comprising professional mathematicians, from beginners to seasoned one.
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)