Here you can find a variety of mathematical texts of varying difficulty. At the top you find the “snapshots of modern mathematics from Oberwolfach” project. This includes short texts written by researchers visiting the Mathematisches Forschungsinstitut Oberwolfach and edited by a dedicated team of editors. Further below, we provide a range of texts, of varying difficulty, i. e. quite technical mathematical texts, but also philosophical texts. The catalogues of the exhibitions, as well as material for schools is also freely available for download. We hope you enjoy your read!
background material
Snapshots of modern mathematics from Oberwolfach
Zerodimensional symmetry CC BYNCSA 
This snapshot is about zerodimensional symmetry. Thanks to recent discoveries we now understand such symmetry better than previously imagined... 


Drugs, herbicides, and numerical simulation , , CC BYNCSA 



Operator theory and the singular value decomposition CC BYNCSA 
This is a snapshot about operator theory and one of its fundamental tools: the... 


The KadisonSinger problem CC BYNCSA 
In quantum mechanics, unlike in classical mechanics, one cannot make precise... 


Swallowtail on the shore , CC BYNCSA 
Platonic solids, Felix Klein, H. S. M. Coxeter and a flap of a swallowtail: The five Platonic... 


Statistics and dynamical phenomena CC BYNCSA 
A friend of mine, an expert in statistical genomics, told me the following story: At a dinner party, an attractive lady asked him, “What do you do... 


Minimizing energy CC BYNCSA 
What is the most efficient way to fence land when you’ve only got so many metres of fence? Or, to put it differently, what is the largest area... 


Arrangements of lines , CC BYNCSA 
We discuss certain open problems in the context of arrangements of lines in the plane.... 


What does ">" really mean? CC BYNCSA 
This Snapshot is about the generalization of “>” from ordinary numbers to socalled fields. At the end, I will touch on some ideas in recent... 


Billiards and flat surfaces CC BYNCSA 
Billiards, the study of a ball bouncing around on a table, is a rich area of current... 


Friezes and tilings CC BYNCSA 
Friezes have occured as architectural ornaments for many centuries. In this snapshot,... 


Chaos and chaotic fluid mixing CC BYNCSA 
Very simple mathematical equations can give rise to surprisingly complicated, chaotic dynamics, with behavior that is sensitive to small... 


Modelling communication and movement: from cells to animals and humans CC BYNCSA 
Communication forms the basis of biological interactions. While the use of a single... 


The ternary Goldbach Problem CC BYNCSA 
Leonhard Euler (1707–1783) – one of the greatest mathematicians of the eighteenth century and of all times – often corresponded with a friend of... 


Factorisation de matrices CC BYNCSA 
Im Folgenden soll ein kurzer Abriss des Themas Matrixfaktorisierungen gegeben werden.... 


Dirichlet Series CC BYNCSA 
Mathematicians are very interested in prime numbers. In this snapshot, we will discuss some problems concerning the distribution of primes and... 

Mathematical background material
Crystals and Mathematics
GertMartin Greuel Licence CC BYNCSA 

Humans have been fascinated by crystals for a long time. Its regular geometry, its special symmetry, but also its diversity in colours surprise and please us. In this article, an overview of the connection between crystals and mathematics is given. It is a contribution to the International Year of Crystallography 2014. 

Geraden, Kurven und Kuspen
Duco van Straten Licence CC BYNCSA 

The algebraic geometer Duco van Straten, Johannes GutenbergUniversity Mainz, Germany gives a beautiful short introduction into the field of algebraic geometry  from lines, curves to cusps. It shows many pictures and also links its content to historical events and applications. 

How to make an IMAGINARY Exhibition  Bridges 2013 Paper
Sebastian Uribe Susanne Schimpf Andreas Daniel Matt Licence CC BYNCSA 

This paper presented at the BRIDGES conference 2013 provides a brief overview of the main steps needed for organizing a math art exhibition. As IMAGINARY visited more locations, we realized the need for providing some hints and advice based on the experience of former exhibitions. Our goal is to motivate you to make your own exhibition and to contribute to the IMAGINARY platform with your own exhibits. 

Martmatics
Fernando Corbalán
Julian Pfeifle, Elena Biaín, Melissa Valdés
Base Digital Licence CC BYNCSA 

Martmatics is a project to show how Mathematics and Art have been related to each other throughout history and how they are still linked today. There are many bonds and the authors have chosen the most attractive and significant ones. You will find a brochure and also an activity book with excercices to accompany the examples from the brochure. 

IMAGINARY Worksheets for Schools
Maria Alberich Jordi Buendía Ferran Dachs Anna Sabater Emilio José Sánchez Licence CC BYNCSA 

A collection of IMAGINARY worksheets for school children. The worksheets are of different levels of difficulty, aimed at children and teenagers aged between 5 and 17 years. The material has been developed for the IMAGINARY exhibitions in Spain and was awarded with a prize of the Initiative “Ciencia en Acción” 2012. For more information, visit http://imaginary. fme. upc.edu. 

A Different Way to Read Off the Time – a New Idea for a Binary Clock
Jörg Pretz Licence CC BYNCSA 

A new idea for a binary clock is presented: It displays the time using a triangular array of 15 bits. 

Didactical Guide Zaragoza
Alexander Aginagalde Nafarrate Pedro Alegría Ezquerra Raúl Ibáñez Torres Álvaro Lozano Rojo Marta Macho Stadler Licence CC BYNCSA 

Didactical guide to the IMAGINARY exhibition 

School Taskbook: From 5 to 15
Vladimir Igorevich Arnold
Victor Goryunov Sabir GuseinZade Licence CC BYNCSA 

The taskbook for school students by renowned Russian mathematician Prof. Vladimir Igorevich Arnold. You can find the original Russian version as well as an English, German, Italian, Vietnamese and Turkish translation. If you are interested to add a new translation, please see the github repository of the booklet for all sources and details. 

Didactical Guide Bilbao
Alexander Aginagalde Nafarrate Pedro Alegría Ezquerra Raúl Ibáñez Torres Álvaro Lozano Rojo Marta Macho Stadler Licence CC BYNCSA 

Didactical guide to the IMAGINARY exhibition 

Planet, Mathematical and Population Dynamics
Philippe Etchecopar Licence CC BYNCSA 

Different models of population dynamics 

The Art of an Algebraic Surface
Andreas Daniel Matt Anna Hartkopf Licence CC BYNCSA 

A short paper to present the artistic side of algebraic surfaces made with the SURFER program. Article written for the VISMATH Book, Hungary 2012. 

Parallax Measurement
Tine Golez Licence CC BYNCSA 

An introduction to parallax measurement 

SURFER – Some Ideas for the Classroom
Andreas Daniel Matt Licence CC BYNCSA 

Some ideas how to use SURFER at school 

Resolution of Singularities
Herwig Hauser Licence CC BYNCSA 

A short introduction to singularity theory for everybody  without equations. 

Solid Möbius Strips as Algebraic Surfaces
Stephan Klaus Licence CC BYNCSA 

How to make a Möbius strip with SURFER. 

Glances at Infinity
Jürgen RichterGebert Licence CC BYNCSA 

Survey article on symmetries and chaos 

Solid Trefoil Knot as an Algebraic Surface
Stephan Klaus Licence CC BYNCSA 

How to make the trefoil knot with SURFER 

World record surfaces
Oliver Labs Marius Kempe (Translation) Licence CC BYNCSA 

Introduction to surfaces with many singularities 