The truth, the whole truth and nothing but the truth: The challenges of reporting on mathematics / George G. Szpiro -- Experimental mathematics in the society of the future / David H. Bailey, Jonathan M. Borwein -- What is the impact of interactive mathematical experiments? / Albrecht Beutelspacher -- Mathematics and finance / Walter Schachermayer -- Statistics in high dimensions / Aad van der Vaart, Wessel van Wieringen -- Filtering theory: Mathematics in engineering, from Gauss to particle filters / Ofer Zeitouni -- Mathematical models for population dynamics: Randomness versus determinism / Jean Bertoin -- The quest for laws and structure / Jürg M. Fröhlich -- Geometry and freeform architecture / Helmut Pottmann, Johannes Wallner -- Some geometries to describe nature / Christiane Rousseau -- Mathematics in industry / Helmut Neunzert -- Mathematics of signal design for communication systems / Holger Boche, Ezra Tampubolon -- Cryptology: Methods, applications and challenges / Claus Diem -- A mathematical view on voting and power / Werner Kirsch -- Numerical methods and scientific computing for climate and geosciences / Jörn Behrens.

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The ubiquity and importance of mathematics in our complex society is generally not in doubt. However, even a scientifically interested layman would be hard pressed to point out aspects of our society where contemporary mathematical research is essential. Most popular examples are finance, engineering, wheather and industry, but the way mathematics comes into play is widely unknown in the public. And who thinks of application fields like biology, encryption, architecture, or voting systems? This volume comprises a number of success stories of mathematics in our society – important areas being shaped by cutting edge mathematical research. The authors are eminent mathematicians with a high sense for public presentation, addressing scientifically interested laymen as well as professionals in mathematics and its application disciplines.