His interests connect discrete and computational geometry (especially polytopes), algebraic and topological methods in combinatorics, discrete mathematics and the theory of linear and integer programming. He is the author of Lectures on Polytopes (Springer 1995) and of Proofs from THE BOOK (with Martin Aigner, Springer-Verlag 1998), which has by now appeared in 14 languages. His latest book is "Darf ich Zahlen? Geschichten aus der Mathematik" ("Do I count? Stories from Mathematics"; English translation just appeared with AK Peters/CRC).
His honors include a Leibniz Prize (2001) of the German Research Foundation DFG, the Chauvenet Prize (2004) of the Mathematical Association of America, and the 2008 Communicator Award of DFG and Stifterverband. He is a member of the executive board of the Berlin-Brandenburg Academy of Sciences, a member of the German National Academy of Sciences Leopoldina, and a Fellow of the American Mathematical Society. For 2006-2008 he was the President of the German Mathematical Society DMV. He initiated and co-organized the German National Science Year Jahr der Mathematik 2008 and now directs the DMV Mathematics Media Office and the DMV Network Office Schools-Universities.