Famous and lesser known problems in “elementary” combinatorial geometry and number theory

author: Moshe Rosenfeld, University of Washington
published: Sept. 7, 2007,   recorded: September 2007,   views: 11399

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Which problems attain great notoriety and which are delegated to collect dust on a shelf? “Elementary” problems tend to attract attention because they are very easy to understand and look “solvable”. It is a mystery to me why some attract a lot of attention while others lie hibernating waiting for some new fresh ideas. In their recent interesting book Research Problems in Discrete Geometry (Springer, New York 2005) P. Brass, W. Moser, J. Pach wrote: “Although Discrete Geometry has a rich history extending more than 150 years, it abounds in open problems that even a high-school student can understand and appreciate. Some of these problems are notoriously difficult and are intimately related to deep questions in other fields of mathematics. But many problems, even old ones, can be solved by a clever undergraduate or a high- school student equipped with an ingenious idea and the kinds of skills used in a mathematical olympiad.”

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