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Erdos on Graphs : His Legacy of Unsolved Problems

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A tribute to Paul Erdos, the wandering mathematician once described as the prince of problem solvers & the absolute monarch of problem posers, examines within the context of his personality & lifestyle the legacy of open problems he left to the world of mathematics after his death in 1996. DLC: Graph theory.

There is no question that Paul Erdos must be counted among the mathematical giants of the 20th century. His fundamental discoveries and profound contributions in so many areas of mathematics form a record which may never again be matched. However, there is one area in which Paul surpassed everyone else by a large margin: his ability to formulate problems. And it wasn't just the quantity of problems that was so unbelievable (they numbered in the thousands). But rather, it was their quality. Paul had the uncanny ability time after time to identify a fundamental roadblock in some particular line of approach and to capture it in a well-chosen (often innocent-looking) problem, one which could seem to be just within reach if you could only stretch yourself out a little more than before. So often the new insights generated by solving such problems led to new tools and techniques for subsequently making substantial advances in the area under investigation. That Paul was able to do this so consistently over his entire lifetime is a mark of his true genius.
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