The puzzle was given a memorable nickname, the “happy ending” problem (or “happy end” problem as originally dubbed by Erdős), for reasons that had nothing to do with math. Instead, it reflected the primary nonmathematical consequence of their discussion of points, lines and shapes: Esther Klein and George Szekeres fell in love and married on June 13, 1937. Yet as the decades passed, mathematicians made virtually no progress in proving the conjecture. (The only other shape whose result is known is a hexagon, which requires at least 17 points, as proved by Szekeres and Lindsay Peters in 2006.) Now, in work recently published in the Journal of the American Mathematical Society, Andrew Suk of the University of Illinois, Chicago, provides nearly decisive evidence that the intuition that guided Erdős and Szekeres more than 80 years ago was correct.
A Puzzle of Clever Connections Nears a Happy End
Hope to add bits of mathematics or mathematical news I find interesting.
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