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How the ‘happy ending problem’ launched a new branch of math—and a romance
['Jack Murtagh', 'Jeanna Bryner']
Scientific American Content: Global
In mathematical terms, must some four of the five dots form a convex quadrilateral?
With only four dots, it’s clearer to see that a convex quadrilateral might elude you, depending on where the dots fall.
Amanda MontañezDoes this three-point configuration always admit a convex quadrilateral?
Erdős dubbed this the “happy ending problem” because, somewhere in the course of trading geometric drawings, Esther Klein and George Szekeres fell in love.
Ramsey’s theorem and the happy ending problem share a common insight: once systems grow large enough, pockets of order become unavoidable.