The Stable Marriage Problem

As often goes with math problems, let’s consider an unrealistic, simplified scenario which is, nevertheless, worthy of study. Imagine an island with 20 women and 20 men. The men and women want to pair up as wedded couples. So, each woman ranks the men in order of her preferences, and each man ranks the women according to his preferences. After pairing up, it would be unfortunate if a woman in one couple preferred a man in another couple to her husband and that man had similar feelings, preferring her to his wife. The two might elope – a very unstable situation!

Is there always a way to pair up the men and women and avoid such unstable situations? And if there is, how does one find such a pairing?

That is the topic of Girls’ Angle’s latest Women-In-Mathematics Video, featuring Harvard University Benjamin Peirce and National Science Foundation postdoctoral fellow Emily Riehl (and filmed by Grace Lyo). Hope you enjoy it!

The Girls’ Angle WIM Video series is the brainchild of Girls’ Angle director Elisenda Grigsby. WIM Videos are often shot on the spur of the moment and feature women in mathematics explaining some piece of math that excited them when they were students. We hope to create a large gallery that will showcase the diverse group of women working in mathematics today. If you support this concept, please consider making a charitable donation to Girls’ Angle. Girls’ Angle is a 501(c)3 and every amount helps!

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One Response to The Stable Marriage Problem

  1. Pingback: Folding Pythagorean Triples with Origami | Girls' Angle

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