The one Nobel Prize you won’t hear announced is for Mathematics―because, in contrast to Chemistry, Physics, and Literature, there is no Nobelity in Math. Rumor has it that it’s because of a sex scandal: Alfred Nobel’s wife had an affair with a mathematician.
Which brings us to the most recent announcement of a Nobel Prize in Economics for Lloyd Shapley and Stanford professor Alvin Roth. No, Roth did not win the prize for inventing the Roth IRA. His first paper was in “lattice theory,” a branch of mathematics which, he told me in 2010, ties in with a lot of research in his field. He worries about how to form stable marriages.
People like to think of mathematics as a cold, dispassionate subject, and of mathematicians as nerds or dweebs, forever losing the hand of their Beatrice to the captain of the football team (unless a time machine is involved). But, perhaps precisely because we spend so much time in the library on Friday nights, we think as much about love as the sonnet-writers of yore.
One of my academic grandfathers, Philip Hall of Cambridge, proved a marvelous theorem about marriage. Suppose you have a bunch of men and women in a village, and you want to marry off all the women―presumably, assuming this village is not in India, to men that they already know. Can this always be done? Clearly not if there are more women than men. But even if there are more men, you might be unable to do it. For instance, you might have Alice and Beatrice, and Charles, David and Elijah, with Alice and Beatrice only knowing Charles. Two women, one guy, and this isn’t nineteenth-century Utah. But what Hall did find out was that if the women in any subset of the entire group of women collectively know at least the same number of men as there are women in the subset, it could be done.
To avoid anyone’s being left standing by the wall in our waltz, suppose we have the same number of men as women―our village is not in China, either―and this time the women all rank the men, and the men rank the women. For instance, Frasier might prefer Diane to Lilith, so he ranks Diane “number 1” and Lilith “2”.
You can’t always get what you want―unless you wrote a song with that title, in which case you can get approximately 4,000 of what you want―so Frasier might have to marry Lilith because Diane is with Sam.
But getting married is only the half of it: what about staying married?
What if Brad is married to Jen, but prefers Angelina, and Angelina is married to Billy, but prefers Brad? Then you have an unstable situation, because Brad and Angelina each prefer each other to their own spouses, and are likely to cheat.
Is it at all possible to find a set of stable marriages for our village, so no two people who are not married to each other are tempted to cheat on their spouses with each other? RAND Corporation employee Lloyd Shapley, who should have been working on ways to keep the Soviets from overrunning western Europe, thought about the stability-of-marriage problem and proved that the answer was “Yes!”
The Swedes honored Shapley and Roth this week for their mathematical work, because it has applications to how one can fairly assign medical doctors to hospitals and children to schools. But I think their work is important for other reasons too: if the prescription for stable marriages were known to the general public, programs like Jerry Springer and Maury would soon be off the air.
Incidentally, remember that story about Alfred Nobel and why there’s no Nobel Prize for Math? Probably false, since Nobel himself never married.
I guess he just never met the right mathematician.
Dr. Jonathan David Farley is an Institute Researcher at the Research Institute for Mathematics (Maine).