I’ve long been a fan of the Gale–Shapley matching algorithm, and related problems, so was happy to see that a Nobel Prize was awarded for it. Having seen Peter Rowlett’s article that laid down the following gauntlet:
“I see ‘Nobel week’ as an opportunity for mathematicians to go in search of the mathematics behind each prize, rather than to retreat and complain about the lack of a prize specifically for mathematics”,
I was surprised that none of the mathsy types in my tiny corner of internet seemed to have noticed that a mathematician won a Nobel prize essentially for mathematics. After growing slightly impatient, I realised I only had myself to blame for not acting earlier, so I sketched a quick news story contribution over at the Aperiodical (it’s short and so reproduced here in full):
There may be no Nobel in mathematics, but that needn’t stop mathematicians winning one: Lloyd Shapley has just won the Nobel prize for economics, for the theory of stable allocations and the practice of market design.1
Lloyd Shapley described himself in an Associated Press interview:
“I consider myself a mathematician and the award is for economics. I never, never in my life took a course in economics.”
But if you don’t take his word for it, look on over at his entry on the Mathematics Genealogy Project, and you’ll find his thesis is on “Additive and Non-Additive Set Functions”.
The Nobel prize website has some details on the theory of stable allocations and market design, but an old AMS feature column gives a gentler mathematical introduction, via the elegant graph theory of Hall’s Marriage theorem.
- Though technically it’s not a Nobel prize, and actually the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel. Perhaps Alfred Nobel’s made-up wife also had an affair with a fantastical economist.
If I had more time, and wasn’t trying to catch the end of a news cycle, I may have also reminded people that co-author David Gale would also have won this noblest of prizes, had he not passed away four years ago. David was described in his obituary as:
‘professor emeritus of mathematics at the University of California, Berkeley, and a puzzle lover who made fundamental contributions to economics and game theory’.
Also on the Mathematical genealogy project, Gale’s wrote a thesis that was entitled “Solutions of Finite Two-Person Games”; he invented the classic, chocolatey game of “Chomp“; wrote a maths and puzzle column, collected into the book “Tracking the Automatic Ant and Other Mathematical Explorations”; and set up MathSite, which contains interactive demonstrations of mathematics, including one of his and Shapley’s algorithm.
And finally, I really should have directed people to David Gale and Lloyd Shapley’s original, elegantly simple paper in The American Mathematical Monthly, which concludes:
“What, then to raise the old question, is mathematics? The answer, it appears, is that any argument which is carried out with sufficient precision is mathematical, and the reason that your friends and ours cannot understand mathematics is not because they have no head for figures, but because they are unable to achieve the degree of concentration required to follow a moderately involved sequence of inferences. This observation will hardly be news to those engaged in the teaching of mathematics, but it may not be so readily accepted by people outside of the profession. For them the foregoing may serve as a useful illustration.”