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Hello and welcome to more or less on the BBC World Service, your numerical guide to news and to life.

I'm Tim Harford. This week we're lavishing our entire eight minutes and 59 seconds on one man.

Why? Because he's Professor Al Roth and this week he won the Nobel Memorial prize in economics.

He didn't win it on his own. He shared the prize with Lloyd Shapley. When Roth was just a boy,

Shapley and a colleague David Gale published an important mathematical paper about something called

matching algorithms. I began my conversation with Al Roth by asking him to explain that work.

In 1962, David Gale and Lloyd Shapley wrote a very remarkable article in which they said,

let's think about how, in abstract, college admissions might work or even marriage,

and they thought about a process of iterative proposals and acceptances and rejections that would

lead to a good outcome. You've got a bunch of men, a bunch of women or you've got a bunch of

students and a bunch of universities and you're trying to fix everybody up with a good enough

match. And their idea was that, say, the men would all start by proposing to their first choice.

Woman and the women would reject all but the offer they most preferred, but they wouldn't

immediately accept that offer. And what the women would do is they would hold the best offer they

had received and reject the rest. And all the men who had been rejected would make a proposal

to their next best choice, to the best choice who hadn't yet rejected them. And at each stage,

every woman who got new proposals would look at any new proposals she got, she'd compare them to

the proposal that she might be holding and she'd choose the best of those and reject the others.

So someone she'd held after round one, she might reject after round two if she got a better offer

to hold. And that would proceed until no men wanted to make any more offers and no more rejections

...