Now let's speak a bit about the connection between mathematics and real life. So, We started with a real life example. And it indeed is practically important. So important that it deserved a Nobel Prize. So there is a Nobel Prizes and also there are Nobel memorial prize in economics. And this prize for 2012 was given to two people, Roth and Shapley. And here is the quote from the press release of the committee. And from this quote you see that Shapley was a theoritician and Roth applied this theory developed by Shapley and actually by Gale to the practical situation. So you see that there are several practical cases that are mentioned here, doctors with hospitals, students with schools, and even a very important but sad case about organ donors and patients. Where each matching is about somebody's life. So what was the origin of all this field? Very funny, the first paper was written by Gale and Shapley. And it was written in 1962 rather long ago. And it was written not in some research journal with high impact with [INAUDIBLE] journal, just the popular journal for a wide audience, as they say in the description of the journal. American Mathematical Monthly. And you can read this paper, here is the reference. And you see it's just very elementary paper and still it turns out to be extremely important. And it deserved a Nobel Memorial Prize. Now a very important warning. So it's about terminology. So you see in the name of the paper, they say the Stability of Marriage. So they use the marriage terminology and we will also, following the tradition, use this terminology. And the terminology, instead of applicant and job which are what we discussed, we will speak about men and women who want to marry. And we will consider the simplest setting when they are men and women and they want to form pair, each man would marry one woman, and so on. And there's also in this terminology what is called matching, in the theory it's called marriage or set of marriages. And what is very important? So we make no claim in this terminology, unlike the case with applicants and jobs. This is completely nothing to do with practice, we make no claims about real life. And so this is not, if we say that some algorithm designs a set of marriages which is stable, we don't mean that you should use this algorithm in practice for anything. Mathematicians usually consider everything in the real world just as a good illustration to some mathematical theory. And they don't bother whether this illustration is really adequate or not, just if it's a funny terminology's, it's okay for mathematicians. And now we will also follow this tradition. So please don't take these claims personally. So just the reason is that, let's say, her husband is much shorter than the applicant that fills this position. And the algorithms are complicated. Not really complicated but just you need to keep track of the details and short terminology is very important. So we will use this short terminology without any practical consenquences. Also, this terminology is more symmetric. You see that men and women are symmetric. So every algorithm can be, of course, reversed and it's clear how to reverse it just to change the names.