Optimizing your wife. From MathPages, via reddit. (This is apparently also known as the secretary problem or the sultan's dowry problem.)
The following is a semi-standard bit of mathematical folklore. Say you expect to meet N possible suitors in your life. You want to maximize your chances of picking the best one, given that you expect to meet these people in a random order, and once you say no to one of them you can never see them again, and that you can say for any two of them either "X is better than Y" or "Y is better than X". (There are no ties, and everybody's comparable.)
My readers who are not mathematicians are probably thinking that these are ridiculous assumptions. This is true. In particular, the first one seems silly to me -- we don't meet people at random, but through other people we know, so I suspect that the longer one spends living the more one tends to find people one likes. This certainly is true in my experience when seeking out friends -- people who I like spending time with tend to know other people I'd like spending time with. The inability to go back to previous suitors seems to be not a horrible approximation. The fact that everyone is rankable seems at first like a bad assumption -- but we manage to do it for economic goods all the time. For example, houses have prices which are scalars, despite the fact that there are multiple dimensions along which houses can be compared. The fourth assumption, that you know how many potential suitors there are, seems the most wrong to me. But combined with the assumption that you meet suitors at a constant rate, this converts strategies which talk about numbers of suitors to strategies which talk about time.
My readers who are mathematicians probably didn't read the previous paragraph.
Anyway, the optimal strategy is to reject the first N/e of the people you meet, and then pick the first person you meet who's better than everyone you'd met previously. The probability of this strategy succeeding -- in that you pick the very best person -- is close to 1/e when N is large.
I'm pretty sure I first heard this around fifteen years ago, and have probably heard it at least once a year since then -- but I didn't know a proof until now. (Strictly speaking, there's some hand-waving in the argument given there, as there always is whenever someone says "X is approximately equal to Y" without giving any sort of bound on X-Y or X/Y -- but I don't plan to use this to prove anything else, so I'm convinced.)