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Today I want to talk to you
about the mathematics of love.

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Now, I think that we can all agree

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that mathematicians
are famously excellent at finding love.

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(Laughter)

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But it's not just because
of our dashing personalities,

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superior conversational skills
and excellent pencil cases.

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It's also because we've actually done
an awful lot of work into the maths

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of how to find the perfect partner.

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Now, in my favorite paper
on the subject, which is entitled,

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"Why I Don't Have a Girlfriend" --

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(Laughter)

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Peter Backus tries to rate
his chances of finding love.

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Now, Peter's not a very greedy man.

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Of all of the available women in the UK,

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all Peter's looking for
is somebody who lives near him,

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somebody in the right age range,

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somebody with a university degree,

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somebody he's likely to get on well with,

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somebody who's likely to be attractive,

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somebody who's likely
to find him attractive.

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(Laughter)

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And comes up with an estimate
of 26 women in the whole of the UK.

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(Laughter)

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It's not looking very good, is it Peter?

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Now, just to put that into perspective,

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that's about 400 times fewer
than the best estimates

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of how many intelligent
extraterrestrial life forms there are.

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And it also gives Peter
a 1 in 285,000 chance

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of bumping into any one
of these special ladies

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on a given night out.

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I'd like to think
that's why mathematicians

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don't really bother
going on nights out anymore.

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The thing is that I personally
don't subscribe

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to such a pessimistic view.

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Because I know,
just as well as all of you do,

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that love doesn't really work like that.

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Human emotion isn't neatly ordered
and rational and easily predictable.

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But I also know that that doesn't mean

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that mathematics hasn't got something
that it can offer us,

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because, love, as with most of life,
is full of patterns

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and mathematics is, ultimately,
all about the study of patterns.

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Patterns from predicting the weather
to the fluctuations in the stock market,

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to the movement of the planets
or the growth of cities.

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And if we're being honest,
none of those things

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are exactly neatly ordered
and easily predictable, either.

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Because I believe that mathematics
is so powerful that it has the potential

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to offer us a new way of looking
at almost anything.

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Even something as mysterious as love.

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And so, to try to persuade you

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of how totally amazing, excellent
and relevant mathematics is,

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I want to give you my top three
mathematically verifiable tips for love.

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(Laughter)

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OK, so Top Tip #1:

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How to win at online dating.

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So my favorite online dating
website is OkCupid,

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not least because it was started
by a group of mathematicians.

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Now, because they're mathematicians,

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they have been collecting data

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on everybody who uses their site
for almost a decade.

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And they've been trying
to search for patterns

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in the way that we talk about ourselves

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and the way that we interact
with each other

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on an online dating website.

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And they've come up with some
seriously interesting findings.

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But my particular favorite

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is that it turns out
that on an online dating website,

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how attractive you are
does not dictate how popular you are,

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and actually, having people
think that you're ugly

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can work to your advantage.

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(Laughter)

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Let me show you how this works.

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In a thankfully voluntary
section of OkCupid,

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you are allowed to rate
how attractive you think people are

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on a scale between one and five.

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Now, if we compare this score,
the average score,

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to how many messages
a selection of people receive,

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you can begin to get a sense

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of how attractiveness links to popularity
on an online dating website.

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This is the graph the OkCupid guys
have come up with.

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And the important thing to notice
is that it's not totally true

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that the more attractive you are,
the more messages you get.

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But the question arises then
of what is it about people up here

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who are so much more popular
than people down here,

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even though they have the same
score of attractiveness?

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And the reason why is that it's not just
straightforward looks that are important.

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So let me try to illustrate
their findings with an example.

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So if you take someone like
Portia de Rossi, for example,

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everybody agrees that Portia de Rossi
is a very beautiful woman.

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Nobody thinks that she's ugly,
but she's not a supermodel, either.

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If you compare Portia de Rossi
to someone like Sarah Jessica Parker,

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now, a lot of people,
myself included, I should say,

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think that Sarah Jessica Parker
is seriously fabulous

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and possibly one
of the most beautiful creatures

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to have ever have walked
on the face of the Earth.

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But some other people,
i.e., most of the Internet ...

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(Laughter)

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seem to think that she looks
a bit like a horse.

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(Laughter)

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Now, I think that if you ask people
how attractive they thought

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Jessica Parker or Portia de Rossi were,

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and you ask them to give
them a score between one and five

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I reckon that they'd average out
to have roughly the same score.

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But the way that people would vote
would be very different.

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So Portia's scores would
all be clustered around the four

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because everybody agrees
that she's very beautiful,

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whereas Sarah Jessica Parker
completely divides opinion.

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There'd be a huge spread in her scores.

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And actually it's this spread that counts.

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It's this spread
that makes you more popular

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on an online Internet dating website.

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So what that means then

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is that if some people
think that you're attractive,

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you're actually better off

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having some other people
think that you're a massive minger.

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That's much better
than everybody just thinking

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that you're the cute girl next door.

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Now, I think this begins
to make a bit more sense

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when you think in terms of the people
who are sending these messages.

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So let's say that you think
somebody's attractive,

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but you suspect that other people
won't necessarily be that interested.

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That means there's
less competition for you

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and it's an extra incentive
for you to get in touch.

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Whereas compare that
to if you think somebody is attractive

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but you suspect that everybody
is going to think they're attractive.

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Well, why would you bother
humiliating yourself, let's be honest?

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But here's where the really
interesting part comes.

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Because when people choose the pictures
that they use on an online dating website,

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they often try to minimize the things

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that they think some people
will find unattractive.

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The classic example is people
who are, perhaps, a little bit overweight

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deliberately choosing
a very cropped photo,

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(Laughter)

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or bald men, for example,

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deliberately choosing pictures
where they're wearing hats.

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But actually this is the opposite
of what you should do

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if you want to be successful.

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You should really, instead,

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play up to whatever it is
that makes you different,

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even if you think that some people
will find it unattractive.

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Because the people who fancy you
are just going to fancy you anyway,

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and the unimportant losers who don't,
well, they only play up to your advantage.

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OK, Top Tip #2:
How to pick the perfect partner.

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So let's imagine then
that you're a roaring success

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on the dating scene.

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But the question arises
of how do you then convert that success

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into longer-term happiness,

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and in particular, how do you decide
when is the right time to settle down?

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Now generally,
it's not advisable to just cash in

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and marry the first person who comes along
and shows you any interest at all.

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But, equally, you don't really
want to leave it too long

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if you want to maximize your chance
of long-term happiness.

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As my favorite author,
Jane Austen, puts it,

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"An unmarried woman of seven and twenty

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can never hope to feel
or inspire affection again."

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(Laughter)

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Thanks a lot, Jane.

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What do you know about love?

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(Laughter)

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So the question is then,

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how do you know when
is the right time to settle down,

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given all the people
that you can date in your lifetime?

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Thankfully, there's a rather delicious bit
of mathematics that we can use

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to help us out here,
called optimal stopping theory.

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So let's imagine, then,

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that you start dating when you're 15

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and ideally, you'd like to be married
by the time that you're 35.

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And there's a number of people

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that you could potentially
date across your lifetime,

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and they'll be at varying
levels of goodness.

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Now the rules are that once
you cash in and get married,

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you can't look ahead to see
what you could have had,

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and equally, you can't go back
and change your mind.

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In my experience at least,

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I find that typically people
don't much like being recalled

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years after being passed up
for somebody else, or that's just me.

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So the math says then
that what you should do

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in the first 37 percent
of your dating window,

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you should just reject everybody
as serious marriage potential.

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(Laughter)

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And then, you should pick
the next person that comes along

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that is better than everybody
that you've seen before.

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So here's the example.

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Now if you do this, it can be
mathematically proven, in fact,

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that this is the best possible way

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of maximizing your chances
of finding the perfect partner.

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Now unfortunately, I have to tell you that
this method does come with some risks.

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For instance, imagine
if your perfect partner appeared

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during your first 37 percent.

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Now, unfortunately,
you'd have to reject them.

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(Laughter)

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Now, if you're following the maths,

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I'm afraid no one else comes along

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that's better than anyone
you've seen before,

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so you have to go on
rejecting everyone and die alone.

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(Laughter)

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Probably surrounded by cats ...

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(Laughter)

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nibbling at your remains.

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OK, another risk is,
let's imagine, instead,

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that the first people that you dated
in your first 37 percent

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are just incredibly dull,
boring, terrible people.

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That's OK, because
you're in your rejection phase,

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so that's fine, you can reject them.

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But then imagine
the next person to come along

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is just marginally less boring,
dull and terrible ...

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(Laughter)

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than everybody that you've seen before.

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Now, if you are following the maths,
I'm afraid you have to marry them ...

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(Laughter)

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and end up in a relationship
which is, frankly, suboptimal.

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Sorry about that.

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But I do think that there's an opportunity
here for Hallmark to cash in on

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and really cater for this market.

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A Valentine's Day card like this.

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(Laughter)

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"My darling husband,
you are marginally less terrible

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than the first 37 percent
of people I dated."

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(Laughter)

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It's actually more romantic
than I normally manage.

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(Laughter)

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OK, so this method doesn't give you
a 100 percent success rate,

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but there's no other possible
strategy that can do any better.

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And actually, in the wild,
there are certain types of fish

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which follow and employ
this exact strategy.

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So they reject every possible
suitor that turns up

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in the first 37 percent
of the mating season,

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and then they pick the next fish
that comes along after that window

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that's, I don't know, bigger and burlier

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than all of the fish
that they've seen before.

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I also think that subconsciously,
humans, we do sort of do this anyway.

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We give ourselves a little bit of time
to play the field,

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get a feel for the marketplace
or whatever when we're young.

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And then we only start looking seriously
at potential marriage candidates

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once we hit our mid-to-late 20s.

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I think this is conclusive proof,
if ever it were needed,

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that everybody's brains are prewired
to be just a little bit mathematical.

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OK, so that was Top Tip #2.

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Now, Top Tip #3: How to avoid divorce.

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OK, so let's imagine then
that you picked your perfect partner

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and you're settling into
a lifelong relationship with them.

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Now, I like to think that everybody
would ideally like to avoid divorce,

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apart from, I don't know,
Piers Morgan's wife, maybe?

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(Laughter)

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But it's a sad fact of modern life

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that one in two marriages
in the States ends in divorce,

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with the rest of the world
not being far behind.

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Now, you can be forgiven, perhaps

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for thinking that the arguments
that precede a marital breakup

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are not an ideal candidate
for mathematical investigation.

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For one thing, it's very hard to know

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what you should be measuring
or what you should be quantifying.

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But this didn't stop a psychologist,
John Gottman, who did exactly that.

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Gottman observed hundreds of couples
having a conversation

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and recorded, well,
everything you can think of.

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So he recorded what was said
in the conversation,

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he recorded their skin conductivity,

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he recorded their facial expressions,

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their heart rates, their blood pressure,

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basically everything apart from whether
or not the wife was actually always right,

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which incidentally she totally is.

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But what Gottman and his team found

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was that one of the most
important predictors

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for whether or not a couple
is going to get divorced

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was how positive or negative each partner
was being in the conversation.

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Now, couples that were very low-risk

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scored a lot more positive points
on Gottman's scale than negative.

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Whereas bad relationships,

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by which I mean,
probably going to get divorced,

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they found themselves getting
into a spiral of negativity.

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Now just by using these very simple ideas,

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Gottman and his group were able to predict

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whether a given couple
was going to get divorced

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with a 90 percent accuracy.

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But it wasn't until he teamed up
with a mathematician, James Murray,

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that they really started to understand

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what causes these negativity spirals
and how they occur.

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And the results that they found,

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I think, are just incredibly
impressively simple and interesting.

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So these equations predict how the wife
or husband is going to respond

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in their next turn of the conversation,

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how positive or negative
they're going to be.

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And these equations depend on

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the mood of the person
when they're on their own,

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the mood of the person when
they're with their partner,

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but most importantly, they depend on

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how much the husband and wife
influence one another.

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Now, I think it's important
to point out at this stage,

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that these exact equations
have also been shown

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to be perfectly able at describing

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what happens between two countries
in an arms race.

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(Laughter)

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So that an arguing couple
spiraling into negativity

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and teetering on the brink of divorce

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00:14:23,834 --> 00:14:28,083
is actually mathematically equivalent
to the beginning of a nuclear war.

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(Laughter)

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00:14:31,021 --> 00:14:33,334
But the really important term
in this equation

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is the influence that people
have on one another,

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and in particular, something called
"the negativity threshold."

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Now, the negativity threshold,

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you can think of as
how annoying the husband can be

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00:14:45,565 --> 00:14:49,828
before the wife starts to get
really pissed off, and vice versa.

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00:14:49,852 --> 00:14:54,384
Now, I always thought that good marriages
were about compromise and understanding

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and allowing the person
to have the space to be themselves.

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So I would have thought that perhaps
the most successful relationships

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00:15:00,571 --> 00:15:03,851
were ones where there was
a really high negativity threshold.

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Where couples let things go

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00:15:05,692 --> 00:15:08,463
and only brought things up
if they really were a big deal.

308
00:15:08,487 --> 00:15:12,738
But actually, the mathematics
and subsequent findings by the team

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00:15:12,762 --> 00:15:15,294
have shown the exact opposite is true.

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00:15:15,799 --> 00:15:18,108
The best couples,
or the most successful couples,

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are the ones with a really low
negativity threshold.

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These are the couples
that don't let anything go unnoticed

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00:15:25,177 --> 00:15:28,375
and allow each other
some room to complain.

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00:15:28,399 --> 00:15:33,633
These are the couples that are continually
trying to repair their own relationship,

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that have a much more positive
outlook on their marriage.

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00:15:36,424 --> 00:15:38,492
Couples that don't let things go

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00:15:38,516 --> 00:15:43,396
and couples that don't let trivial things
end up being a really big deal.

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00:15:44,426 --> 00:15:49,684
Now of course, it takes a bit more
than just a low negativity threshold

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and not compromising
to have a successful relationship.

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00:15:54,100 --> 00:15:56,626
But I think that it's quite interesting

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00:15:56,650 --> 00:15:59,004
to know that there is really
mathematical evidence

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to say that you should never
let the sun go down on your anger.

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So those are my top three tips

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00:16:04,188 --> 00:16:07,359
of how maths can help you
with love and relationships.

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00:16:07,383 --> 00:16:09,778
But I hope, that aside from
their use as tips,

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00:16:09,802 --> 00:16:13,904
they also give you a little bit of insight
into the power of mathematics.

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00:16:13,928 --> 00:16:18,269
Because for me, equations
and symbols aren't just a thing.

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00:16:18,684 --> 00:16:23,095
They're a voice that speaks out
about the incredible richness of nature

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00:16:23,119 --> 00:16:24,905
and the startling simplicity

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00:16:24,929 --> 00:16:29,742
in the patterns that twist and turn
and warp and evolve all around us,

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00:16:29,766 --> 00:16:32,346
from how the world works to how we behave.

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00:16:32,370 --> 00:16:34,680
So I hope that perhaps,
for just a couple of you,

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00:16:34,704 --> 00:16:37,189
a little bit of insight
into the mathematics of love

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00:16:37,213 --> 00:16:40,510
can persuade you to have
a little bit more love for mathematics.

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00:16:40,534 --> 00:16:41,733
Thank you.

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00:16:41,757 --> 00:16:48,757
(Applause)