why shouldn’t you invite mathematicians to a party because they can’t drink and
to a party because they can’t drink and
to a party because they can’t drink and derive well if you want to find out if
derive well if you want to find out if
derive well if you want to find out if this very bad job makes any sense
this very bad job makes any sense
this very bad job makes any sense try me tonight at the reception but for
try me tonight at the reception but for
try me tonight at the reception but for now I can promise that maths is so much
now I can promise that maths is so much
now I can promise that maths is so much more than derivation integrals or
more than derivation integrals or
more than derivation integrals or numbers and that mathematicians aren’t
numbers and that mathematicians aren’t
numbers and that mathematicians aren’t necessarily socially awkward elderly men
necessarily socially awkward elderly men
necessarily socially awkward elderly men okay
okay
okay so what’s on the left it’s only part of
so what’s on the left it’s only part of
so what’s on the left it’s only part of our job best ideas often comes in
our job best ideas often comes in
our job best ideas often comes in situations such as the one on the right
situations such as the one on the right
situations such as the one on the right maths is for the young and the old girls
maths is for the young and the old girls
maths is for the young and the old girls and guys smartest and average introverts
and guys smartest and average introverts
and guys smartest and average introverts and extroverts maths is in everything we
and extroverts maths is in everything we
and extroverts maths is in everything we do we human beings not necessarily
do we human beings not necessarily
do we human beings not necessarily mathematicians do you need a proof let
mathematicians do you need a proof let
mathematicians do you need a proof let me invite you to a maths party but
me invite you to a maths party but
me invite you to a maths party but before we go anywhere we have to do
before we go anywhere we have to do
before we go anywhere we have to do something about our hair and you know
something about our hair and you know
something about our hair and you know when I start preparing for a party and I
when I start preparing for a party and I
when I start preparing for a party and I look into a mirror I assess combing my
look into a mirror I assess combing my
look into a mirror I assess combing my hair as an impossible task so let’s
hair as an impossible task so let’s
hair as an impossible task so let’s simplify this problem a bit for a moment
simplify this problem a bit for a moment
simplify this problem a bit for a moment forget about your head think about a
forget about your head think about a
forget about your head think about a hairy bowl yeah mathematicians are
hairy bowl yeah mathematicians are
hairy bowl yeah mathematicians are creative when it comes to theorem names
creative when it comes to theorem names
creative when it comes to theorem names the hairy ball theorem is a very
the hairy ball theorem is a very
the hairy ball theorem is a very important result in an area of
important result in an area of
important result in an area of mathematics called algebraic topology
mathematics called algebraic topology
mathematics called algebraic topology that studies features of shapes
that studies features of shapes
that studies features of shapes basically topologies care about the
basically topologies care about the
basically topologies care about the number of holes in objects and they even
number of holes in objects and they even
number of holes in objects and they even get paid for it anyway back to hairy
get paid for it anyway back to hairy
get paid for it anyway back to hairy balls
balls
balls in fact the shape doesn’t really matter
in fact the shape doesn’t really matter
in fact the shape doesn’t really matter here as the theorem works for any hairy
here as the theorem works for any hairy
here as the theorem works for any hairy creature that can be deformed into a
creature that can be deformed into a
creature that can be deformed into a ball without touching tearing or other
ball without touching tearing or other
ball without touching tearing or other aggressive behaviour so imagine you want
aggressive behaviour so imagine you want
aggressive behaviour so imagine you want to come down a ball continuously covered
to come down a ball continuously covered
to come down a ball continuously covered with very fine hair
with very fine hair
with very fine hair calmed it down in a way that doesn’t
calmed it down in a way that doesn’t
calmed it down in a way that doesn’t create an attacks nothing is sticking
create an attacks nothing is sticking
create an attacks nothing is sticking out it’s all smooth and flat how can we
out it’s all smooth and flat how can we
out it’s all smooth and flat how can we do that we can’t the hairy ball theorem
do that we can’t the hairy ball theorem
do that we can’t the hairy ball theorem says it’s impossible and there’s one
says it’s impossible and there’s one
says it’s impossible and there’s one thing you should know about maps no
thing you should know about maps no
thing you should know about maps no means no so the tech tieran doesn’t tell
means no so the tech tieran doesn’t tell
means no so the tech tieran doesn’t tell us that we just haven’t found a good
us that we just haven’t found a good
us that we just haven’t found a good method of coming to her it says we’ll
method of coming to her it says we’ll
method of coming to her it says we’ll never find it it doesn’t exist
never find it it doesn’t exist
never find it it doesn’t exist now before you Stipe start blaming maps
now before you Stipe start blaming maps
now before you Stipe start blaming maps for tasks on your head
for tasks on your head
for tasks on your head think about the assumptions of the
think about the assumptions of the
think about the assumptions of the theorem are you continuously covered
theorem are you continuously covered
theorem are you continuously covered with her if you are then indeed maths is
with her if you are then indeed maths is
with her if you are then indeed maths is to blame for the bad hair day however
to blame for the bad hair day however
to blame for the bad hair day however most of us have hairy and less hairy
most of us have hairy and less hairy
most of us have hairy and less hairy parts of the body so the theorem doesn’t
parts of the body so the theorem doesn’t
parts of the body so the theorem doesn’t apply but is it completely useless and
apply but is it completely useless and
apply but is it completely useless and why on earth do mathematicians study
why on earth do mathematicians study
why on earth do mathematicians study hairy balls because of the earth in it
hairy balls because of the earth in it
hairy balls because of the earth in it it’s a ball isn’t it it’s not hairy but
it’s a ball isn’t it it’s not hairy but
it’s a ball isn’t it it’s not hairy but we have something similar here winds
we have something similar here winds
we have something similar here winds surprisingly they behave in a very
surprisingly they behave in a very
surprisingly they behave in a very similar way we treat wind speeds as
similar way we treat wind speeds as
similar way we treat wind speeds as vectors these little arrows that you
vectors these little arrows that you
vectors these little arrows that you might remember from school and in this
might remember from school and in this
might remember from school and in this case the theorem says that there there
case the theorem says that there there
case the theorem says that there there is a tuft which means there is one point
is a tuft which means there is one point
is a tuft which means there is one point on the earth at all times where the wind
on the earth at all times where the wind
on the earth at all times where the wind isn’t blowing where the wind speed is
isn’t blowing where the wind speed is
isn’t blowing where the wind speed is zero is this theorem useless do I have
zero is this theorem useless do I have
zero is this theorem useless do I have to persuade you how useful understanding
to persuade you how useful understanding
to persuade you how useful understanding wind behavior is for weather predictions
wind behavior is for weather predictions
wind behavior is for weather predictions right so thanks to the apology we are
right so thanks to the apology we are
right so thanks to the apology we are ready for a party a birthday party in
ready for a party a birthday party in
ready for a party a birthday party in fact and you know what I bet 10 quid
fact and you know what I bet 10 quid
fact and you know what I bet 10 quid then in this room we can find at least
then in this room we can find at least
then in this room we can find at least one pair of people celebrating birthday
one pair of people celebrating birthday
one pair of people celebrating birthday on the same day of the year but before
on the same day of the year but before
on the same day of the year but before you take this bet a little spoiler I
you take this bet a little spoiler I
you take this bet a little spoiler I will win with a probability of 90
will win with a probability of 90
will win with a probability of 90 nine point nine nine nine nine nine well
nine point nine nine nine nine nine well
nine point nine nine nine nine nine well you get the idea
you get the idea
you get the idea percent all right but we have 365 days
percent all right but we have 365 days
percent all right but we have 365 days of the year and it’s only 150 of us in
of the year and it’s only 150 of us in
of the year and it’s only 150 of us in the room today so why am I so confident
the room today so why am I so confident
the room today so why am I so confident I will win the bet let’s do the maths
I will win the bet let’s do the maths
I will win the bet let’s do the maths but before we do any calculations a few
but before we do any calculations a few
but before we do any calculations a few assumptions first all birthdays are
assumptions first all birthdays are
assumptions first all birthdays are independent so if we have twins in the
independent so if we have twins in the
independent so if we have twins in the room could you please leave now the same
room could you please leave now the same
room could you please leave now the same concerns people burn on the 29th of
concerns people burn on the 29th of
concerns people burn on the 29th of February
February
February no leap years and finally all dates are
no leap years and finally all dates are
no leap years and finally all dates are equally likely so there are no peaks in
equally likely so there are no peaks in
equally likely so there are no peaks in birthdays nine months after son
birthdays nine months after son
birthdays nine months after son Valentine’s Day or other events like
Valentine’s Day or other events like
Valentine’s Day or other events like that all right so you in the bed if
that all right so you in the bed if
that all right so you in the bed if there are no two people in the room
there are no two people in the room
there are no two people in the room celebrating birthday on the same day of
celebrating birthday on the same day of
celebrating birthday on the same day of the year what’s the probability of that
the year what’s the probability of that
the year what’s the probability of that now must alert
now must alert
now must alert we will see some fractions so if it
we will see some fractions so if it
we will see some fractions so if it might be too traumatizing focus on the
might be too traumatizing focus on the
might be too traumatizing focus on the hitter Alice and Bob our first guest to
hitter Alice and Bob our first guest to
hitter Alice and Bob our first guest to arrive to a party Alice was born on
arrive to a party Alice was born on
arrive to a party Alice was born on Sunday of the year so bob has unique
Sunday of the year so bob has unique
Sunday of the year so bob has unique birthday if he was born on any of the
birthday if he was born on any of the
birthday if he was born on any of the remaining 364 days so every next person
remaining 364 days so every next person
remaining 364 days so every next person coming into the room has one day less to
coming into the room has one day less to
coming into the room has one day less to pick from which means that the last
pick from which means that the last
pick from which means that the last French person the hundred-fifty person
French person the hundred-fifty person
French person the hundred-fifty person must have been born on any of the
must have been born on any of the
must have been born on any of the remaining 216 days so to get the
remaining 216 days so to get the
remaining 216 days so to get the probability of everyone having unique
probability of everyone having unique
probability of everyone having unique birthday so of you winning the bet we
birthday so of you winning the bet we
birthday so of you winning the bet we have to multiply all these fractions
have to multiply all these fractions
have to multiply all these fractions don’t worry I’ve done it for you so the
don’t worry I’ve done it for you so the
don’t worry I’ve done it for you so the probability of you winning the bet is
probability of you winning the bet is
probability of you winning the bet is pretty much zero percent well that was a
pretty much zero percent well that was a
pretty much zero percent well that was a bit too extreme so let’s ask another
bit too extreme so let’s ask another
bit too extreme so let’s ask another question what is the smallest number of
question what is the smallest number of
question what is the smallest number of people I would have together to make the
people I would have together to make the
people I would have together to make the odds in my favor so what’s the smaller
odds in my favor so what’s the smaller
odds in my favor so what’s the smaller group of people that will still make
group of people that will still make
group of people that will still make probability of you winning
probability of you winning
probability of you winning but smaller than 50% in fact in a group
but smaller than 50% in fact in a group
but smaller than 50% in fact in a group of only 23 people yes only a group of
of only 23 people yes only a group of
of only 23 people yes only a group of only 23 people the probability that
only 23 people the probability that
only 23 people the probability that someone is sharing birthday is slightly
someone is sharing birthday is slightly
someone is sharing birthday is slightly over 50% and in fact you can use this
over 50% and in fact you can use this
over 50% and in fact you can use this knowledge next time you watch a football
knowledge next time you watch a football
knowledge next time you watch a football game so you can bet your mates that on
game so you can bet your mates that on
game so you can bet your mates that on the pitch you will find a pair of
the pitch you will find a pair of
the pitch you will find a pair of birthday twins you aren’t guaranteed to
birthday twins you aren’t guaranteed to
birthday twins you aren’t guaranteed to win but maybe your chances are slightly
win but maybe your chances are slightly
win but maybe your chances are slightly higher than betting on the victory of
higher than betting on the victory of
higher than betting on the victory of your team you figured it’s – exactly 23
your team you figured it’s – exactly 23
your team you figured it’s – exactly 23 men men on the pitch two teams of eleven
men men on the pitch two teams of eleven
men men on the pitch two teams of eleven and one referee Thursday problem is just
and one referee Thursday problem is just
and one referee Thursday problem is just a fun fact but similar calculations are
a fun fact but similar calculations are
a fun fact but similar calculations are the basis of many science I insist using
the basis of many science I insist using
the basis of many science I insist using probability probability and statistics
probability probability and statistics
probability probability and statistics so pretty much every science you can
so pretty much every science you can
so pretty much every science you can think of for example I guess most of you
think of for example I guess most of you
think of for example I guess most of you check the weather forecast today before
check the weather forecast today before
check the weather forecast today before leaving your house and did your favorite
leaving your house and did your favorite
leaving your house and did your favorite app tell you if it’s going to rain in
app tell you if it’s going to rain in
app tell you if it’s going to rain in London today
London today
London today it shouldn’t have instead of a definite
it shouldn’t have instead of a definite
it shouldn’t have instead of a definite it will or it won’t rain you should have
it will or it won’t rain you should have
it will or it won’t rain you should have seen a probability of precipitation so
seen a probability of precipitation so
seen a probability of precipitation so how likely it is that any rain will fall
how likely it is that any rain will fall
how likely it is that any rain will fall in London today and to get this number
in London today and to get this number
in London today and to get this number we basically make do a more complicated
we basically make do a more complicated
we basically make do a more complicated version of the birthday problem
version of the birthday problem
version of the birthday problem probabilities are everywhere I don’t
probabilities are everywhere I don’t
probabilities are everywhere I don’t know about you but mass makes me hungry
know about you but mass makes me hungry
know about you but mass makes me hungry and it’s a maths party so was the
and it’s a maths party so was the
and it’s a maths party so was the classic party food pizza if you know how
classic party food pizza if you know how
classic party food pizza if you know how to eat pizza properly there are two
to eat pizza properly there are two
to eat pizza properly there are two possibilities you either excel in math
possibilities you either excel in math
possibilities you either excel in math or you’re Italian
or you’re Italian
or you’re Italian otherwise you’re way too familiar with
otherwise you’re way too familiar with
otherwise you’re way too familiar with this problem pizzas are delivered you’re
this problem pizzas are delivered you’re
this problem pizzas are delivered you’re ready to bite into your delicious slice
ready to bite into your delicious slice
ready to bite into your delicious slice and this happens again the slice flops
and this happens again the slice flops
and this happens again the slice flops over and all the toppings are on your
over and all the toppings are on your
over and all the toppings are on your favorite shirt is it because you’re
favorite shirt is it because you’re
favorite shirt is it because you’re sloppy
sloppy
sloppy no it’s because you haven’t paid enough
no it’s because you haven’t paid enough
no it’s because you haven’t paid enough attention to mathematics let’s go back
attention to mathematics let’s go back
attention to mathematics let’s go back to the 19th century to meet an ingenious
to the 19th century to meet an ingenious
to the 19th century to meet an ingenious mathematician mr. gauss one-half of his
mathematician mr. gauss one-half of his
mathematician mr. gauss one-half of his hobbies was studying curved surfaces and
hobbies was studying curved surfaces and
hobbies was studying curved surfaces and in fact we can quantify how much a
in fact we can quantify how much a
in fact we can quantify how much a surface is curved using a number called
surface is curved using a number called
surface is curved using a number called a curvature example a piece of paper
a curvature example a piece of paper
a curvature example a piece of paper it’s completely flat its curvature is
it’s completely flat its curvature is
it’s completely flat its curvature is zero but when we roll it into a cylinder
zero but when we roll it into a cylinder
zero but when we roll it into a cylinder see what happens if you were a tiny
see what happens if you were a tiny
see what happens if you were a tiny little creature you could trace a circle
little creature you could trace a circle
little creature you could trace a circle so a curved path or follow up a straight
so a curved path or follow up a straight
so a curved path or follow up a straight path or something in between like a
path or something in between like a
path or something in between like a helix and this made cows very very
helix and this made cows very very
helix and this made cows very very unhappy because one object shouldn’t
unhappy because one object shouldn’t
unhappy because one object shouldn’t have many different curvatures right so
have many different curvatures right so
have many different curvatures right so he defined a Gaussian curvature which
he defined a Gaussian curvature which
he defined a Gaussian curvature which intuitively is a product so a
intuitively is a product so a
intuitively is a product so a multiplication of the smallest and the
multiplication of the smallest and the
multiplication of the smallest and the biggest curvatures at a given point
biggest curvatures at a given point
biggest curvatures at a given point don’t panic
don’t panic
don’t panic details don’t matter here what matters
details don’t matter here what matters
details don’t matter here what matters is a remarkable theorem by Gauss
is a remarkable theorem by Gauss
is a remarkable theorem by Gauss literally remarkable as we translate the
literally remarkable as we translate the
literally remarkable as we translate the original Latin name terima aggregor
original Latin name terima aggregor
original Latin name terima aggregor this theorem tells us that gaussian
this theorem tells us that gaussian
this theorem tells us that gaussian curvature doesn’t change even if we bend
curvature doesn’t change even if we bend
curvature doesn’t change even if we bend the surface as long as we don’t shrink
the surface as long as we don’t shrink
the surface as long as we don’t shrink stretch or tear it why am I talking
stretch or tear it why am I talking
stretch or tear it why am I talking about geometry while your pizza is
about geometry while your pizza is
about geometry while your pizza is getting cold because the remarkable
getting cold because the remarkable
getting cold because the remarkable theorem is really remarkable it provides
theorem is really remarkable it provides
theorem is really remarkable it provides us with a pizza eating strategy so you
us with a pizza eating strategy so you
us with a pizza eating strategy so you have a slice lying flat on your plate so
have a slice lying flat on your plate so
have a slice lying flat on your plate so the curvatures in all directions are 0
the curvatures in all directions are 0
the curvatures in all directions are 0 again I want to define them precisely
again I want to define them precisely
again I want to define them precisely but come on what else could they be the
but come on what else could they be the
but come on what else could they be the pizza slice is completely flat now the
pizza slice is completely flat now the
pizza slice is completely flat now the trick is to bend the slice in half and
trick is to bend the slice in half and
trick is to bend the slice in half and see what happens
see what happens
see what happens so in one direction it
so in one direction it
so in one direction it it’s definitely curved its curvature in
it’s definitely curved its curvature in
it’s definitely curved its curvature in fact it’s negative but remember the
fact it’s negative but remember the
fact it’s negative but remember the Gaussian curvature stays the same stays
Gaussian curvature stays the same stays
Gaussian curvature stays the same stays zero so if you multiply the negative
zero so if you multiply the negative
zero so if you multiply the negative number by the curvature in the direction
number by the curvature in the direction
number by the curvature in the direction pointing towards your mouth we still
pointing towards your mouth we still
pointing towards your mouth we still need to get zero which means that in
need to get zero which means that in
need to get zero which means that in this direction the curvature will still
this direction the curvature will still
this direction the curvature will still be zero the pizza slice will stay flat
be zero the pizza slice will stay flat
be zero the pizza slice will stay flat it won’t flop over thank you guys for
it won’t flop over thank you guys for
it won’t flop over thank you guys for saving our shirts
saving our shirts
saving our shirts Tara McGregor has many applications some
Tara McGregor has many applications some
Tara McGregor has many applications some of them a bit more serious than eating
of them a bit more serious than eating
of them a bit more serious than eating pizza although what can be more serious
pizza although what can be more serious
pizza although what can be more serious than eating pizza when you think about
than eating pizza when you think about
than eating pizza when you think about it for example all maps are distorted in
it for example all maps are distorted in
it for example all maps are distorted in some way because we are trying to
some way because we are trying to
some way because we are trying to translate something from a globe with
translate something from a globe with
translate something from a globe with positive positive curvature on a flat
positive positive curvature on a flat
positive positive curvature on a flat map with curvature 0 and because of
map with curvature 0 and because of
map with curvature 0 and because of Gauss we know it’s impossible it’s like
Gauss we know it’s impossible it’s like
Gauss we know it’s impossible it’s like trying to get a peel of an orange and
trying to get a peel of an orange and
trying to get a peel of an orange and put it a flat on a plate without cutting
put it a flat on a plate without cutting
put it a flat on a plate without cutting it
it
it that’s why cartography is such a tricky
that’s why cartography is such a tricky
that’s why cartography is such a tricky field and why some of us think that
field and why some of us think that
field and why some of us think that Greenland is the same size as Africa
Greenland is the same size as Africa
Greenland is the same size as Africa even though it’s 14 times smaller it’s
even though it’s 14 times smaller it’s
even though it’s 14 times smaller it’s because we are used to the so-called
because we are used to the so-called
because we are used to the so-called Mercator projection that saves the
Mercator projection that saves the
Mercator projection that saves the shapes of land masses but deserts their
shapes of land masses but deserts their
shapes of land masses but deserts their sizes and again because of gals we know
sizes and again because of gals we know
sizes and again because of gals we know we can’t keep both be either party or
we can’t keep both be either party or
we can’t keep both be either party or earth sciences we can’t avoid mass it is
earth sciences we can’t avoid mass it is
earth sciences we can’t avoid mass it is literally everywhere no matter if we
literally everywhere no matter if we
literally everywhere no matter if we want it or not in everyday life we
want it or not in everyday life we
want it or not in everyday life we encounter its different areas in
encounter its different areas in
encounter its different areas in everything we do involves mathematics
everything we do involves mathematics
everything we do involves mathematics big theorems aren’t just for big
big theorems aren’t just for big
big theorems aren’t just for big scientists to solve big problems they
scientists to solve big problems they
scientists to solve big problems they can help you compare hair impress
can help you compare hair impress
can help you compare hair impress birthday guests or eat pizza properly
birthday guests or eat pizza properly
birthday guests or eat pizza properly but while you are getting rid of Tufts
but while you are getting rid of Tufts
but while you are getting rid of Tufts on your head we can study wind behavior
on your head we can study wind behavior
on your head we can study wind behavior while you
while you
while you taking bets on birthday party we
taking bets on birthday party we
taking bets on birthday party we calculate the probability of
calculate the probability of
calculate the probability of precipitation while you’re enjoying your
precipitation while you’re enjoying your
precipitation while you’re enjoying your pizza cartographers are figuring out new
pizza cartographers are figuring out new
pizza cartographers are figuring out new ways of making more adequate maps maps
ways of making more adequate maps maps
ways of making more adequate maps maps helps us solve problems global like
helps us solve problems global like
helps us solve problems global like climate change or epidemics but are also
climate change or epidemics but are also
climate change or epidemics but are also very personal ones such as how to cut a
very personal ones such as how to cut a
very personal ones such as how to cut a cake properly or how many people should
cake properly or how many people should
cake properly or how many people should you date before you get married but
you date before you get married but
you date before you get married but maybe even more importantly maths is fun
maybe even more importantly maths is fun
maybe even more importantly maths is fun thank you
thank you
thank you [Applause]
[Applause]
[Applause] [Music]
[Music]
[Music] [Applause]
”
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