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