so I’ve got this drawer full of socks that I just happened to carry around
that I just happened to carry around
that I just happened to carry around with me and so you never know when
with me and so you never know when
with me and so you never know when you’re gonna need some socks right so
you’re gonna need some socks right so
you’re gonna need some socks right so imagine this I need a pair of socks and
imagine this I need a pair of socks and
imagine this I need a pair of socks and I need them to match but I’m not going
I need them to match but I’m not going
I need them to match but I’m not going to let myself look in the drawer so
to let myself look in the drawer so
to let myself look in the drawer so think for yourself how many pulls will
think for yourself how many pulls will
think for yourself how many pulls will it be before I’m guaranteed to get a
it be before I’m guaranteed to get a
it be before I’m guaranteed to get a pair okay so the first one’s black and
pair okay so the first one’s black and
pair okay so the first one’s black and the second one happens to be white this
the second one happens to be white this
the second one happens to be white this time I’m sure enough I did not get a
time I’m sure enough I did not get a
time I’m sure enough I did not get a pair but on my third pull I have a black
pair but on my third pull I have a black
pair but on my third pull I have a black one so what sort of thinking is this
one so what sort of thinking is this
one so what sort of thinking is this well picture for yourself an empty box
well picture for yourself an empty box
well picture for yourself an empty box the first box it’s kind of like a
the first box it’s kind of like a
the first box it’s kind of like a pigeonhole or an empty space so into the
pigeonhole or an empty space so into the
pigeonhole or an empty space so into the first box you must put white or black
first box you must put white or black
first box you must put white or black and in the second box you must put white
and in the second box you must put white
and in the second box you must put white or black so in the third box you are
or black so in the third box you are
or black so in the third box you are guaranteed to have a pair
guaranteed to have a pair
guaranteed to have a pair so that’s mathematical thinking and
so that’s mathematical thinking and
so that’s mathematical thinking and indeed that problem comes to us from
indeed that problem comes to us from
indeed that problem comes to us from from Martin Gardner who wrote thousands
from Martin Gardner who wrote thousands
from Martin Gardner who wrote thousands of those for Scientific American and in
of those for Scientific American and in
of those for Scientific American and in his books and so he believed that all of
his books and so he believed that all of
his books and so he believed that all of us should have the pleasure of playing
us should have the pleasure of playing
us should have the pleasure of playing with big and powerful mathematical ideas
with big and powerful mathematical ideas
with big and powerful mathematical ideas and I believe that too and that’s what
and I believe that too and that’s what
and I believe that too and that’s what I’m here to talk about so I just
I’m here to talk about so I just
I’m here to talk about so I just happened to also be carrying around
happened to also be carrying around
happened to also be carrying around jumbo oversized novelty dice and
jumbo oversized novelty dice and
jumbo oversized novelty dice and actually I also have green ones but
actually I also have green ones but
actually I also have green ones but today I have these black ones and you
today I have these black ones and you
today I have these black ones and you know if you’ve ever played any board
know if you’ve ever played any board
know if you’ve ever played any board games for any length of time you
games for any length of time you
games for any length of time you probably have a certain intuition that
probably have a certain intuition that
probably have a certain intuition that at seven that is a total of seven comes
at seven that is a total of seven comes
at seven that is a total of seven comes up a lot and that’s kind of like the
up a lot and that’s kind of like the
up a lot and that’s kind of like the easy outcome for a lot of different
easy outcome for a lot of different
easy outcome for a lot of different games and you might have the sense also
games and you might have the sense also
games and you might have the sense also that two and twelve don’t tend to come
that two and twelve don’t tend to come
that two and twelve don’t tend to come up a lot I’ll say this seven doesn’t get
up a lot I’ll say this seven doesn’t get
up a lot I’ll say this seven doesn’t get you out of jail in monopoly okay this
you out of jail in monopoly okay this
you out of jail in monopoly okay this time
time
time [Music]
[Music]
[Music] and it comes up eight so I didn’t get
and it comes up eight so I didn’t get
and it comes up eight so I didn’t get seven but imagine for yourself a bar
seven but imagine for yourself a bar
seven but imagine for yourself a bar graph with all the possible outcomes so
graph with all the possible outcomes so
graph with all the possible outcomes so – all the way up to seven which indeed
– all the way up to seven which indeed
– all the way up to seven which indeed incurs the most occurs the most all the
incurs the most occurs the most all the
incurs the most occurs the most all the way back down to twelve it’s very
way back down to twelve it’s very
way back down to twelve it’s very symmetrical so they’re most possible
symmetrical so they’re most possible
symmetrical so they’re most possible outcomes that can make seven and so I
outcomes that can make seven and so I
outcomes that can make seven and so I think that’s something really
think that’s something really
think that’s something really interesting to talk about and it
interesting to talk about and it
interesting to talk about and it involves mathematical thinking and it’s
involves mathematical thinking and it’s
involves mathematical thinking and it’s in our play so what do I believe for
in our play so what do I believe for
in our play so what do I believe for kids I think that kids and adults should
kids I think that kids and adults should
kids I think that kids and adults should have should all feel the power and
have should all feel the power and
have should all feel the power and pleasure of playing with their
pleasure of playing with their
pleasure of playing with their mathematics I mean think about it
mathematics I mean think about it
mathematics I mean think about it math should be a thinking tool and not
math should be a thinking tool and not
math should be a thinking tool and not just a subject in school and it should
just a subject in school and it should
just a subject in school and it should give us pleasure
give us pleasure
give us pleasure so we’re humans we’re thinking beings
so we’re humans we’re thinking beings
so we’re humans we’re thinking beings were born to think and we’re born to
were born to think and we’re born to
were born to think and we’re born to play so I want a pedagogy of mathematics
play so I want a pedagogy of mathematics
play so I want a pedagogy of mathematics where kids say this is surprising and
where kids say this is surprising and
where kids say this is surprising and it’s wonderful and it fills me with joy
it’s wonderful and it fills me with joy
it’s wonderful and it fills me with joy and it’s awe-inspiring so the exact
and it’s awe-inspiring so the exact
and it’s awe-inspiring so the exact opposite of which some of you may have
opposite of which some of you may have
opposite of which some of you may have experienced hopefully not too many and
experienced hopefully not too many and
experienced hopefully not too many and it leaves me this with this sense of
it leaves me this with this sense of
it leaves me this with this sense of wonder at just how just how amazing it
wonder at just how just how amazing it
wonder at just how just how amazing it actually is that’s what I want for all
actually is that’s what I want for all
actually is that’s what I want for all of us and then so what do kids say if
of us and then so what do kids say if
of us and then so what do kids say if you have any kids you might want to ask
you have any kids you might want to ask
you have any kids you might want to ask them this question later and kids say
them this question later and kids say
them this question later and kids say interesting things when you do ask them
interesting things when you do ask them
interesting things when you do ask them Melissa Penner and students in Brampton
Melissa Penner and students in Brampton
Melissa Penner and students in Brampton in grade three said this they said all
in grade three said this they said all
in grade three said this they said all of these things so sure enough they said
of these things so sure enough they said
of these things so sure enough they said math as fractions and time and and math
math as fractions and time and and math
math as fractions and time and and math is cookies because for grade three
is cookies because for grade three
is cookies because for grade three there’s there’s a lot of cookie math and
there’s there’s a lot of cookie math and
there’s there’s a lot of cookie math and a lot of problems about cookies right so
a lot of problems about cookies right so
a lot of problems about cookies right so time money fractions is also important
time money fractions is also important
time money fractions is also important but you’ll notice most of all that they
but you’ll notice most of all that they
but you’ll notice most of all that they said that math is fun and we want that
said that math is fun and we want that
said that math is fun and we want that for all kids you know and then think for
for all kids you know and then think for
for all kids you know and then think for yourself what is mathematics really
yourself what is mathematics really
yourself what is mathematics really because you make just have experienced
because you make just have experienced
because you make just have experienced it in school
it in school
it in school so you we might come to definitions like
so you we might come to definitions like
so you we might come to definitions like it’s the science of patterns and that
it’s the science of patterns and that
it’s the science of patterns and that works depending on the type of
works depending on the type of
works depending on the type of mathematician you are the science of
mathematician you are the science of
mathematician you are the science of shapes base quantity and arrangements
shapes base quantity and arrangements
shapes base quantity and arrangements that works depending what kind of
that works depending what kind of
that works depending what kind of mathematician you are but we want to
mathematician you are but we want to
mathematician you are but we want to know what what
know what what
know what what kids say so kids are born to wonder and
kids say so kids are born to wonder and
kids say so kids are born to wonder and and this is our human birthright because
and this is our human birthright because
and this is our human birthright because we’re thinking beings and we’re just
we’re thinking beings and we’re just
we’re thinking beings and we’re just born into this unending stream of
born into this unending stream of
born into this unending stream of consciousness from birth till death
consciousness from birth till death
consciousness from birth till death that’s what I say and these two who
that’s what I say and these two who
that’s what I say and these two who happen to be my sons are always
happen to be my sons are always
happen to be my sons are always wondering so their their life is a
wondering so their their life is a
wondering so their their life is a constant state of wonderment from birth
constant state of wonderment from birth
constant state of wonderment from birth on and why should that’s ever stopped at
on and why should that’s ever stopped at
on and why should that’s ever stopped at the door of math class which has some of
the door of math class which has some of
the door of math class which has some of the most big massive world-changing and
the most big massive world-changing and
the most big massive world-changing and surprising ideas so thinking about this
surprising ideas so thinking about this
surprising ideas so thinking about this arrangement of deck of a deck of cards
arrangement of deck of a deck of cards
arrangement of deck of a deck of cards so this deck happens to be brand new so
so this deck happens to be brand new so
so this deck happens to be brand new so it’s perfectly ordered so and it’ll
it’s perfectly ordered so and it’ll
it’s perfectly ordered so and it’ll never be more perfectly ordered so the
never be more perfectly ordered so the
never be more perfectly ordered so the ace of spades is actually on the bottom
ace of spades is actually on the bottom
ace of spades is actually on the bottom and so every time I shuffle it and deal
and so every time I shuffle it and deal
and so every time I shuffle it and deal it out from here it’s going to be in a
it out from here it’s going to be in a
it out from here it’s going to be in a different arrangement so let’s think
different arrangement so let’s think
different arrangement so let’s think about that they didn’t fly as far as I
about that they didn’t fly as far as I
about that they didn’t fly as far as I wanted so some of them are still in
wanted so some of them are still in
wanted so some of them are still in order but if you were to perfectly
order but if you were to perfectly
order but if you were to perfectly shuffle them like with a shuffling
shuffle them like with a shuffling
shuffle them like with a shuffling machine and deal them out again there’s
machine and deal them out again there’s
machine and deal them out again there’s a decent chance that that arrangement
a decent chance that that arrangement
a decent chance that that arrangement has never happened on this planet can
has never happened on this planet can
has never happened on this planet can all the recreational poker games all the
all the recreational poker games all the
all the recreational poker games all the games of Go Fish and so on so picture
games of Go Fish and so on so picture
games of Go Fish and so on so picture for yourself the same visualization tool
for yourself the same visualization tool
for yourself the same visualization tool just make it an empty box this time and
just make it an empty box this time and
just make it an empty box this time and so we could place any one of 52 cards in
so we could place any one of 52 cards in
so we could place any one of 52 cards in that empty box
that empty box
that empty box that leaves 51 to go and 50 and so on
that leaves 51 to go and 50 and so on
that leaves 51 to go and 50 and so on all the way down to the last card well
all the way down to the last card well
all the way down to the last card well because the counting principle has us
because the counting principle has us
because the counting principle has us multiply we can multiply 52 times 51 and
multiply we can multiply 52 times 51 and
multiply we can multiply 52 times 51 and times 50 and so on and all of a sudden
times 50 and so on and all of a sudden
times 50 and so on and all of a sudden there’s more possible arrangements of
there’s more possible arrangements of
there’s more possible arrangements of that deck than there are atoms in the in
that deck than there are atoms in the in
that deck than there are atoms in the in the universe and that’s absolutely
the universe and that’s absolutely
the universe and that’s absolutely astounding you could not duplicate that
astounding you could not duplicate that
astounding you could not duplicate that flip of a deck of cards if you tried and
flip of a deck of cards if you tried and
flip of a deck of cards if you tried and I think that’s an idea worth playing
I think that’s an idea worth playing
I think that’s an idea worth playing with and speaking of really really large
with and speaking of really really large
with and speaking of really really large numbers have you ever asked a kid what’s
numbers have you ever asked a kid what’s
numbers have you ever asked a kid what’s the biggest number you know and so when
the biggest number you know and so when
the biggest number you know and so when they’re little they might just say five
they’re little they might just say five
they’re little they might just say five okay because they’ve learned one too
okay because they’ve learned one too
okay because they’ve learned one too many one two and many so they might know
many one two and many so they might know
many one two and many so they might know five cookies or five blocks later we’ll
five cookies or five blocks later we’ll
five cookies or five blocks later we’ll say a hundred and then they’ll get this
say a hundred and then they’ll get this
say a hundred and then they’ll get this of a million and then there’ll always be
of a million and then there’ll always be
of a million and then there’ll always be some kid who’s just heard of infinity
some kid who’s just heard of infinity
some kid who’s just heard of infinity because it’s out there and I’ll say
because it’s out there and I’ll say
because it’s out there and I’ll say infinity and then some kid will say oh
infinity and then some kid will say oh
infinity and then some kid will say oh yeah the biggest number I know is
yeah the biggest number I know is
yeah the biggest number I know is infinity and one this is the sort of
infinity and one this is the sort of
infinity and one this is the sort of thing the kids love to talk about they
thing the kids love to talk about they
thing the kids love to talk about they just love it and so we are accounting
just love it and so we are accounting
just love it and so we are accounting beings and this is my son counting I
said we’re counting beings because kids
said we’re counting beings because kids love to count they love to count and
love to count they love to count and
love to count they love to count and they know it but it’s this concept of
they know it but it’s this concept of
they know it but it’s this concept of infinity that disrupts our idea of what
infinity that disrupts our idea of what
infinity that disrupts our idea of what counting actually is right so what’s in
counting actually is right so what’s in
counting actually is right so what’s in a set so what is infinity dr. Eugenia
a set so what is infinity dr. Eugenia
a set so what is infinity dr. Eugenia Chiang and her great book beyond
Chiang and her great book beyond
Chiang and her great book beyond infinity says infinity goes on forever
infinity says infinity goes on forever
infinity says infinity goes on forever infinity is bigger than any number
infinity is bigger than any number
infinity is bigger than any number infinity is bigger than anything we can
infinity is bigger than anything we can
infinity is bigger than anything we can think of and if you add one to it it’s
think of and if you add one to it it’s
think of and if you add one to it it’s still infinity so all of a sudden our
still infinity so all of a sudden our
still infinity so all of a sudden our sense of one two three and so on it’s
sense of one two three and so on it’s
sense of one two three and so on it’s completely broken and indeed arithmetic
completely broken and indeed arithmetic
completely broken and indeed arithmetic breaks when we work with infinity but
breaks when we work with infinity but
breaks when we work with infinity but kids want to know about this sort of
kids want to know about this sort of
kids want to know about this sort of thing and it belongs in classrooms so
thing and it belongs in classrooms so
thing and it belongs in classrooms so Jennifer Santos who also is grade sevens
Jennifer Santos who also is grade sevens
Jennifer Santos who also is grade sevens said infinity is indescribable
said infinity is indescribable
said infinity is indescribable it’s just the idea of a number and so
it’s just the idea of a number and so
it’s just the idea of a number and so therefore they figured this out okay
therefore they figured this out okay
therefore they figured this out okay that you subtract one it’s still going
that you subtract one it’s still going
that you subtract one it’s still going to be infinity and in my experience kids
to be infinity and in my experience kids
to be infinity and in my experience kids want to know about these sorts of things
want to know about these sorts of things
want to know about these sorts of things and so I wanted no limits mathematics
and so I wanted no limits mathematics
and so I wanted no limits mathematics for kids so if we think about it if we
for kids so if we think about it if we
for kids so if we think about it if we define our imagination as having no
define our imagination as having no
define our imagination as having no limits then probably it is limitless
limits then probably it is limitless
limits then probably it is limitless what we can do with mathematics and
what we can do with mathematics and
what we can do with mathematics and indeed the mathematical world it’s I’ve
indeed the mathematical world it’s I’ve
indeed the mathematical world it’s I’ve just read so much about recently there
just read so much about recently there
just read so much about recently there are so many more things interesting
are so many more things interesting
are so many more things interesting things than they ever taught us in
things than they ever taught us in
things than they ever taught us in school I want that for kids and so after
school I want that for kids and so after
school I want that for kids and so after 15 years of teaching mathematics I’m
15 years of teaching mathematics I’m
15 years of teaching mathematics I’m just thinking about what are my actual
just thinking about what are my actual
just thinking about what are my actual pedagogical principles and I think first
pedagogical principles and I think first
pedagogical principles and I think first of all we’ve got to know the curriculum
of all we’ve got to know the curriculum
of all we’ve got to know the curriculum even more importantly know the big ideas
even more importantly know the big ideas
even more importantly know the big ideas of the math
of the math
of the math second of all just give kids interesting
second of all just give kids interesting
second of all just give kids interesting tasks and let them play give kids
tasks and let them play give kids
tasks and let them play give kids interesting mathematics to play with let
interesting mathematics to play with let
interesting mathematics to play with let them play let them talk and think and
them play let them talk and think and
them play let them talk and think and conjecture and wonder let them play
conjecture and wonder let them play
conjecture and wonder let them play and so dr. Cathy Bruce defines a
and so dr. Cathy Bruce defines a
and so dr. Cathy Bruce defines a pedagogy of playful mathematics as a
pedagogy of playful mathematics as a
pedagogy of playful mathematics as a kind of guided play with teachers
kind of guided play with teachers
kind of guided play with teachers guiding children through the big and
guiding children through the big and
guiding children through the big and powerful ideas of mathematics and I
powerful ideas of mathematics and I
powerful ideas of mathematics and I think we can have that in our classrooms
think we can have that in our classrooms
think we can have that in our classrooms so for me a pedagogy of playful
so for me a pedagogy of playful
so for me a pedagogy of playful mathematics is all about kids talking
mathematics is all about kids talking
mathematics is all about kids talking about interesting things it is kids
about interesting things it is kids
about interesting things it is kids talking about talking to each other and
talking about talking to each other and
talking about talking to each other and making conjectures about things like
making conjectures about things like
making conjectures about things like infinity it is kids playing with numbers
infinity it is kids playing with numbers
infinity it is kids playing with numbers it is kids using mathematical thinking
it is kids using mathematical thinking
it is kids using mathematical thinking to break things down to their their
to break things down to their their
to break things down to their their basic level so dr. Frances sue says and
basic level so dr. Frances sue says and
basic level so dr. Frances sue says and is absolutely astounding talk called
is absolutely astounding talk called
is absolutely astounding talk called mathematics for human flourishing which
mathematics for human flourishing which
mathematics for human flourishing which he gave is outgoing president of the
he gave is outgoing president of the
he gave is outgoing president of the mathematical Association of America well
mathematical Association of America well
mathematical Association of America well he says he situates play as one of five
he says he situates play as one of five
he says he situates play as one of five basic human needs and he says that play
basic human needs and he says that play
basic human needs and he says that play gives hope play builds hope and so if we
gives hope play builds hope and so if we
gives hope play builds hope and so if we define mathematics as a playful endeavor
define mathematics as a playful endeavor
define mathematics as a playful endeavor if we say mathematics is play then it
if we say mathematics is play then it
if we say mathematics is play then it should follow that math gives hope as
should follow that math gives hope as
should follow that math gives hope as well and indeed this talk was about an
well and indeed this talk was about an
well and indeed this talk was about an inmate who used mathematics to better
inmate who used mathematics to better
inmate who used mathematics to better himself so literally was able to build
himself so literally was able to build
himself so literally was able to build mathematical worlds for himself to
mathematical worlds for himself to
mathematical worlds for himself to escape confinement all the bars and
escape confinement all the bars and
escape confinement all the bars and barbed wire and later to make a career
barbed wire and later to make a career
barbed wire and later to make a career when he was no longer incarcerated but
when he was no longer incarcerated but
when he was no longer incarcerated but kids know all about play ok it’s us who
kids know all about play ok it’s us who
kids know all about play ok it’s us who forgotten or maybe some of us have so we
forgotten or maybe some of us have so we
forgotten or maybe some of us have so we go to work and there’s going to be 4200
go to work and there’s going to be 4200
go to work and there’s going to be 4200 emails
emails
emails 22 of them have that exclamation point
22 of them have that exclamation point
22 of them have that exclamation point beside that means you must read me now
beside that means you must read me now
beside that means you must read me now there’s three meetings happening your
there’s three meetings happening your
there’s three meetings happening your boss wants something you need to get
boss wants something you need to get
boss wants something you need to get your car into the shop for its oil
your car into the shop for its oil
your car into the shop for its oil change and their swimming lessons and so
change and their swimming lessons and so
change and their swimming lessons and so on
on
on but kids know so try interrupting them
but kids know so try interrupting them
but kids know so try interrupting them when they’re then when they’re in this
when they’re then when they’re in this
when they’re then when they’re in this deep state of play if they’re like my
deep state of play if they’re like my
deep state of play if they’re like my children they forget to eat even can go
children they forget to eat even can go
children they forget to eat even can go to the bathroom sometimes which is a
to the bathroom sometimes which is a
to the bathroom sometimes which is a problem but this could be making
problem but this could be making
problem but this could be making something with Lego making something
something with Lego making something
something with Lego making something with Lego or playing with stuffed
with Lego or playing with stuffed
with Lego or playing with stuffed animals or creating a world with action
animals or creating a world with action
animals or creating a world with action figures or just playing in that bush
figures or just playing in that bush
figures or just playing in that bush that’s beside your house they don’t want
that’s beside your house they don’t want
that’s beside your house they don’t want to stop so they’re in this deep state of
to stop so they’re in this deep state of
to stop so they’re in this deep state of flow what the Hungarian psychologist
flow what the Hungarian psychologist
flow what the Hungarian psychologist Sushma Haile calls flow where you’re
Sushma Haile calls flow where you’re
Sushma Haile calls flow where you’re beyond time time seems to disappear and
beyond time time seems to disappear and
beyond time time seems to disappear and you’re just doing it and you’re deriving
you’re just doing it and you’re deriving
you’re just doing it and you’re deriving so much pleasure from it everything
so much pleasure from it everything
so much pleasure from it everything disappears the worlds out the world
disappears the worlds out the world
disappears the worlds out the world outside and think about for us when do
outside and think about for us when do
outside and think about for us when do we get into that state of flow and so
we get into that state of flow and so
we get into that state of flow and so what I’m feeling right now is that we do
what I’m feeling right now is that we do
what I’m feeling right now is that we do need to just play for the parents out
need to just play for the parents out
need to just play for the parents out there we need to play board games dice
there we need to play board games dice
there we need to play board games dice games with our kids card games we can do
games with our kids card games we can do
games with our kids card games we can do all the spatial things like Lego and
all the spatial things like Lego and
all the spatial things like Lego and blocks find the math in the world around
blocks find the math in the world around
blocks find the math in the world around us when we’re shopping it’s there for us
us when we’re shopping it’s there for us
us when we’re shopping it’s there for us to find play with it and for the adults
to find play with it and for the adults
to find play with it and for the adults who maybe don’t have kids there’s so
who maybe don’t have kids there’s so
who maybe don’t have kids there’s so much out there now let’s find a book by
much out there now let’s find a book by
much out there now let’s find a book by olives Alex bellos for example who
olives Alex bellos for example who
olives Alex bellos for example who writes for The Guardian or a book by
writes for The Guardian or a book by
writes for The Guardian or a book by Martin Gardner and let’s find some
Martin Gardner and let’s find some
Martin Gardner and let’s find some interesting math to play with and let’s
interesting math to play with and let’s
interesting math to play with and let’s teach herself to think mathematically
teach herself to think mathematically
teach herself to think mathematically remember I said mathematics is a
remember I said mathematics is a
remember I said mathematics is a thinking tool not just something that
thinking tool not just something that
thinking tool not just something that you learn in school and we should all
you learn in school and we should all
you learn in school and we should all play with the big and powerful ideas of
play with the big and powerful ideas of
play with the big and powerful ideas of mathematics and I’m actually going to
mathematics and I’m actually going to
mathematics and I’m actually going to leave you with this the penny toss is
leave you with this the penny toss is
leave you with this the penny toss is guaranteed not to fail like the card
guaranteed not to fail like the card
guaranteed not to fail like the card toss did that may have made some point
toss did that may have made some point
toss did that may have made some point about probability but it wasn’t the
about probability but it wasn’t the
about probability but it wasn’t the point I wanted to make but so I’m now if
point I wanted to make but so I’m now if
point I wanted to make but so I’m now if I can I’ve just notated heads with an H
I can I’ve just notated heads with an H
I can I’ve just notated heads with an H and if I toss this and if I land in a
and if I toss this and if I land in a
and if I toss this and if I land in a configuration where I’m able to gather
configuration where I’m able to gather
configuration where I’m able to gather up 20 heads but I’m prepared to pay
up 20 heads but I’m prepared to pay
up 20 heads but I’m prepared to pay $1,000,000 to everyone in this audience
okay that’s the heads it’s the maple
okay that’s the heads it’s the maple leaf and you know what I’m not even
leaf and you know what I’m not even
leaf and you know what I’m not even gonna say I got lucky cuz I knew I
gonna say I got lucky cuz I knew I
gonna say I got lucky cuz I knew I wasn’t paying off on that bed and you
wasn’t paying off on that bed and you
wasn’t paying off on that bed and you could think about how I knew that
could think about how I knew that
could think about how I knew that so in summary let us play with the big
so in summary let us play with the big
so in summary let us play with the big and powerful ideas of mathematics thank
and powerful ideas of mathematics thank
and powerful ideas of mathematics thank you very much
you very much
you very much [Applause]
”
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