[Music]
[Applause]
you know it’s not longer since I
finished high school I have many great
memories socializing competing
publishing and presenting at
international conferences but all of
which happened outside the classroom I’m
sure you all have great memories of your
high school some of us might even
remember our teachers reflecting back I
realize that teachers in Queensland
needed to teach a certain curriculum in
a certain way there wasn’t much room for
manoeuvre which in a way made everybody
the same so I guess it is fair to say
that your typical classroom environment
will consist of desks whiteboards a
pre-programmed teacher and a group of
students robotically copying down
word-for-word everything the teacher was
narrating there’s only one way to put an
end to this automated learning
environment and that was someone to ask
but that all was necessary for the exam
and that was the key to high school
knowing what you didn’t need to know I
spent most of my high school learning
about things I didn’t need to know for
me maths is a journey and the most
interesting journeys are the ones in
which you explore and gain experience so
I believe math should be taught as a
journey not a set of equations to be
applied to something as if maths is a
set of dusty tools in the shed of
science for me my maths journey Sawa is
really young
I’ve always loved numbers and my parents
realized that early on when I started
doing Negra number addition at 3 years
old
I also loved squaring numbers and at one
stage I could do five digit
multiplication
my head actually had a book where I’d
write down little tricks and formula
used to solve such equations quicker
part of the writing I was only 5 years
old so yes I love maths and my very
school’s public in competitions at age
of 13 I was spotted by the national
director of the Australian mathematical
trust who put me in training for the
Australian limpia team and it was there
that I discover that actually wasn’t
that a good at geometry I was and still
am bad at drawing and this made me
scared of the subject how could I
possibly prove that three points line a
line when my lines look like circles so
I worked on geometry problems to
maximize my chances of winning and it
was there that discovered the unexpected
beauty in geometry not in the drawing
part of course but in the way certain
mathematically challenging concepts
could be explained simply through
visualization what is the infinite sum
of 1/2 plus 1/4 plus 1/8 plus 1/16 etc
well to some of you this met this some
may seem daunting if you look at this
animation where each time we’re adding
half the previous rectangle it does make
sense that these rectangles will
eventually add up to a square that has
area 1 but if I now ask you where the
parallel lines do meet well parent lines
are defined not to meet if you look at
it in a certain angle it does appear
that these lines will eventually meet at
a point at infinity and it turns out
this point is used extensively in
mathematics nowadays I was learning all
this outside the classroom
luckily nowadays you have the internet
where we can learn things in our own
time in fact I didn’t need school
classes at all because participating in
mathematical forums was like a class of
its own I was so involved in online
communities that I actually start
Blagh were post solutions to problems
that I found beautiful especially ones
people can solve and it was there that I
met zooming Liang who lives in America
at the time we were both 16 and loved
geometry is and solving mathematical
problems in general coincidentally
zooming in our boat stuck on the same
open problem and it took us five days to
solve this problem a cycle where I
worked through the night and zooming
we’ll continue our left off swimming
would do the same
repeat the time zone difference actually
worked quite well
we had eyes on the prom for 120 hours
straight now reflect on your high school
experience we had to solve 30 problems
in one and a half hours is it really
testing our ability to think creatively
unlike in high school where you could
submit your solutions to be marked
assuming and I weren’t even done we
stumbled upon a new theorem in
mathematics extending the one we had
just solved what a theorem stated was
that a point in the Triangle plane lies
an isomorphic equivalent to I superior
cubics in its petal triangles but here’s
a diagram for the theorem it’s bit
simplified unfortunately we too had no
idea how to prove this problem and it
took us six months to finally figure out
a way just to start the proof and
another week to solve it let alone nine
months for it to be published who could
have thought by the end of it that our
diagram would look like this what a
theorem did was that it made the complex
field of I so people cubics easier to
deal with and allows difficult
geometrical problems to be solved by
people with only high school level
understanding of geometry it avoids
pages of calculation – more elegant and
quicker approaches in fact
when I tried to solve the equations of
our theorem my computer timed out so
clearly maths isn’t just a set of
equations but more like a crime thriller
where the build build up to the ending
is far more important than the ending
itself something I had to create new
theory in the field of AI spooler cubics
in order to solve our new theorem and it
turned out that these subsidiary results
end up being the most important and
widely applicable part of our article
for mass loss theorem is a perfect
example of this back in the 1700s one
was formulated people had no idea how to
prove the simple looking problem but
fast forward to the 20th century with
whole new fields of analytical number
theory and an algebraic number theory
had to be invented in order to solve the
problem it was finally resolved Andrew
Wiles but in contribution were hundreds
of mathematicians worldwide so just
imagine learning the result a to the X
plus PDV x equals c DX what are you
actually learning the whole concept of
thinking of mathematics of the journey
follows from the idea that the ability
to think creatively is far more
important than the ability to know and
to apply in 2015 alphago was placed in
competition with lee solo in the game go
while the computer did win four out of
five times is where the computer lost
which begs the question how could a
computer that could compute a surplus of
a hundred moves ahead lose to a mere
human and it was there that I realized
that we have an edge over computers to
visualize geometrically to think
abstractly and out of the box and to use
these qualities to create innovation
what this means is our human imagination
and creativity cannot be replicated by a
computer
so the question is are we as the younger
generation being given the best
opportunities to use our talents in
qualities in the best possible way and
currently I don’t believe our education
system understands the importance of
creativity in schools we’re taught to
set a follow of rules procedures we’re
taught to accept rather than question to
test rather than experiment what is the
point of 12 years of teaching if a
simple computer program could do the
exact same thing billions of times
faster but being told that wrong is bad
and in the process we’re losing the
fundamental property that makes us human
creativity just imagine the world with
complex numbers didn’t exist and now
imagine a poor inquisitive child asking
his teacher why aren’t there solutions
to x squared equals negative 1 we have
solutions for x squared equals 1 1 4 2 9
3 but why not negative numbers and just
imagine a response such as just accept
that there isn’t or even worse being
ridiculed for claiming such numbers
should exist then the whole field of
complex analysis and it’s ubiquitous
applications in engineering wouldn’t
have been invented we won’t be able to
fly planes or even watch movies in our
cinemas so comfortably today so just
imagine what kinds of innovations you
might be losing nowadays to encourage
creativity I believe we need to
introduce real mathematics from an
earlier age that is true we need to
understand the concept of logical
thinking and proof writing earlier for
example instead of homework being to
repeatedly apply the same technique for
50 differently worded problems why can’t
it be think of this theorem or problem
and how would you prove it and then in
the next class discuss strategies or
what the students thought and show them
how the proof would work out and instead
of losing half of the students during
class I believe we need to incorporate
methods of active learning where
students will read content in advance
and the teacher would go over what they
do not understand lastly I believe we
need to make it clear that being wrong
is okay because in my experience I’ve
learnt the most out of being wrong and
knowing where I’ve gone wrong
coincidentally has given me a better
understanding of mathematics as a whole
similar ideas – I’ll just be mentioning
have been employed in Finland and look
what that’s got them that the best
education system in the world they
understand that our human imagination
and creativity should be praised is more
important to visualize them to know and
to follow a procedure just like you
cannot appreciate a story by reading its
ending you cannot appreciate maths
physics art or any subject by set of
rules and ways to apply them we need to
teach these subjects what they are a
journey
[Applause]
[Music]
[Applause]
you know it’s not longer since I
finished high school I have many great
memories socializing competing
publishing and presenting at
international conferences but all of
which happened outside the classroom I’m
sure you all have great memories of your
high school some of us might even
remember our teachers reflecting back I
realize that teachers in Queensland
needed to teach a certain curriculum in
a certain way there wasn’t much room for
manoeuvre which in a way made everybody
the same so I guess it is fair to say
that your typical classroom environment
will consist of desks whiteboards a
pre-programmed teacher and a group of
students robotically copying down
word-for-word everything the teacher was
narrating there’s only one way to put an
end to this automated learning
environment and that was someone to ask
but that all was necessary for the exam
and that was the key to high school
knowing what you didn’t need to know I
spent most of my high school learning
about things I didn’t need to know for
me maths is a journey and the most
interesting journeys are the ones in
which you explore and gain experience so
I believe math should be taught as a
journey not a set of equations to be
applied to something as if maths is a
set of dusty tools in the shed of
science for me my maths journey Sawa is
really young
I’ve always loved numbers and my parents
realized that early on when I started
doing Negra number addition at 3 years
old
I also loved squaring numbers and at one
stage I could do five digit
multiplication
my head actually had a book where I’d
write down little tricks and formula
used to solve such equations quicker
part of the writing I was only 5 years
old so yes I love maths and my very
school’s public in competitions at age
of 13 I was spotted by the national
director of the Australian mathematical
trust who put me in training for the
Australian limpia team and it was there
that I discover that actually wasn’t
that a good at geometry I was and still
am bad at drawing and this made me
scared of the subject how could I
possibly prove that three points line a
line when my lines look like circles so
I worked on geometry problems to
maximize my chances of winning and it
was there that discovered the unexpected
beauty in geometry not in the drawing
part of course but in the way certain
mathematically challenging concepts
could be explained simply through
visualization what is the infinite sum
of 1/2 plus 1/4 plus 1/8 plus 1/16 etc
well to some of you this met this some
may seem daunting if you look at this
animation where each time we’re adding
half the previous rectangle it does make
sense that these rectangles will
eventually add up to a square that has
area 1 but if I now ask you where the
parallel lines do meet well parent lines
are defined not to meet if you look at
it in a certain angle it does appear
that these lines will eventually meet at
a point at infinity and it turns out
this point is used extensively in
mathematics nowadays I was learning all
this outside the classroom
luckily nowadays you have the internet
where we can learn things in our own
time in fact I didn’t need school
classes at all because participating in
mathematical forums was like a class of
its own I was so involved in online
communities that I actually start
Blagh were post solutions to problems
that I found beautiful especially ones
people can solve and it was there that I
met zooming Liang who lives in America
at the time we were both 16 and loved
geometry is and solving mathematical
problems in general coincidentally
zooming in our boat stuck on the same
open problem and it took us five days to
solve this problem a cycle where I
worked through the night and zooming
we’ll continue our left off swimming
would do the same
repeat the time zone difference actually
worked quite well
we had eyes on the prom for 120 hours
straight now reflect on your high school
experience we had to solve 30 problems
in one and a half hours is it really
testing our ability to think creatively
unlike in high school where you could
submit your solutions to be marked
assuming and I weren’t even done we
stumbled upon a new theorem in
mathematics extending the one we had
just solved what a theorem stated was
that a point in the Triangle plane lies
an isomorphic equivalent to I superior
cubics in its petal triangles but here’s
a diagram for the theorem it’s bit
simplified unfortunately we too had no
idea how to prove this problem and it
took us six months to finally figure out
a way just to start the proof and
another week to solve it let alone nine
months for it to be published who could
have thought by the end of it that our
diagram would look like this what a
theorem did was that it made the complex
field of I so people cubics easier to
deal with and allows difficult
geometrical problems to be solved by
people with only high school level
understanding of geometry it avoids
pages of calculation – more elegant and
quicker approaches in fact
when I tried to solve the equations of
our theorem my computer timed out so
clearly maths isn’t just a set of
equations but more like a crime thriller
where the build build up to the ending
is far more important than the ending
itself something I had to create new
theory in the field of AI spooler cubics
in order to solve our new theorem and it
turned out that these subsidiary results
end up being the most important and
widely applicable part of our article
for mass loss theorem is a perfect
example of this back in the 1700s one
was formulated people had no idea how to
prove the simple looking problem but
fast forward to the 20th century with
whole new fields of analytical number
theory and an algebraic number theory
had to be invented in order to solve the
problem it was finally resolved Andrew
Wiles but in contribution were hundreds
of mathematicians worldwide so just
imagine learning the result a to the X
plus PDV x equals c DX what are you
actually learning the whole concept of
thinking of mathematics of the journey
follows from the idea that the ability
to think creatively is far more
important than the ability to know and
to apply in 2015 alphago was placed in
competition with lee solo in the game go
while the computer did win four out of
five times is where the computer lost
which begs the question how could a
computer that could compute a surplus of
a hundred moves ahead lose to a mere
human and it was there that I realized
that we have an edge over computers to
visualize geometrically to think
abstractly and out of the box and to use
these qualities to create innovation
what this means is our human imagination
and creativity cannot be replicated by a
computer
so the question is are we as the younger
generation being given the best
opportunities to use our talents in
qualities in the best possible way and
currently I don’t believe our education
system understands the importance of
creativity in schools we’re taught to
set a follow of rules procedures we’re
taught to accept rather than question to
test rather than experiment what is the
point of 12 years of teaching if a
simple computer program could do the
exact same thing billions of times
faster but being told that wrong is bad
and in the process we’re losing the
fundamental property that makes us human
creativity just imagine the world with
complex numbers didn’t exist and now
imagine a poor inquisitive child asking
his teacher why aren’t there solutions
to x squared equals negative 1 we have
solutions for x squared equals 1 1 4 2 9
3 but why not negative numbers and just
imagine a response such as just accept
that there isn’t or even worse being
ridiculed for claiming such numbers
should exist then the whole field of
complex analysis and it’s ubiquitous
applications in engineering wouldn’t
have been invented we won’t be able to
fly planes or even watch movies in our
cinemas so comfortably today so just
imagine what kinds of innovations you
might be losing nowadays to encourage
creativity I believe we need to
introduce real mathematics from an
earlier age that is true we need to
understand the concept of logical
thinking and proof writing earlier for
example instead of homework being to
repeatedly apply the same technique for
50 differently worded problems why can’t
it be think of this theorem or problem
and how would you prove it and then in
the next class discuss strategies or
what the students thought and show them
how the proof would work out and instead
of losing half of the students during
class I believe we need to incorporate
methods of active learning where
students will read content in advance
and the teacher would go over what they
do not understand lastly I believe we
need to make it clear that being wrong
is okay because in my experience I’ve
learnt the most out of being wrong and
knowing where I’ve gone wrong
coincidentally has given me a better
understanding of mathematics as a whole
similar ideas – I’ll just be mentioning
have been employed in Finland and look
what that’s got them that the best
education system in the world they
understand that our human imagination
and creativity should be praised is more
important to visualize them to know and
to follow a procedure just like you
cannot appreciate a story by reading its
ending you cannot appreciate maths
physics art or any subject by set of
rules and ways to apply them we need to
teach these subjects what they are a
journey
[Applause]
[Music]
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