"I love mathematics"
(Laughter)
is exactly what to say at a party
if you want to spend the next couple of hours
sipping your drink alone
in the least cool corner of the room.
And that's because when it comes to this subject -
all the numbers, formulas,
symbols, and calculations -
the vast majority of us are outsiders,
and that includes me.
That's why today I want to share with you
an outsider's perspective of mathematics -
what I understand of it,
from someone who's always struggled with the subject.
And what I've discovered,
as someone who went from being an outsider to making maths my career,
is that, surprisingly, we are all deep down born to be mathematicians.
(Laughter)
But back to me being an outsider.
I know what you're thinking:
"Wait a second, Eddie.
What would you know?
You're a maths teacher.
You went to a selective school.
You wear glasses, and you're Asian."
(Laughter)
Firstly, that's racist.
(Laughter)
Secondly, that's wrong.
When I was in school,
my favorite subjects were English and history.
And this caused a lot of angst for me as a teenager
because my high school truly honored mathematics.
Your status in the school pretty much correlated
with which mathematics class you ranked in.
There were eight classes.
So if you were in maths 4, that made you just about average.
If you were in maths 1, you were like royalty.
Each year,
our school entered the prestigious Australian Mathematics Competition
and would print out a list of everyone in the school
in order of our scores.
Students who received prizes and high distinctions
were pinned up at the start of a long corridor,
far, far away from the dark and shameful place
where my name appeared.
Maths was not really my thing.
Stories, characters, narratives - this is where I was at home.
And that's why
I raised my sails and set course to become an English and history teacher.
But a chance encounter at Sydney University
altered my life forever.
I was in line to enroll at the faculty of education
when I started the conversation with one of its professors.
He noticed that while my academic life had been dominated by humanities,
I had actually attempted some high-level maths at school.
What he saw was not that I had a problem with maths,
but that I had persevered with maths.
And he knew something I didn't -
that there was a critical shortage of mathematics educators
in Australian schools,
a shortage that remains to this day.
So he encouraged me to change my teaching area to mathematics.
Now, for me, becoming a teacher
wasn't about my love for a particular subject.
It was about having a personal impact on the lives of young people.
I'd seen firsthand at school
what a lasting and positive difference a great teacher can make.
I wanted to do that for someone,
and it didn't matter to me what subject I did it in.
If there was an acute need in mathematics,
then it made sense for me to go there.
As I studied my degree, though,
I discovered that mathematics was a very different subject
to what I'd originally thought.
I'd made the same mistake about mathematics
that I'd made earlier in my life
about music.
Like a good migrant child,
I dutifully learned to play the piano when I was young.
(Laughter)
My weekends were filled with endlessly repeating scales
and memorizing every note in the piece,
spring and winter.
I lasted two years before my career was abruptly ended
when my teacher told my parents,
"His fingers are too short. I will not teach him anymore."
(Laughter)
At seven years old, I thought of music like torture.
It was a dry, solitary, joyless exercise
that I only engaged with because someone else forced me to.
It took me 11 years to emerge from that sad place.
In year 12,
I picked up a steel string acoustic guitar
for the first time.
I wanted to play it for church,
and there was also a girl I was fairly keen on impressing.
So I convinced my brother to teach me a few chords.
And slowly, but surely, my mind changed.
I was engaged in a creative process.
I was making music, and I was hooked.
I started playing in a band,
and I felt the delight of rhythm pulsing through my body
as we brought our sounds together.
I'd been surrounded by a musical ocean
my entire life,
and for the first time, I realized I could swim in it.
I went through an almost identical experience
when it came to mathematics.
I used to believe that maths was about rote learning inscrutable formulas
to solve abstract problems that didn't mean anything to me.
But at university, I began to see that mathematics is immensely practical
and even beautiful,
that it's not just about finding answers
but also about learning to ask the right questions,
and that mathematics isn't about mindlessly crunching numbers
but rather about forming new ways to see problems
so we can solve them by combining insight with imagination.
It gradually dawned on me that mathematics is a sense.
Mathematics is a sense just like sight and touch;
it's a sense that allows us to perceive realities
which would be otherwise intangible to us.
You know, we talk about a sense of humor and a sense of rhythm.
Mathematics is our sense for patterns, relationships, and logical connections.
It's a whole new way to see the world.
Now, I want to show you a mathematical reality
that I guarantee you've seen before
but perhaps never really perceived.
It's been hidden in plain sight your entire life.
This is a river delta.
It's a beautiful piece of geometry.
Now, when we hear the word geometry,
most of us think of triangles and circles.
But geometry is the mathematics of all shapes,
and this meeting of land and sea
has created shapes with an undeniable pattern.
It has a mathematically recursive structure.
Every part of the river delta,
with its twists and turns,
is a microversion of the greater whole.
So I want you to see the mathematics in this.
But that's not all.
I want you to compare this river delta
with this amazing tree.
It's a wonder in itself.
But focus with me on the similarities between this and the river.
What I want to know
is why on earth should these shapes look so remarkably alike?
Why should they have anything in common?
Things get even more perplexing when you realize
it's not just water systems and plants that do this.
If you keep your eyes open,
you'll see these same shapes are everywhere.
Lightning bolts disappear so quickly
that we seldom have the opportunity to ponder their geometry.
But their shape is so unmistakable and so similar to what we've just seen
that one can't help but be suspicious.
And then there's the fact
that every single person in this room is filled with these shapes too.
Every cubic centimeter of your body
is packed with blood vessels that trace out this same pattern.
There's a mathematical reality woven into the fabric of the universe
that you share with winding rivers,
towering trees, and raging storms.
These shapes are examples of what we call "fractals,"
as mathematicians.
Fractals get their name
from the same place as fractions and fractures -
it's a reference to the broken and shattered shapes
we find around us in nature.
Now, once you have a sense for fractals,
you really do start to see them everywhere:
a head of broccoli,
the leaves of a fern,
even clouds in the sky.
Like the other senses,
our mathematical sense can be refined with practice.
It's just like developing perfect pitch or a taste for wines.
You can learn to perceive the mathematics around you
with time and the right guidance.
Naturally, some people are born with sharper senses than the rest of us,
others are born with impairment.
As you can see, I drew a short straw in the genetic lottery
when it came to my eyesight.
Without my glasses, everything is a blur.
I've wrestled with this sense my entire life,
but I would never dream of saying,
"Well, seeing has always been a struggle for me.
I guess I'm just not a seeing kind of person."
(Laughter)
Yet I meet people every day
who feel it quite natural to say exactly that about mathematics.
Now, I'm convinced
we close ourselves off from a huge part of the human experience if we do this.
Because all human beings are wired to see patterns.
We live in a patterned universe, a cosmos.
That's what cosmos means - orderly and patterned -
as opposed to chaos, which means disorderly and random.
It isn't just seeing patterns that humans are so good at.
We love making patterns too.
And the people who do this well have a special name.
We call them artists, musicians,
sculptors, painters, cinematographers -
they're all pattern creators.
Music was once described
as the joy that people feel when they are counting but don't know it.
(Laughter)
Some of the most striking examples of mathematical patterns
are in Islamic art and design.
An aversion to depicting humans and animals
led to a rich history of intricate tile arrangements and geometric forms.
The aesthetic side of mathematical patterns like these
brings us back to nature itself.
For instance,
flowers are a universal symbol of beauty.
Every culture around the planet and throughout history
has regarded them as objects of wonder.
And one aspect of their beauty
is that they exhibit a special kind of symmetry.
Flowers grow organically from a center
that expands outwards in the shape of a spiral,
and this creates what we call "rotational symmetry."
You can spin a flower around and around,
and it still looks basically the same.
But not all spirals are created equal.
It all depends on the angle of rotation that goes into creating the spiral.
For instance, if we build a spiral from an angle of 90 degrees,
we get a cross that is neither beautiful nor efficient.
Huge parts of the flowers area are wasted and don't produce seeds.
Using an angle of 62 degrees is better and produces a nice circular shape,
like what we usually associate with flowers.
But it's still not great.
There's still large parts of the area
that are a poor use of resources for the flower.
However, if we use 137.5 degrees,
(Laughter)
we get this beautiful pattern.
It's astonishing,
and it is exactly the kind of pattern used by that most majestic of flowers -
the sunflower.
Now, 137.5 degrees might seem pretty random,
but it actually emerges out of a special number
that we call the "golden ratio."
The golden ratio is a mathematical reality
that, like fractals, you can find everywhere -
from the phalanges of your fingers to the pillars of the Parthenon.
That's why even at a party of 5000 people,
I'm proud to declare,
"I love mathematics!"
(Cheers) (Applause)