"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.