WEBVTT

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"I love mathematics"

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(Laughter)

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is exactly what to say at a party

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if you want to spend
the next couple of hours

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sipping your drink alone

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in the least cool corner of the room.

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And that's because
when it comes to this subject -

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all the numbers, formulas,

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symbols, and calculations -

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the vast majority of us are outsiders,

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and that includes me.

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That's why today I want to share with you

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an outsider's perspective of mathematics -

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what I understand of it,

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from someone who's always
struggled with the subject.

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And what I've discovered,

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as someone who went from being an outsider
to making maths my career,

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is that, surprisingly, we are all
deep down born to be mathematicians.

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(Laughter)

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But back to me being an outsider.

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I know what you're thinking:

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"Wait a second, Eddie.

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What would you know?

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You're a maths teacher.

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You went to a selective school.

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You wear glasses, and you're Asian."

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(Laughter)

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Firstly, that's racist.

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(Laughter)

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Secondly, that's wrong.

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When I was in school,

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my favorite subjects
were English and history.

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And this caused a lot of angst
for me as a teenager

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because my high school
truly honored mathematics.

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Your status in the school
pretty much correlated

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with which mathematics class
you ranked in.

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There were eight classes.

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So if you were in maths 4,
that made you just about average.

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If you were in maths 1,
you were like royalty.

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Each year,

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our school entered the prestigious
Australian Mathematics Competition

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and would print out a list
of everyone in the school

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in order of our scores.

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Students who received
prizes and high distinctions

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were pinned up at the start
of a long corridor,

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far, far away from the dark
and shameful place

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where my name appeared.

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Maths was not really my thing.

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Stories, characters, narratives -
this is where I was at home.

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And that's why

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I raised my sails and set course
to become an English and history teacher.

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But a chance encounter
at Sydney University

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altered my life forever.

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I was in line to enroll
at the faculty of education

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when I started the conversation
with one of its professors.

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He noticed that while my academic life
had been dominated by humanities,

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I had actually attempted
some high-level maths at school.

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What he saw was not
that I had a problem with maths,

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but that I had persevered with maths.

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And he knew something I didn't -

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that there was a critical shortage
of mathematics educators

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in Australian schools,

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a shortage that remains to this day.

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So he encouraged me to change
my teaching area to mathematics.

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Now, for me, becoming a teacher

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wasn't about my love
for a particular subject.

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It was about having a personal impact
on the lives of young people.

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I'd seen firsthand at school

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what a lasting and positive difference
a great teacher can make.

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I wanted to do that for someone,

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and it didn't matter to me
what subject I did it in.

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If there was an acute need in mathematics,

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then it made sense for me to go there.

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As I studied my degree, though,

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I discovered that mathematics
was a very different subject

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to what I'd originally thought.

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I'd made the same mistake
about mathematics

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that I'd made earlier in my life

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about music.

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Like a good migrant child,

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I dutifully learned
to play the piano when I was young.

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(Laughter)

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My weekends were filled
with endlessly repeating scales

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and memorizing every note in the piece,

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spring and winter.

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I lasted two years
before my career was abruptly ended

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when my teacher told my parents,

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"His fingers are too short.
I will not teach him anymore."

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(Laughter)

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At seven years old,
I thought of music like torture.

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It was a dry, solitary, joyless exercise

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that I only engaged with
because someone else forced me to.

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It took me 11 years
to emerge from that sad place.

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In year 12,

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I picked up a steel string acoustic guitar

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for the first time.

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I wanted to play it for church,

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and there was also a girl
I was fairly keen on impressing.

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So I convinced my brother
to teach me a few chords.

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And slowly, but surely, my mind changed.

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I was engaged in a creative process.

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I was making music, and I was hooked.

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I started playing in a band,

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and I felt the delight
of rhythm pulsing through my body

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as we brought our sounds together.

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I'd been surrounded by a musical ocean

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my entire life,

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and for the first time,
I realized I could swim in it.

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I went through
an almost identical experience

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when it came to mathematics.

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I used to believe that maths was about 
rote learning inscrutable formulas

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to solve abstract problems
that didn't mean anything to me.

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But at university, I began to see
that mathematics is immensely practical

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and even beautiful,

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that it's not just about finding answers

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but also about learning to ask
the right questions,

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and that mathematics isn't
about mindlessly crunching numbers

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but rather about forming
new ways to see problems

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so we can solve them
by combining insight with imagination.

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It gradually dawned on me
that mathematics is a sense.

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Mathematics is a sense
just like sight and touch;

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it's a sense that allows us
to perceive realities

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which would be otherwise intangible to us.

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You know, we talk about a sense of humor
and a sense of rhythm.

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Mathematics is our sense for patterns,
relationships, and logical connections.

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It's a whole new way to see the world.

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Now, I want to show you
a mathematical reality

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that I guarantee you've seen before

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but perhaps never really perceived.

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It's been hidden in plain sight
your entire life.

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This is a river delta.

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It's a beautiful piece of geometry.

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Now, when we hear the word geometry,

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most of us think of triangles and circles.

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But geometry is
the mathematics of all shapes,

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and this meeting of land and sea

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has created shapes
with an undeniable pattern.

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It has a mathematically
recursive structure.

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Every part of the river delta,

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with its twists and turns,

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is a microversion of the greater whole.

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So I want you to see
the mathematics in this.

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But that's not all.

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I want you to compare this river delta

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with this amazing tree.

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It's a wonder in itself.

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But focus with me on the similarities
between this and the river.

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What I want to know

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is why on earth should these shapes
look so remarkably alike?

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Why should they have anything in common?

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Things get even more perplexing
when you realize

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it's not just water systems
and plants that do this.

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If you keep your eyes open,

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you'll see these same shapes
are everywhere.

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Lightning bolts disappear so quickly

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that we seldom have the opportunity
to ponder their geometry.

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But their shape is so unmistakable
and so similar to what we've just seen

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that one can't help but be suspicious.

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And then there's the fact

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that every single person in this room
is filled with these shapes too.

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Every cubic centimeter of your body

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is packed with blood vessels
that trace out this same pattern.

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There's a mathematical reality
woven into the fabric of the universe

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that you share with winding rivers,

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towering trees, and raging storms.

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These shapes are examples
of what we call "fractals,"

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as mathematicians.

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Fractals get their name

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from the same place
as fractions and fractures -

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it's a reference to the broken
and shattered shapes

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we find around us in nature.

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Now, once you have a sense for fractals,

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you really do start
to see them everywhere:

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a head of broccoli,

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the leaves of a fern,

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even clouds in the sky.

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Like the other senses,

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our mathematical sense
can be refined with practice.

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It's just like developing perfect pitch
or a taste for wines.

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You can learn to perceive
the mathematics around you

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with time and the right guidance.

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Naturally, some people are born
with sharper senses than the rest of us,

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others are born with impairment.

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As you can see, I drew a short straw
in the genetic lottery

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when it came to my eyesight.

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Without my glasses, everything is a blur.

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I've wrestled with this sense
my entire life,

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but I would never dream of saying,

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"Well, seeing has always been
a struggle for me.

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I guess I'm just not
a seeing kind of person."

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(Laughter)

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Yet I meet people every day

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who feel it quite natural
to say exactly that about mathematics.

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Now, I'm convinced

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we close ourselves off from a huge part
of the human experience if we do this.

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Because all human beings
are wired to see patterns.

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We live in a patterned universe, a cosmos.

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That's what cosmos means -
orderly and patterned -

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as opposed to chaos,
which means disorderly and random.

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It isn't just seeing patterns
that humans are so good at.

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We love making patterns too.

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And the people who do this well
have a special name.

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We call them artists, musicians,

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sculptors, painters, cinematographers -

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they're all pattern creators.

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Music was once described

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as the joy that people feel
when they are counting but don't know it.

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(Laughter)

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Some of the most striking examples
of mathematical patterns

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are in Islamic art and design.

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An aversion to depicting
humans and animals

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led to a rich history of intricate
tile arrangements and geometric forms.

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The aesthetic side
of mathematical patterns like these

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brings us back to nature itself.

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For instance,

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flowers are a universal symbol of beauty.

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Every culture around the planet
and throughout history

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has regarded them as objects of wonder.

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And one aspect of their beauty

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is that they exhibit
a special kind of symmetry.

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Flowers grow organically from a center

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that expands outwards
in the shape of a spiral,

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and this creates what we call
"rotational symmetry."

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You can spin a flower around and around,

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and it still looks basically the same.

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But not all spirals are created equal.

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It all depends on the angle of rotation
that goes into creating the spiral.

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For instance, if we build a spiral
from an angle of 90 degrees,

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we get a cross that is neither
beautiful nor efficient.

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Huge parts of the flowers area
are wasted and don't produce seeds.

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Using an angle of 62 degrees is better
and produces a nice circular shape,

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like what we usually
associate with flowers.

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But it's still not great.

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There's still large parts of the area

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that are a poor use
of resources for the flower.

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However, if we use 137.5 degrees,

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(Laughter)

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we get this beautiful pattern.

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It's astonishing,

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and it is exactly the kind of pattern
used by that most majestic of flowers -

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the sunflower.

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Now, 137.5 degrees
might seem pretty random,

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but it actually emerges
out of a special number

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that we call the "golden ratio."

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The golden ratio is a mathematical reality

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that, like fractals,
you can find everywhere -

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from the phalanges of your fingers
to the pillars of the Parthenon.

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That's why even at a party of 5000 people,

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I'm proud to declare,

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"I love mathematics!"

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(Cheers) (Applause)