Mathematics is the sense you never knew you had | Eddie Woo | TEDxSydney

In this illuminating talk, high school mathematics teacher and YouTube star Eddie Woo shares his passion for mathematics, declaring that "mathematics is a sense, just like sight and touch" and one we can all embrace. Using surprising examples of geometry, he encourages everyone to seek out the patterns around us, for "a whole new way to see the world". A public high school teacher for more than 10 years, Eddie Woo gained international attention when he posted videos of his classroom lessons online to assist an ill student. His YouTube channel, WooTube, has more than 200,000 subscribers and over 13 million views.

Eddie believe that mathematics can be embraced and even enjoyed by absolutely everybody. He was named Australia's Local Hero and was a Top 10 Finalist in the Global Teacher Prize for his love of teaching mathematics.

This talk was given at a TEDx event using the TED conference format but independently organized by a local community. Learn more at https://www.ted.com/tedx

"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)