0:00:14.079,0:00:16.405
"I love mathematics"

0:00:16.405,0:00:18.005
(Laughter)

0:00:19.155,0:00:21.316
is exactly what to say at a party

0:00:21.316,0:00:23.446
if you want to spend[br]the next couple of hours

0:00:23.446,0:00:25.577
sipping your drink alone

0:00:25.577,0:00:28.268
in the least cool corner of the room.

0:00:28.378,0:00:30.784
And that's because[br]when it comes to this subject -

0:00:30.784,0:00:32.899
all the numbers, formulas,

0:00:32.899,0:00:34.705
symbols, and calculations -

0:00:34.705,0:00:37.876
the vast majority of us are outsiders,

0:00:37.876,0:00:39.480
and that includes me.

0:00:39.720,0:00:41.678
That's why today I want to share with you

0:00:41.678,0:00:44.264
an outsider's perspective of mathematics -

0:00:44.264,0:00:45.843
what I understand of it,

0:00:45.843,0:00:49.053
from someone who's always[br]struggled with the subject.

0:00:49.373,0:00:50.747
And what I've discovered,

0:00:50.747,0:00:55.519
as someone who went from being an outsider[br]to making maths my career,

0:00:55.519,0:01:00.920
is that, surprisingly, we are all[br]deep down born to be mathematicians.

0:01:00.920,0:01:02.180
(Laughter)

0:01:02.919,0:01:04.510
But back to me being an outsider.

0:01:04.510,0:01:06.090
I know what you're thinking:

0:01:06.090,0:01:07.874
"Wait a second, Eddie.

0:01:07.874,0:01:09.918
What would you know?

0:01:09.918,0:01:11.416
You're a maths teacher.

0:01:11.526,0:01:13.037
You went to a selective school.

0:01:13.117,0:01:15.934
You wear glasses, and you're Asian."

0:01:15.934,0:01:18.020
(Laughter)

0:01:19.953,0:01:22.767
Firstly, that's racist.

0:01:22.767,0:01:24.340
(Laughter)

0:01:24.340,0:01:26.781
Secondly, that's wrong.

0:01:26.781,0:01:28.179
When I was in school,

0:01:28.179,0:01:31.230
my favorite subjects[br]were English and history.

0:01:31.230,0:01:33.618
And this caused a lot of angst[br]for me as a teenager

0:01:33.618,0:01:37.181
because my high school[br]truly honored mathematics.

0:01:37.181,0:01:39.456
Your status in the school[br]pretty much correlated

0:01:39.456,0:01:41.669
with which mathematics class[br]you ranked in.

0:01:41.669,0:01:43.283
There were eight classes.

0:01:43.283,0:01:46.738
So if you were in maths 4,[br]that made you just about average.

0:01:46.738,0:01:50.729
If you were in maths 1,[br]you were like royalty.

0:01:50.729,0:01:51.731
Each year,

0:01:51.731,0:01:55.234
our school entered the prestigious[br]Australian Mathematics Competition

0:01:55.234,0:01:58.087
and would print out a list[br]of everyone in the school

0:01:58.087,0:02:01.050
in order of our scores.

0:02:01.070,0:02:04.177
Students who received[br]prizes and high distinctions

0:02:04.177,0:02:07.957
were pinned up at the start[br]of a long corridor,

0:02:07.957,0:02:11.934
far, far away from the dark[br]and shameful place

0:02:11.934,0:02:13.830
where my name appeared.

0:02:13.830,0:02:15.901
Maths was not really my thing.

0:02:16.101,0:02:21.183
Stories, characters, narratives -[br]this is where I was at home.

0:02:21.183,0:02:22.192
And that's why

0:02:22.192,0:02:27.001
I raised my sails and set course[br]to become an English and history teacher.

0:02:27.841,0:02:30.852
But a chance encounter[br]at Sydney University

0:02:30.852,0:02:32.794
altered my life forever.

0:02:33.134,0:02:35.517
I was in line to enroll[br]at the faculty of education

0:02:35.517,0:02:38.716
when I started the conversation[br]with one of its professors.

0:02:38.716,0:02:43.073
He noticed that while my academic life[br]had been dominated by humanities,

0:02:43.073,0:02:46.612
I had actually attempted[br]some high-level maths at school.

0:02:46.612,0:02:50.295
What he saw was not[br]that I had a problem with maths,

0:02:50.295,0:02:53.262
but that I had persevered with maths.

0:02:53.362,0:02:55.470
And he knew something I didn't -

0:02:55.470,0:02:58.311
that there was a critical shortage[br]of mathematics educators

0:02:58.311,0:02:59.678
in Australian schools,

0:02:59.678,0:03:02.480
a shortage that remains to this day.

0:03:02.840,0:03:07.658
So he encouraged me to change[br]my teaching area to mathematics.

0:03:07.678,0:03:09.402
Now, for me, becoming a teacher

0:03:09.402,0:03:11.819
wasn't about my love[br]for a particular subject.

0:03:11.819,0:03:16.263
It was about having a personal impact[br]on the lives of young people.

0:03:16.553,0:03:17.926
I'd seen firsthand at school

0:03:17.926,0:03:22.357
what a lasting and positive difference[br]a great teacher can make.

0:03:22.357,0:03:24.123
I wanted to do that for someone,

0:03:24.123,0:03:27.021
and it didn't matter to me[br]what subject I did it in.

0:03:27.021,0:03:29.390
If there was an acute need in mathematics,

0:03:29.390,0:03:32.020
then it made sense for me to go there.

0:03:32.957,0:03:34.939
As I studied my degree, though,

0:03:34.939,0:03:37.792
I discovered that mathematics[br]was a very different subject

0:03:37.792,0:03:40.140
to what I'd originally thought.

0:03:40.140,0:03:42.458
I'd made the same mistake[br]about mathematics

0:03:42.458,0:03:44.522
that I'd made earlier in my life

0:03:44.522,0:03:46.245
about music.

0:03:46.531,0:03:47.986
Like a good migrant child,

0:03:47.986,0:03:50.565
I dutifully learned[br]to play the piano when I was young.

0:03:50.565,0:03:51.790
(Laughter)

0:03:51.790,0:03:55.178
My weekends were filled[br]with endlessly repeating scales

0:03:55.178,0:03:57.515
and memorizing every note in the piece,

0:03:57.515,0:03:59.349
spring and winter.

0:03:59.629,0:04:02.546
I lasted two years[br]before my career was abruptly ended

0:04:02.546,0:04:04.552
when my teacher told my parents,

0:04:04.552,0:04:07.817
"His fingers are too short.[br]I will not teach him anymore."

0:04:07.817,0:04:10.432
(Laughter)

0:04:10.752,0:04:14.838
At seven years old,[br]I thought of music like torture.

0:04:14.938,0:04:18.578
It was a dry, solitary, joyless exercise

0:04:18.578,0:04:22.392
that I only engaged with[br]because someone else forced me to.

0:04:23.460,0:04:26.756
It took me 11 years[br]to emerge from that sad place.

0:04:26.756,0:04:27.782
In year 12,

0:04:27.782,0:04:30.255
I picked up a steel string acoustic guitar

0:04:30.255,0:04:31.769
for the first time.

0:04:32.119,0:04:34.095
I wanted to play it for church,

0:04:34.485,0:04:38.168
and there was also a girl[br]I was fairly keen on impressing.

0:04:38.168,0:04:40.995
So I convinced my brother[br]to teach me a few chords.

0:04:40.995,0:04:46.340
And slowly, but surely, my mind changed.

0:04:46.497,0:04:49.429
I was engaged in a creative process.

0:04:49.429,0:04:52.546
I was making music, and I was hooked.

0:04:52.896,0:04:54.270
I started playing in a band,

0:04:54.270,0:04:57.269
and I felt the delight[br]of rhythm pulsing through my body

0:04:57.269,0:04:59.529
as we brought our sounds together.

0:04:59.529,0:05:02.207
I'd been surrounded by a musical ocean

0:05:02.207,0:05:03.586
my entire life,

0:05:03.586,0:05:07.726
and for the first time,[br]I realized I could swim in it.

0:05:08.446,0:05:10.540
I went through[br]an almost identical experience

0:05:10.540,0:05:12.361
when it came to mathematics.

0:05:12.361,0:05:16.359
I used to believe that maths was about [br]rote learning inscrutable formulas

0:05:16.359,0:05:19.850
to solve abstract problems[br]that didn't mean anything to me.

0:05:20.420,0:05:25.519
But at university, I began to see[br]that mathematics is immensely practical

0:05:25.519,0:05:27.832
and even beautiful,

0:05:27.832,0:05:29.878
that it's not just about finding answers

0:05:29.878,0:05:34.338
but also about learning to ask[br]the right questions,

0:05:34.338,0:05:37.467
and that mathematics isn't[br]about mindlessly crunching numbers

0:05:37.467,0:05:41.517
but rather about forming[br]new ways to see problems

0:05:41.517,0:05:45.917
so we can solve them[br]by combining insight with imagination.

0:05:46.667,0:05:52.199
It gradually dawned on me[br]that mathematics is a sense.

0:05:52.529,0:05:56.809
Mathematics is a sense[br]just like sight and touch;

0:05:56.809,0:05:59.350
it's a sense that allows us[br]to perceive realities

0:05:59.350,0:06:02.356
which would be otherwise intangible to us.

0:06:02.356,0:06:07.089
You know, we talk about a sense of humor[br]and a sense of rhythm.

0:06:07.634,0:06:13.024
Mathematics is our sense for patterns,[br]relationships, and logical connections.

0:06:13.037,0:06:16.315
It's a whole new way to see the world.

0:06:16.672,0:06:18.909
Now, I want to show you[br]a mathematical reality

0:06:18.909,0:06:21.431
that I guarantee you've seen before

0:06:21.466,0:06:24.528
but perhaps never really perceived.

0:06:24.528,0:06:27.916
It's been hidden in plain sight[br]your entire life.

0:06:29.070,0:06:31.921
This is a river delta.

0:06:31.921,0:06:34.394
It's a beautiful piece of geometry.

0:06:34.394,0:06:36.108
Now, when we hear the word geometry,

0:06:36.108,0:06:38.555
most of us think of triangles and circles.

0:06:38.555,0:06:41.597
But geometry is[br]the mathematics of all shapes,

0:06:41.597,0:06:44.192
and this meeting of land and sea

0:06:44.192,0:06:47.932
has created shapes[br]with an undeniable pattern.

0:06:47.932,0:06:50.919
It has a mathematically[br]recursive structure.

0:06:50.919,0:06:52.844
Every part of the river delta,

0:06:52.844,0:06:54.575
with its twists and turns,

0:06:54.575,0:06:58.038
is a microversion of the greater whole.

0:06:58.038,0:07:01.571
So I want you to see[br]the mathematics in this.

0:07:02.242,0:07:03.869
But that's not all.

0:07:03.869,0:07:06.964
I want you to compare this river delta

0:07:06.964,0:07:09.610
with this amazing tree.

0:07:10.060,0:07:11.866
It's a wonder in itself.

0:07:11.866,0:07:16.395
But focus with me on the similarities[br]between this and the river.

0:07:17.199,0:07:18.552
What I want to know

0:07:18.552,0:07:23.083
is why on earth should these shapes[br]look so remarkably alike?

0:07:23.083,0:07:25.606
Why should they have anything in common?

0:07:25.606,0:07:27.882
Things get even more perplexing[br]when you realize

0:07:27.882,0:07:30.452
it's not just water systems[br]and plants that do this.

0:07:30.452,0:07:32.408
If you keep your eyes open,

0:07:32.408,0:07:36.289
you'll see these same shapes[br]are everywhere.

0:07:37.210,0:07:38.934
Lightning bolts disappear so quickly

0:07:38.934,0:07:42.291
that we seldom have the opportunity[br]to ponder their geometry.

0:07:42.291,0:07:46.964
But their shape is so unmistakable[br]and so similar to what we've just seen

0:07:46.964,0:07:50.267
that one can't help but be suspicious.

0:07:50.369,0:07:51.746
And then there's the fact

0:07:51.746,0:07:57.401
that every single person in this room[br]is filled with these shapes too.

0:07:58.221,0:08:01.201
Every cubic centimeter of your body

0:08:01.201,0:08:06.515
is packed with blood vessels[br]that trace out this same pattern.

0:08:06.515,0:08:10.617
There's a mathematical reality[br]woven into the fabric of the universe

0:08:10.617,0:08:13.097
that you share with winding rivers,

0:08:13.097,0:08:16.438
towering trees, and raging storms.

0:08:16.708,0:08:19.699
These shapes are examples[br]of what we call "fractals,"

0:08:19.699,0:08:21.131
as mathematicians.

0:08:21.131,0:08:22.309
Fractals get their name

0:08:22.309,0:08:25.793
from the same place[br]as fractions and fractures -

0:08:25.793,0:08:28.335
it's a reference to the broken[br]and shattered shapes

0:08:28.335,0:08:30.693
we find around us in nature.

0:08:30.693,0:08:32.644
Now, once you have a sense for fractals,

0:08:32.644,0:08:36.026
you really do start[br]to see them everywhere:

0:08:36.396,0:08:37.959
a head of broccoli,

0:08:38.614,0:08:40.403
the leaves of a fern,

0:08:40.603,0:08:43.350
even clouds in the sky.

0:08:43.630,0:08:44.838
Like the other senses,

0:08:44.838,0:08:48.495
our mathematical sense[br]can be refined with practice.

0:08:48.495,0:08:52.837
It's just like developing perfect pitch[br]or a taste for wines.

0:08:52.837,0:08:55.777
You can learn to perceive[br]the mathematics around you

0:08:55.777,0:08:58.820
with time and the right guidance.

0:08:59.170,0:09:03.152
Naturally, some people are born[br]with sharper senses than the rest of us,

0:09:03.152,0:09:05.702
others are born with impairment.

0:09:05.702,0:09:08.818
As you can see, I drew a short straw[br]in the genetic lottery

0:09:08.818,0:09:10.635
when it came to my eyesight.

0:09:10.635,0:09:14.652
Without my glasses, everything is a blur.

0:09:16.082,0:09:19.317
I've wrestled with this sense[br]my entire life,

0:09:19.317,0:09:21.748
but I would never dream of saying,

0:09:21.748,0:09:24.251
"Well, seeing has always been[br]a struggle for me.

0:09:24.251,0:09:27.270
I guess I'm just not[br]a seeing kind of person."

0:09:27.270,0:09:28.781
(Laughter)

0:09:30.561,0:09:33.296
Yet I meet people every day

0:09:33.296,0:09:38.090
who feel it quite natural[br]to say exactly that about mathematics.

0:09:38.090,0:09:39.095
Now, I'm convinced

0:09:39.095,0:09:43.574
we close ourselves off from a huge part[br]of the human experience if we do this.

0:09:43.574,0:09:48.129
Because all human beings[br]are wired to see patterns.

0:09:48.129,0:09:51.983
We live in a patterned universe, a cosmos.

0:09:51.983,0:09:56.090
That's what cosmos means -[br]orderly and patterned -

0:09:56.090,0:10:01.846
as opposed to chaos,[br]which means disorderly and random.

0:10:01.846,0:10:05.159
It isn't just seeing patterns[br]that humans are so good at.

0:10:05.159,0:10:07.443
We love making patterns too.

0:10:07.443,0:10:10.858
And the people who do this well[br]have a special name.

0:10:10.858,0:10:15.198
We call them artists, musicians,

0:10:15.198,0:10:18.525
sculptors, painters, cinematographers -

0:10:18.525,0:10:21.812
they're all pattern creators.

0:10:21.812,0:10:23.049
Music was once described

0:10:23.049,0:10:27.595
as the joy that people feel[br]when they are counting but don't know it.

0:10:27.595,0:10:28.748
(Laughter)

0:10:28.748,0:10:32.015
Some of the most striking examples[br]of mathematical patterns

0:10:32.015,0:10:34.883
are in Islamic art and design.

0:10:34.883,0:10:37.260
An aversion to depicting[br]humans and animals

0:10:37.260,0:10:42.316
led to a rich history of intricate[br]tile arrangements and geometric forms.

0:10:42.636,0:10:45.661
The aesthetic side[br]of mathematical patterns like these

0:10:45.661,0:10:48.234
brings us back to nature itself.

0:10:48.572,0:10:49.850
For instance,

0:10:49.850,0:10:53.129
flowers are a universal symbol of beauty.

0:10:53.129,0:10:55.673
Every culture around the planet[br]and throughout history

0:10:55.673,0:10:59.041
has regarded them as objects of wonder.

0:10:59.041,0:11:00.500
And one aspect of their beauty

0:11:00.500,0:11:03.411
is that they exhibit[br]a special kind of symmetry.

0:11:03.411,0:11:06.002
Flowers grow organically from a center

0:11:06.002,0:11:09.737
that expands outwards[br]in the shape of a spiral,

0:11:09.737,0:11:13.842
and this creates what we call[br]"rotational symmetry."

0:11:13.842,0:11:16.510
You can spin a flower around and around,

0:11:16.510,0:11:19.240
and it still looks basically the same.

0:11:19.900,0:11:22.412
But not all spirals are created equal.

0:11:22.412,0:11:27.680
It all depends on the angle of rotation[br]that goes into creating the spiral.

0:11:27.680,0:11:33.402
For instance, if we build a spiral[br]from an angle of 90 degrees,

0:11:33.402,0:11:37.279
we get a cross that is neither[br]beautiful nor efficient.

0:11:38.337,0:11:43.029
Huge parts of the flowers area[br]are wasted and don't produce seeds.

0:11:43.529,0:11:48.948
Using an angle of 62 degrees is better[br]and produces a nice circular shape,

0:11:48.948,0:11:51.661
like what we usually[br]associate with flowers.

0:11:51.661,0:11:53.294
But it's still not great.

0:11:53.294,0:11:55.365
There's still large parts of the area

0:11:55.365,0:11:58.766
that are a poor use[br]of resources for the flower.

0:11:59.641,0:12:06.585
However, if we use 137.5 degrees,

0:12:06.585,0:12:07.757
(Laughter)

0:12:07.757,0:12:10.786
we get this beautiful pattern.

0:12:11.696,0:12:13.530
It's astonishing,

0:12:13.910,0:12:18.861
and it is exactly the kind of pattern[br]used by that most majestic of flowers -

0:12:18.861,0:12:20.547
the sunflower.

0:12:20.547,0:12:25.128
Now, 137.5 degrees[br]might seem pretty random,

0:12:25.128,0:12:27.876
but it actually emerges[br]out of a special number

0:12:27.876,0:12:30.624
that we call the "golden ratio."

0:12:30.624,0:12:32.826
The golden ratio is a mathematical reality

0:12:32.826,0:12:36.652
that, like fractals,[br]you can find everywhere -

0:12:36.652,0:12:41.536
from the phalanges of your fingers[br]to the pillars of the Parthenon.

0:12:41.736,0:12:45.684
That's why even at a party of 5000 people,

0:12:45.684,0:12:47.696
I'm proud to declare,

0:12:47.696,0:12:50.092
"I love mathematics!"

0:12:50.092,0:12:52.762
(Cheers) (Applause)