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  • Transcriber: Helen Chang Reviewer: Tanya Cushman

  • "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.