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

Summary

In this engaging talk, the speaker shares an outsider's journey into the world of mathematics, challenging the common perception that math is only for the elite. They recount their personal transformation from struggling with math to embracing it as a career, revealing math's practicality and beauty. The speaker illustrates the omnipresence of mathematical patterns in nature, such as fractals, and encourages the audience to develop their 'mathematical sense' to perceive the universe's inherent order and beauty.

Takeaways

• 🎉 The speaker humorously admits that professing a love for mathematics at a party might not win popularity contests, but it's a passion they embrace.
• 🧐 The speaker identifies as an 'outsider' to mathematics, having struggled with the subject and not finding it their strength in school.
• 🏆 The speaker's high school valued mathematics highly, with social status tied to one's rank in math classes, which contributed to the speaker's initial aversion to the subject.
• 📚 A conversation with a professor at Sydney University led to a pivotal change in the speaker's life, encouraging them to switch to teaching mathematics due to a shortage of math educators.
• 🤓 The speaker discovered that mathematics is not just about rote learning and abstract problem-solving but is deeply practical and even beautiful.
• 🔍 Mathematics is presented as a 'sense' that allows us to perceive patterns, relationships, and logical connections, much like our other senses allow us to perceive the world.
• 🌊 The concept of fractals is introduced, showing how mathematical patterns are evident in natural phenomena like river deltas, trees, lightning, and even our blood vessels.
• 🌳 Fractals are found everywhere in nature, from plants to clouds, and recognizing them can enhance our appreciation for the mathematical beauty in the world around us.
• 🎼 The speaker draws parallels between the patterns in mathematics and those found in art, music, and design, emphasizing the universality of pattern recognition and creation.
• 💐 The golden ratio and rotational symmetry in flowers illustrate how mathematics is not only present in nature but also contributes to its beauty and efficiency.
• 🤓 The speaker challenges the notion that some people are not 'mathematical' by highlighting our innate ability to recognize and create patterns, a skill shared by artists and mathematicians alike.
• 🎉 The speaker concludes with an enthusiastic declaration of love for mathematics, proud to embrace it even in a crowd, emphasizing its importance and beauty.

Q & A

What was the speaker's initial attitude towards mathematics?

The speaker initially struggled with mathematics and considered themselves an outsider to the subject, preferring English and history.

Why did the speaker change their career path to become a mathematics teacher?

The speaker changed their career path after a conversation with a professor at Sydney University who pointed out a critical shortage of mathematics educators in Australian schools and encouraged them to switch their teaching area to mathematics.

How did the speaker's perspective on mathematics change during their university studies?

During university, the speaker discovered that mathematics was practical and beautiful, not just about finding answers but also about asking the right questions, and about forming new ways to see problems.

What is the significance of the river delta example in the speaker's talk?

The river delta example is used to illustrate the concept of fractals, which are shapes with a recursive structure found in nature, and to show the mathematical patterns that are hidden in plain sight.

What is a fractal and why are they important in the context of the speaker's message?

A fractal is a shape that exhibits a repeating pattern at different scales. They are important because they represent the mathematical reality woven into the fabric of the universe, connecting various natural phenomena and demonstrating the ubiquity of mathematical patterns.

How does the speaker relate the patterns found in nature to our inherent human ability to perceive and create patterns?

The speaker relates the patterns found in nature to our human ability by suggesting that we are all born with a 'mathematical sense' that allows us to perceive patterns, relationships, and logical connections, just as we have senses for sight, sound, and touch.

What is the 'golden ratio' mentioned in the script, and where can it be found?

The 'golden ratio' is a mathematical constant approximately equal to 1.618, often found in aesthetically pleasing proportions. It can be found in various places such as the arrangement of sunflower seeds, the human body, and architectural designs.

Why does the speaker compare the study of mathematics to learning to play a musical instrument?

The speaker compares mathematics to learning an instrument to convey how his initial experience with both was tedious and unenjoyable, but later, with the right approach and understanding, he found both to be engaging and creative processes.

What is the speaker's view on the importance of recognizing and appreciating mathematical patterns in our lives?

The speaker believes that recognizing and appreciating mathematical patterns is crucial as it allows us to fully engage with and understand the world around us, and that dismissing mathematics as uninteresting closes us off from a significant part of the human experience.

How does the speaker use the example of Islamic art and design to illustrate mathematical patterns?

The speaker uses Islamic art and design to show how mathematical patterns can be both aesthetically pleasing and intricate, highlighting the cultural and historical appreciation for geometric forms and symmetry.

What is the significance of the 137.5-degree angle in the context of the speaker's discussion on flower patterns?

The 137.5-degree angle is significant because it creates an efficient and aesthetically pleasing pattern in the arrangement of seeds in a sunflower, which is related to the 'golden ratio' and demonstrates the presence of mathematical patterns in nature.

Outlines

00:00

🎓 From Outsider to Maths Enthusiast

The speaker, Eddie, humorously admits that professing a love for mathematics isn't a party icebreaker, reflecting his own past struggles with the subject. Despite being an English and history enthusiast, he was encouraged to become a maths teacher due to a shortage in the field. This career shift led him to discover the beauty and practicality of maths, which he likens to a sense that perceives patterns and relationships, much like sight or touch. He shares his journey from being an outsider to embracing mathematics as a career, emphasizing that everyone has the innate ability to appreciate and excel in it.

05:02

🌳 The Universal Language of Fractals

Eddie illustrates the concept of fractals, complex shapes found in nature that exhibit self-similarity at different scales. He uses the river delta as an example, showing how its structure is a microcosm of the larger pattern. This pattern is mirrored in trees, lightning, and even the blood vessels within our bodies. Eddie argues that our ability to perceive these mathematical patterns is akin to our other senses and can be honed with practice. He challenges the notion that some people are not 'mathematical' by highlighting our innate pattern recognition abilities, which are evident in various aspects of life, including art and nature.

10:05

🎨 The Aesthetics of Mathematical Patterns

In this paragraph, Eddie delves into the aesthetic appeal of mathematical patterns, drawing parallels between art, music, and nature. He discusses how artists, musicians, and other creators excel at making patterns, with music described as the joy of counting without realizing it. Islamic art's intricate geometric designs and the rotational symmetry of flowers, particularly sunflowers and their association with the golden ratio, are highlighted. Eddie emphasizes that the golden ratio is a mathematical reality found ubiquitously in nature and human-made structures, concluding with the assertion that mathematics is an integral part of the human experience and should be celebrated.

Keywords

💡Mathematics

Mathematics is a field of study that involves the properties and relationships of numbers, quantities, shapes, and patterns. In the video, the speaker initially presents mathematics as a subject that many find daunting and inaccessible, but later reveals its beauty and practicality, showing how it is deeply intertwined with the natural world and our everyday experiences.

💡Outsider

An outsider is someone who is not part of a particular group or activity and may lack familiarity or acceptance within it. The speaker identifies as an outsider to mathematics, having struggled with the subject and feeling disconnected from it. However, this perspective allows the speaker to approach the subject with fresh eyes and ultimately discover its inherent appeal.

💡Fractals

Fractals are complex geometric shapes that can be split into parts, each of which is a reduced-scale copy of the whole. They are a key concept in the video as the speaker uses them to illustrate the prevalence of mathematical patterns in nature, such as in river deltas, trees, and lightning bolts, emphasizing the interconnectedness of mathematical concepts and the natural world.

💡Golden Ratio

The golden ratio is an irrational number, approximately equal to 1.618, that is found by dividing a line into two parts so that the ratio of the whole line to the longer part is equal to the ratio of the longer part to the shorter part. In the video, the golden ratio is highlighted as a mathematical reality that appears in various natural phenomena, including the arrangement of sunflower seeds and the proportions of the Parthenon.

💡Patterns

Patterns are regularities in the arrangement or sequence of elements. The video emphasizes the human ability to recognize and create patterns, which is a fundamental aspect of mathematics. The speaker argues that our innate sense for patterns is what makes us 'born mathematicians,' and uses examples from nature and art to demonstrate this.

💡Insight

Insight refers to the understanding or perspective gained from deep thought or knowledge. In the context of the video, insight is presented as a crucial component of mathematical problem-solving, where one must not only find answers but also learn to ask the right questions, combining this insight with imagination.

💡Imagination

Imagination is the ability to form new ideas or images in the mind that are not present to the senses. The speaker in the video argues that mathematics is not just about calculation but also about using imagination to see problems in new ways, thus solving them more effectively.

💡Rotational Symmetry

Rotational symmetry is a property of an object to appear unchanged after rotation about an axis. The video uses the example of a sunflower's spiral seeds to explain rotational symmetry, showing how mathematics can be found in the beauty and efficiency of natural forms.

💡Islamic Art

Islamic Art refers to the visual arts produced from the 7th century in the Islamic world. The video mentions Islamic art as an example of the aesthetic beauty that can be derived from mathematical patterns, particularly in the intricate tile arrangements and geometric forms that avoid the depiction of living beings.

💡Genetic Lottery

The term 'genetic lottery' metaphorically refers to the random distribution of genetic traits that one inherits from their parents. The speaker uses this term to humorously describe their own eyesight, which requires glasses for clear vision, drawing a parallel to how some people may feel about their natural affinity for mathematics.

Highlights

The speaker humorously admits that saying 'I love mathematics' at a party may lead to social isolation.

The majority of people feel like outsiders when it comes to mathematics due to its complex nature.

The speaker shares a personal journey from struggling with math to making it a career.

A chance encounter at Sydney University led to a life-changing decision to become a math teacher.

The speaker emphasizes the importance of perseverance in math despite initial struggles.

The speaker's initial interest in English and history was challenged by the prestige of math in high school.

The Australian Mathematics Competition highlights the cultural significance of math in the speaker's school.

The speaker's shift from seeing math as a chore to recognizing its beauty and practicality.

Mathematics is described as a sense that allows us to perceive realities not otherwise tangible.

The concept of fractals is introduced as a fundamental pattern found throughout nature.

The similarity between natural phenomena like river deltas, trees, and lightning bolts is highlighted.

The presence of fractals in the human body, specifically in blood vessels, is noted.

The speaker argues that everyone is born with an innate ability to perceive patterns, a 'mathematical sense'.

The importance of developing one's 'mathematical sense' through practice and guidance is emphasized.

The speaker refutes the idea that one cannot appreciate math due to a lack of natural ability.

The beauty and symmetry in flowers, related to the golden ratio, is used to illustrate mathematical patterns in nature.

The golden ratio is presented as a mathematical reality found in various aspects of art, architecture, and nature.

The speaker concludes with pride in their love for mathematics, challenging the stigma around it.

Transcripts

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.

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

I'm proud to declare,

"I love mathematics!"

(Cheers) (Applause)