In November 2014, I spoke at the Victorian prize ceremony for the Australian Mathematics Competition. As guest of honour, these were my remarks to the students, families, teachers and others at the ceremony.
Thank you for all coming along tonight to recognise the achievements of these prizewinners.
The Australian Mathematics Competition is one of the largest school maths competitions in the world –– since 1978 it’s grown to have around 400,000 competitors in Australia alone, not to mention all the other countries.
Prizes go to the top 1 / 300’th of students. That’s the top 0.3%. To one decimal place, anyway.
So the students receiving prizes tonight are really extremely clever and talented. It’s really something to be quite proud of.
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Well, I’d like to talk to you about maths for a bit. That’s what we’re here for after all.
I am a mathematician. Maths is what I do for a living. I do it every day. I like this fact.
If you’re here to receive a prize, you’re clearly quite good at doing maths problems. And I might even surmise that you enjoyed it.
It’s fun to solve problems. Extending your abilities in something in which you’ve got talent, is good for you, it feels good. You move closer to achieving your potential — just as a talented tennis player improves their abilities by playing against challenging opponents.
All of you who have topped this competition know that solving challenging maths problems is not simple, not routine, not formulaic. It doesn’t mean you can add really big numbers or know really big formulas. There are no formulas to solve hard maths problems you’ve never seen before.
You know that to solve difficult problems you have to think laterally, think creatively, find different approaches, ask what’s going on, ask why –– until you break through the barrier, and find an insight that illuminates the problem. And then you have the idea, and you get the answer.
Well, unless it’s one of those dastardly trick questions — but otherwise, you’ll get it!
Many people don’t really understand what this sort of mathematics is about. But when you do understand this, you also understand what wonderful achievements we are recognising tonight.
Because what does it look like from the outside, as you blaze through the Australian Maths Competition? From the outside, all someone sees is you sitting at a desk working with pen and paper. Or maybe even a pencil.
But from the inside? From the inside, it’s an epic struggle against a series of increasingly powerful adversaries, a struggle so great that most of the time you can’t even see what you’re struggling against.
There’s a good pop culture reference that for what’s going on here. I think some of our prizewinners might be a bit young to know it, but most of the parents here should know about it.
What they’re doing looks passive from the outside; but it conceals a great adventure going on in an inner dimension, a virtual dimension, on the inside. While they’re plugged into these problems their minds exist solely in this inner, virtual dimension.
Just like… the Matrix. That’s right parents, your children, in taking on these maths problems, are essentially heroes in the Matrix.
Well — except without the violence, without being trapped in a computer simulation where you’re enslaved by killer robots — but apart from that! And in fact, on the contrary, in solving these problems, you learn critical thinking skills that will help you be a better citizen.
So while you thought your children were just solving maths problems, actually they were taking on the Matrix using nothing but their own minds. They are all The One.
Neo’s got nothing on that. But of course Neo wasn’t doing mathematics.
* * *
I think that the Matrix is a pretty good analogy for how we ought to think about solving maths problems. But, to be frank, our society tends to think of solving maths problems rather… differently.
We live in a society where it’s socially acceptable, even normal, to declare “Oh I hate maths!”
How often do you hear, on the other hand, someone say: “Oh I hate geography! I was never any good at it!” If someone’s going on a holiday to a different country, people don’t blurt out how they never heard of that place and don’t really care about it but they just hate the whole subject and then they rant about a teacher they didn’t like. No, that usually doesn’t happen. But if anyone mentions maths, you watch how quickly, and how often, this happens.
If someone does admit their ignorance of geography, they’re generally ashamed of it — ignorance is not socially acceptable. But sadly, sometimes it is with mathematics.
Mathematics is the most feared subject around. There’s even a psychological condition known as “mathematical anxiety”, where people have such fear and loathing of mathematics that even the mention of it can fill them with anxiety of such a level that it requires counselling.
Well, what mathematical problem-solving means to me, and what I learned through mathematics activities like the AMC, is that one can take a mathematical problem, and play with it.
To play is to not be afraid, to not worry about grades, but simply to explore.
Fear breeds anxiety, suspicion, and hostility; but play breeds joy, fun, and imagination.
One traps the mind; the other — frees it.
And our prizewinners tonight have such free, dexterous, resourceful minds as to succeed against some devilishly difficult problems.
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For myself, it was through problem-solving that I saw how interesting, surprising, and creative mathematics could be.
Along the way I learned astounding facts. I learned that the square root of 2 is not a fraction. I learned that I could add as many numbers as I wanted by clever tricks. I learned not only what Pythagoras’ theorem is, but why it is true. These were not only some of the most surprising things I’d learned, but also the most certain facts I had ever known.
In high school I did the Australian Maths Competition, and the enrichment programs run by the Australian Maths Trust and Olympiad Committees. The problems got harder, the challenges became tougher, the mathematics became more interesting. I understood why the philosopher John Locke described mathematical proofs as “like diamonds:” they were very hard, and very clear — brilliant.
OK, well, my proofs were not always very clear. As diamonds went they were sometimes pretty opaque. Or maybe they were just rocks.
I eventually made it into the Australian team for the International Mathematical Olympiad. I went overseas twice representing Australia. I got a bronze and then a silver medal.
Studying other subjects, like chemistry and physics, I learned that mathematics underlies them. I learned, in fact, that at the deepest levels the laws of our universe appear to be mathematical in nature. In learning mathematics I was not only learning something that was wonderful, creative and surprising: I was also learning the ideas which run the universe.
I learned about why things are the way they are, the forces that shape our world.
For me, this applied whether those forces were mathematical, or not –– they apply as much to history, to society, as to mathematics.
I went on to university. I wanted to learn everything. I studied… maths, of course. But I also wanted to learn the laws of the universe. So I studied physics. And I wanted to learn the laws of our society. So I studied… law.
Now, there may well be a few parents here who are lawyers, but I’m sure that they would agree that the law is not exactly a very… mathematical kind of thing.
But in fact, in addition to being a mathematician, I’m “almost” a lawyer. For me, they are both about understanding how the world works — just at different levels. Well, you can’t change physical laws, but you can change law laws –– just as well, because the law is sometimes not very logical! Or very good!
But it turns out that you can use the critical and creative thinking skills that you learn in mathematics everywhere you look. Even in the most unlikely places… like law.
After I finished my degrees I went overseas to do my PhD in mathematics. I went to Stanford University, which is in California. There are a lot of good mathematicians at Stanford University and it was good to learn from them. Also, one good thing about studying mathematics is that you can do it anywhere. Also, one good thing about California is that it has a lot of beaches. Lying on the beach can be “working on my PhD”, sure it can.
From there I went to do research in mathematics in France, and then in the US again, in Boston — and then I came home. I now work at Monash University.
So now, when you finish school, you can study at Monash from their excellent maths department.
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So, being a mathematician is pretty good. You get to do maths problems every day. You get to decide what you want to work on, each day. Not many jobs are like that. When you like to play with maths problems, then the job of a mathematician is basically always playtime.
Mathematics can be put to many uses, for better or worse. It’s used to land a spacecraft on a comet hundreds of millions of kilometres away; to contain the spread of disease; to protect your communications; to model the climate; and much, much more. At the same time, it’s also used to design lethal weapons; to eavesdrop on your communications; and bad mathematics played a role in causing the global financial crisis.
All of you winning awards tonight have got some wonderful gifts. It’s worth asking: what is the best use you can make of your talents, for yourself and for others?
Now –– and this is especially for parents –– while I’ve said that not everyone treats mathematics with the respect it deserves, there is one particular group that does — employers! So, parents –– If you’re worried that your children won’t get a job because of studying a subject which isn’t always directly applicable to the real world, I refer you to the Wall Street Journal list of “Best Jobs of 2014”:
Number 1, mathematician. (It’s nice to be on top.)
Number 2, university academic. That include university mathematicians, you know.
Number 3, statistician. A different kind of mathematician.
Number 4, actuary. A specialist mathematician, important in insurance companies.
So — Want to explore interesting problems, challenge yourself, learn amazing things — and, as it turns out, have the best economic prospects?
Then have I got the subject for you!
And lucky for all of you, you’re all winning prizes in it.