I gave the keynote speech at JD's old high school on Wednesday. I shall record the speech here for posterity.
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| Me, with the guy the high school is named after. |
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What an honour to celebrate you, [science high school] students, staff, parents. This school has a special place in my heart, because my own child graduated from here three years ago, and [science high school] put him on a path for success in university and beyond. Special thanks to [retiring principal], who has done so much good for this wonderful school.
I am a mathematician. When I was in high school, I didn't really know that my current job existed. I knew about maths teachers, but I didn't realise how much maths there was in the world.
I remember showing up to the first day of a high school calculus class. The teacher, Mr Peahrson, welcomed us to the FUN ZONE.
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Yes, we all kind of snickered at that, just as you did. But he called us on it. He said, you wouldn't be here if you didn't think mathematics was fun.
And I peered deep into my teenage heart and realised, maths IS fun.
Accepting that, following maths where it led me, I am now a mathematician full time. Now, not all of you will get to be mathematicians full time. But I hope you'll also find fun in your futures.
Since I have you captive for about ten more minutes, I'm going to give you three pieces of advice. First, keep learning, and develop the unique talents you have, and the courage to use them. Second, lift others. And third, get back up again.
First, develop your unique talents, and have the courage to use them. Some of my research studies mathematical knots. These are just what you think they are -- start with a shoe lace, tie it up in a knot, then fuse the ends together. That is a mathematical knot. The mathematical question is, can you untie the knot without cutting it? This is actually a hard question. A similar question: if the person sitting next to you has also created a knot, how do you know whether your knot and their knot are the same? You can move the string around to try to make it look like theirs, but if it doesn't look like theirs, is it because your knots are different? Or because you haven't yet moved the string correctly? How do you know when to stop trying? These are actually quite difficult mathematical problems.
One of the first people to study knots was the physicist Peter Guthrie Tait, who in the late 1800s started classifying knots. There was a theory at the time that the fundamental building blocks of the universe were "knotted vortices in the ether" -- whatever that means. So Tait thought that by classifying knots, he was building a periodic table of the elements.
Well, it turns out that atoms are the fundamental building blocks, and not knotted vortices in the ether, but Tait's work still was very important, as it laid the foundations of a new mathematical field. By the 1960s and 1970s, hundreds and thousands of knots had been classified, due to work of people like Tait, Mary Hasemeyer, John Conway, and others. Let me mention John Conway in particular. He was a Princeton mathematician who studied tangles. He had a knot named after him: the Conway knot. Its simplest presentation has 11 crossings. This takes us up to about the 1970s.
Fast forward to 2020: We now know that knots give insight into 4-dimensional space. It is easy to imagine 3-dimensional space: we can move through three dimensions, rotate and handle objects. It isn't as easy to understand four dimensions. Knots give some insight. Some, but not all, knots are slice, meaning they are the slice of a knotted 2-dimensional sphere in 4-dimensional space ....
That's pretty incomprehensible, but the point is, they are important! They detect 4-dimensional maths.
Is the Conway knot slice? Whether or not a knot was slice was known for all the knots up to 10 crossings. But no one could figure out the Conway knot, for decades. In the late 2010s, a postgraduate student, Lisa Piccarillo at the University of Texas, heard a talk about this problem and wondered, could the new maths invariant that I've been working on answer this question?
So for a couple of evenings, in her spare time, she tried out her invariant, and within a few days she had an answer:
NO.
No it is not slice.
This was a huge discovery! It was widely publicised, including written up in a Quanta Magazine article. In the corresponding research paper, Lisa Piccarillo states that no one has made any progress with the Conway knot. Instead, she shows that there is another knot -- now called the Piccarillo knot -- and Conway is slice if and only if Piccarillo is slice.
Piccarillo is not slice.
Long story. Great ending.
Advice: Use your own knot.
Develop your own skills to face challenges from your own perspective. You have unique ideas and skills. Build these. Train them. Keep learning. Become a person who sees a challenge and asks, can my tools address that? And then try it!
Advice number two. Lift others. It is so easy to tear down. But there is so much good to celebrate.
From 2020 to 2023 I was the Associate Dean of Research of Monash Science. Basically that means I was the champion of all scientific discoveries coming out of Monash Science for three years, and an advocate for research across all of Monash. I got to learn about all the amazing things happening in Science right now!
For example, there are Monash chemists who are developing new sources for clean energy. Monash physicists are progressing quantum computers, and astrophysicists are learning how stars form and explode. In earth, atmosphere, and environmental science, Monash is leading a team across all of Australia to model weather of our changing planet. In maths, we are calculating the mathematics of heartbeats and disease spread, in addition to the 4-dimensional knotted surfaces that you now know all about. In biological sciences, they are tracking birds and plants, and learning tools for staving off extinction. And that is just Science! Engineering, medicine, pharmacy, economics, business, arts -- we are making huge rapid knowledge advances.
This is an amazing time to be young, stepping into a future of so much possibility!
This is also a frightening time to be young. There are social, geopolitical, and environmental challenges that we are facing that are bigger than what one person can tackle alone. We need people with us. We need to support each other, to support all the good that needs to be done.
It is so easy to tear down. But instead, build up.
As you develop your unique talents, help others develop theirs. Work with them.
I am currently the President of the Australian Mathematical Society. In that role, I attended a meeting a few months ago in which Distinguished Professor Ian Chubb, who was Australia's Chief Scientist from 2011 to 2016, gave a presentation. He shared concerns that many people didn't understand the breadth and depth and good that science can do, especially in tandem with others from the social sciences, arts, law, etc. Science is being devalued.
I raised my hand and asked, what can I do? What can we do? The Australian Mathematical Society has over 1000 members, who have all signed up because they love maths and want to help. What can we do?
His response, in my words, was: Never pass up an opportunity to lift science, to promote science.
Lift science. Lift others. When you find yourself with unique tools to solve the world's challenges, help others to see and solve them with you.
Advice number three: Get back up again.
You will fail. It will hurt.
Tonight is a night of well-deserved celebration. We are celebrating your wonderful accomplishments and your success. But you will not be successful if you do not fail.
I'm a pretty fancy person -- Associate Dean Research, President of the Australian Mathematical Society. But I fail all the time. Grant denied. Paper rejected. Team member doesn't get the job -- my people fail too, and it hurts. Parents -- you know what I mean. You watch your child work so hard for something that doesn't come through, and it hurts, sometimes more than your own failure.
On the same note, but slightly different story, a couple of weeks ago I took the bus from the Huntingdale station to Monash. As I stepped off the bus, I tripped, and fell. I watched myself keep falling, almost in slow motion, superman style, until I was sprawled across the bus stop, hundreds of people watching. I was mortified. I really wanted to roll back into the bus and go home. But of course I didn't. I had to get up, dust myself off, and go be fancy again.
When you fail, grieve, but then dust yourself off, look back to see if there is something to change, and then move forward again.
It is the end of the semester. I am cleaning out my office. I have recently recycled stacks of failed calculations. I have been trying to understand a certain problem, and it looks like finally, we do have some answers. But there is nothing like a physical stack of failure to help you realise how important failure is to achievement.
Get up again.
In summary, first, develop your unique talents, and have the courage to use them.
Second, lift others. Lift science. Work with people.
Third, get back up again when you fail.
You have an amazing future in front of you -- with challenges -- but opportunities the world has never seen. I wish you all the best in an amazing future.
