When I was growing up, I knew I wanted to be a mathematician, but I had no idea what that entailed.
I always liked numbers.
One can think of any given axiom system as being like a computer with a certain limited amount of memory or processing power. One could switch to a computer with even more storage, but no matter how large an amount of storage space the computer has, there will still exist some tasks that are beyond its ability.
I often don't know what I'll be working on next year or a year from now. There is often a chance meeting, or something that I worked on 10 years ago suddenly becomes important again.
When you're concentrating hard, hours can fly by, and it's just you and a math problem.
A lot of the math that I do, it's not sort of premeditated. I talk online or with a colleague, and I get interested, and I just follow where it leads.
I remember having this vague idea that what mathematicians did was that some authority, someone, gave them problems to solve, and they just sort of solved them.
I always liked situations where there were very clear rules of what to do.
In 1992, when I was 16, I moved to the United States to start working on my Ph.D. at Princeton University in New Jersey.
My life is more than just my work. I am a husband and a father and a proud citizen of two countries: my homeland of Australia and my adopted country here in the United States.
I have been lucky to find very good collaborators who have taught me a lot, have introduced me to several new fields of mathematics, or have shown me new insights.
I tend to change research direction every few years or so.
I recall being fascinated by numbers even at age three and viewed their manipulation as a kind of game.
I am still very fond of Australia, but my life is now in Los Angeles.
Math education has changed over the years. In the 19th century, they taught spherical trigonometry because one of the biggest applications of mathematics was navigating the ocean. This is no longer so relevant.
Can you make fancy patterns of water that actually have some computation power? I'm betting that fluids are complex enough to do this.
Mathematicians are fairly cheap.
What interests me is the connection between maths and the real world.
I don't like accepting things at face value.
It is very humbling to receive the Fields Medal. The words of a Fields Medallist carry a lot of weight within mathematics - for instance, in framing future directions of research - which means that I have to watch what I say more carefully now!
