Mathematical problems, or puzzles, are important to real mathematics (like solving real-life problems), just as fables, stories and anecdotes are important to the young in understanding real life
The standard high school curriculum traditionally has been focused towards physics and engineering. So calculus, differential equations, and linear algebra have always been the most emphasized, and for good reason - these are very important.
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.
Can you make fancy patterns of water that actually have some computation power? I'm betting that fluids are complex enough to do this.
It was traditional to not actually cash the prizes that Erdos did award while he was alive. People usually framed the cheque instead.
You want to get to the top of the cliff. But that's not what you focus on immediately. You focus on the next ledge just beyond your reach, because you need to do one clever thing to get up there. And then, once you get there, you do it again. A lot of this is rather boring and not very glamorous. But you can't jump cliffs in a single bound.
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.
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 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!
I enjoy a good meal, a good vacation, or a good movie, much as anyone else would.
I was never very good at school with... humanities... anything which was more a matter of opinion.
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.
Most students who take math classes aren't going to be mathematicians. They're going to be engineers, statisticians - in many ways, that's the more important mission of math education.
Mathematicians are fairly cheap.
When I was seven or eight, whenever I was getting too rowdy at night, my parents would give me a maths workbook to work on to quieten me down.
The accuracy of Wikipedia can be dodgy in some places, but in maths, it's really quite good.
What interests me is the connection between maths and the real world.
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.
Research sometimes feels like an ongoing TV series in which some amazing revelations have already been made, but there are still plenty of cliff-hangers and unresolved plotlines that you want to see resolved. But unlike TV, we have to do the work ourselves to figure out what happens next.
