Terence Tao

I still remember the realization in college at Flinders University in Australia that mathematics was not just an abstract game of symbols but could be used as a tool to analyze and understand the modern world.

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.

For me, I guess the main motivation is the satisfaction of finally understanding some tricky mathematical concept or phenomenon and then explaining it to others.

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 recall being fascinated by numbers even at age three and viewed their manipulation as a kind of game.

Talent is important, but how one develops and nurtures it is even more so.

When I was growing up, I knew I wanted to be a mathematician, but I had no idea what that entailed.

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.

When you're concentrating hard, hours can fly by, and it's just you and a math problem.

Math research is more like a marathon.

If I experiment enough, I get a deeper understanding.

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 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.

There might be a hidden structure in pi that we simply haven't discovered.

If there is something that I should know how to do but don't, it bugs me. I feel like I have to sit down and work out exactly what the problem is.

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.