Terence Tao
Talent is important, but how one develops and nurtures it is even more so.
I was never very good at school with... humanities... anything which was more a matter of opinion.
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 enjoy a good meal, a good vacation, or a good movie, much as anyone else would.
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.
I don't have any magical ability. I look at a problem, play with it, work out a strategy.
When you're concentrating hard, hours can fly by, and it's just you and a math problem.
If I experiment enough, I get a deeper understanding.
Math research is more like a marathon.
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.
There might be a hidden structure in pi that we simply haven't discovered.
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.
Mathematicians are fairly cheap.
When I was growing up, I knew I wanted to be a mathematician, but I had no idea what that entailed.
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.
Most of what I do does not save lives.
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 numbers.
I always liked situations where there were very clear rules of what to do.
It was traditional to not actually cash the prizes that Erdos did award while he was alive. People usually framed the cheque instead.
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.
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.
I think one nice thing about mathematics is that we don't really have one prize that dominates all the others, like the Nobel prizes.
The accuracy of Wikipedia can be dodgy in some places, but in maths, it's really quite good.
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.
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.
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.
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.
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.
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.
What interests me is the connection between maths and the real world.
If I don't understand something properly, every single component, it really bugs me.
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!
Education is a complex, multifaceted, and painstaking process, and being gifted does not make this less so.Collection: Doe
Ultimately you should follow advice not because someone tells you to, but because it was something that you already knew you should be doing.Collection: Advice
... it can often be profitable to try a technique on a problem even if you know in advance that it cannot possibly solve the problem completely.Collection: Math
Pointing out that countless great mathematicians had tried to solve the problem and failed before you came along is in particularly bad taste and should be avoided completely.Collection: Taste
Unsolicited surprise requests from strangers are essentially guaranteed to be met with a negative response.Collection: Negative
At a purely formal level, one could call probability theory the study of measure spaces with total measure one, but that would be like calling number theory the study of strings of digits which terminate.Collection: Probability Theory
Volume grows spatially slower than scaling.Collection: Volume