Terence Tao

In mathematics, the journey is often more important than the destination.

There are two ways to do great mathematics. The first is to be smarter than everybody else. The second is to be stupider than everybody else—but persistent.

The most useful skill a mathematician can have is the ability to analogize.

A proof is a story where the characters are mathematical objects and the plot is logic.

If you are stuck on a problem, explain it to someone else, even a rubber duck. Often, the act of explaining reveals the solution.

Mathematics does not consist of plugging numbers into formulas. It consists of grasping the relationships between concepts.

Theorems are permanent; proofs are ephemeral.

A mathematician is a device for turning coffee into theorems.

The heart of mathematics is its problems.

It is better to solve one problem five different ways than to solve five problems one way.

In mathematics, you should not say 'I don't know,' but 'I haven't found out yet.'

The beauty of mathematics only shows itself to more patient followers.

The greatest discoveries often arise from noticing something that everyone else overlooked because it seemed too simple or too obvious.

The objective in a mathematical proof is not simply to prove something, but to prove it in a way that illuminates why it is true.

There's a difference between not knowing and not knowing yet.

I believe that one of the reasons that the language of mathematics has evolved the way it has is to be able to facilitate these ‘chunking’ and abstraction processes.

The truth of a statement does not depend on how much effort was put into proving it.

In mathematics, there's a tradition of creating notational and conceptual frameworks that are so natural that they become invisible.

A good problem should be more than just a puzzle; it should connect to deeper principles.

One can roughly divide mathematical education into three stages: the ‘pre-rigorous’, the ‘rigorous’, and the ‘post-rigorous’ stages.