Terence Tao

The problem with mathematics is that it's not a spectator sport. You can't just watch someone else do it and expect to understand it.

The 'difficulty' of a problem is often a subjective measure, depending on the tools and techniques available to the solver.

One of the great things about mathematics is that it's a cumulative subject. You build on the work of others.

The best way to learn mathematics is to do mathematics.

Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding.

The goal of mathematics is to understand, not just to calculate.

The beauty of mathematics lies in its simplicity and its power.

Mathematics is the language of the universe.

The most profound insights often come from looking at old problems in new ways.

Don't be afraid to make mistakes. They are an essential part of the learning process.

The journey of discovery is often more rewarding than the destination.

Mathematics is a creative art, not just a logical one.

The power of abstraction is one of the greatest tools in mathematics.

It's not enough to just know the answer; you have to understand why it's the answer.

The best mathematicians are not necessarily the smartest, but the most persistent.

Mathematics is a conversation, not a monologue.

The true joy of mathematics comes from the moment of understanding, the 'aha!' moment.

The more you learn, the more you realize how much you don't know.

Mathematics is a tool for thinking clearly about complex problems.

The most elegant solutions are often the simplest.