Terence Tao

The 'art of problem-solving' is a skill that can be learned and honed, not just an innate talent.

The 'value of failure' in mathematics is often overlooked; it's a crucial part of the learning process.

The 'interconnectedness of mathematical ideas' is one of its most beautiful and powerful features.

The 'future of mathematical research' will be increasingly collaborative and interdisciplinary.

The objective in mathematics is not to obtain the highest ranking, the most ‘likes’, or the most citations; it is to understand and to enjoy understanding.

Good mathematics is not about following rules, it's about creating and understanding new patterns.

I don’t have any magical ability. I look at a problem, play with it, work out a small example, and gradually I build up a solution.

The truth is, you don’t need to be a genius to do mathematics. You just need to be determined.

In mathematics, there's a difference between knowing the path and walking the path.

The 'soft analysis' way is to avoid hard estimates and instead focus on conceptual understanding and high-level structure.

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

The enemy of understanding is coverage.

It’s not about being the first to solve a problem; it’s about solving it in a way that adds to the tapestry of mathematics.

Mathematics is not a spectator sport.

A common mistake is to try to force a tool onto a problem, rather than letting the problem suggest the tool.

The most profound breakthroughs often come from seeing an old problem from a new perspective.

I often spend more time trying to understand the question than answering it.

In research, it's perfectly fine to work on problems you don't know how to solve. That's the point.

The goal of mathematics is to explain, not just to derive.

A good problem should be easy to state, hard to solve, and important.