MasterClass: Terence Tao Teaches Mathematical Thinking

Terence Tao invites you to see math the way he does—as a beautiful piece of art—and encourages you to open yourself to a new understanding of mathematics as an accessible and exciting opportunity for exploration.

Looking back, Terence can’t remember life before math. He was always drawn to it and naturally loved it. In this lesson, he shares the inner workings of a mathematical life and the difference between mathematical competitions and research.

Terence explains that the outlook on math in education used to be that it was impractical; it was like learning complicated magic just to pass a test. He also emphasizes that anyone can lean into an innate ability to think like a mathematician.

Not every problem requires a formula or mathematical training to find a solution. Terence shows you how you can apply math in everyday situations, such as wine measuring, and offers suggestions for enjoying the process of learning.

Terence challenges you to choose problems just outside your range and shares a case study in which he applies math to make airports more efficient. This example illustrates how asking questions in a different way can help you make progress.

Using the analogy of a detective solving a mystery, Terence explains how curiosity and storytelling offer a creative approach to problem-solving. The process of elimination, building narratives, and asking questions are key to moving forward.

Visualization, thinking about a problem in a different way—sometimes even in a physical way—may help lead you to solutions. This process of transforming your thinking can help you move beyond the limitations of intuition and preconceived ideas.

Terence has always been drawn to imaginary scenarios that operate within a set of guidelines or rules. He demonstrates a puzzle and how it can actually provide a life-saving solution, and he converts a math puzzle into tic-tac-toe.

Forget the intense pressure of giving the correct answer on a school math test. Terence shares a personal life lesson to teach you that there is a benefit to failing: There may be clues in your failed process that lead to breakthroughs later.

As you pursue your understanding of math, you will likely encounter roadblocks in solving problems. Terence offers tips for unlocking clues and shares how gaining knowledge by directing your attention to other problems can bring you full circle.

Math has evolved into a team activity, and being open to input from others is key to success. Terence explains how he leans on research from fellow mathematicians—and how students and peers interact with him in the same way through blogs.

We are all part of a larger math story. Terence is one of many mathematical figures who influences our understanding of the world, and there will be many after him. The human tendency to ask questions means math and science are ever-evolving.