Science & Tech


Terence Tao

Lesson time 06:43 min

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.

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Topics include: Stumped When You’re Stuck Overcoming a Mental Block Getting Stuck Is Normal Letting Problems Go


INSTRUCTOR: The natural state of a research mathematician is to be frustrated, to be stuck. We are always surrounded by problems that we would love to solve, but we can't. Sometimes, it just tells you the problem is it's not ready. It's before it's time, and progress on some other problem has to happen first. This is one thing, by the way, that computer games have taught me. There are many computer games, where you know that your treasure lies behind the door, but the door is locked. So you need a key, so you just-- you're stuck. But the moment you find a key, you know, then you race back to this door, and you can unlock the door hopefully. It is very satisfying sometimes to pick up a problem that you couldn't solve 10 years ago, and now, there's more tools. There's more technology, and the problem gets solved. There are problems, which I've spent years working on and not having the right idea for many, many months. But the process of trying things and seeing why they didn't work, again and again, was instrumental. When I, finally, found the approach that did work, all the partial successes I had before, which weren't enough to lead to a full solution, they often came in very handy at the end, and often, things snowballed. Sometimes, solving a tough math problem is like trying to budge a door that's stuck, and you keep slamming your shoulder against it. And it doesn't move, but every time you do it, it loosens the door a little bit. And then, when you, finally, find the right way to hit it, it falls open, and you just stumble through. When I was a graduate student, I was always impressed when I worked on a problem. I would spend a week bashing my head against it, trying all kinds of things, and I would show what I did to my advisor. And he would think for a few minutes and say, oh, you know, this problem you're facing, it reminds me of what so-and-so did in this paper. And he would go to his filing cabinet, and fish out a little pre-print and say read this. This paper had the same issue that you had, and their solution would probably work for you as well. And I would go home and read it, and he was usually right. The techniques they had solved the problem that I spent hours working on, and what this showed me is that, often, experience trumps energy, that, if you know what to do, you can save yourself a lot of effort. As I get older, I find myself have less energy. I can't spend hours and hours on a single problem, like I used to. But I can often see the connections to an existing problem. I can use my experience a lot more effectively than I could before. Sometimes, a task is just too big and scary to even get started, and you have to mentally break it up into smaller pieces. There was once a project, where the five of us were working on a quite hard problem, and we had thought we had solved it very early on in the process. We worked together for just a few weeks, and we had this method. And it seemed t...

About the Instructor

A MacArthur Fellow and Fields Medal winner, Terence Tao, PhD, was studying university-level math by age 9. Now the “Mozart of Math” is breaking down his approach to everyday problem-solving—without complex equations or formulas. Learn how to deconstruct challenges, use storytelling as a tool, and discover solutions, whether you’re trying to level up in a computer game or just catch your plane on time.

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Terence Tao

World-renowned mathematician Dr. Terence Tao teaches you his approach to everyday problem-solving—without complex equations or formulas.

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