Science & Tech

Math Fails

Terence Tao

Lesson time 08:46 min

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.

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Topics include: Math Fails Embrace Failure Failures Are Clues Failure Is Cheap Eureka!?


[MUSIC PLAYING] - Trial and error is one of the most important aspects of problem solving. It's one that you often don't see when you see a problem solved presented in a textbook or class or research paper. The tendency is almost always to only present the correct solution, the one that worked. And you don't see the outtakes, which is a shame, actually, because that's often the most informative part. We don't often show our embarrassingly stupid first attempts at solving a problem. But it is extremely important. And you need to have the freedom to try things that are potentially stupid. Well, of course, A, they might actually work. But, B, because the way in which they fail is often very instructive. It gives you clues to figure out what the solution should be. I think the physicist Niels Bohr once said that an expert is someone who has made all the mistakes that can be made in a very narrow field. The only reason why experts seem so competent is because they've already screwed up in every conceivable way, that they know how to not do that in the future. [MUSIC PLAYING] I must confess that my first one or two years in graduate school was not super productive. I did some math. And I took some classes. But I did spend too much time doing computer games and discovering the world wide web, which was very recent at that time. So about halfway through graduate school, there was this rather intimidating exam, which we call the general example, or the generals. It's a two or three hour oral exam where you pick three topics in mathematics. And three faculty in the department-- they quiz you about these topics. And if you get the questions right, they ask you even harder questions. If you get them wrong, they ask you easier questions. Most of the other students in my class-- you know, they spent months and months practicing this. They had-- they quizzed each other. They had these mock general exams. I basically studied a little bit, maybe for a few weeks. But I'd figured I would wing it. I did not do very well. My knowledge was very superficial. Whenever there was a follow-up question, I could not provide a good answer. And the questions became easier and easier. And I could barely solve most of them. The only reason I even passed the exam was because the one topic which I thought was the most challenging for me was the only one I actually tried to study for. And that one I actually managed to answer enough correct questions that I could pass. But my graduate advisor afterwards took me aside and said he was quite disappointed in a very gentle and encouraging way and that I really should try to do better. I was used to doing well in mathematics without working super hard. And so it was a shock to me to realize that that mode of thinking had limits, that you had to think more systematically. You have to actually plan your study. You have to actually learn from your mistakes. And so, yeah, those was important l...

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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