Science & Tech
Lesson time 07:44 min
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.
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Topics include: Demystifying Math Is There a Math Gene? Abstraction Math Is a Language Math Makes the World Less Scary
Teaches Mathematical Thinking
World-renowned mathematician Dr. Terence Tao teaches you his approach to everyday problem-solving—without complex equations or formulas.Sign Up
[MUSIC PLAYING] - There is a perception that mathematics is some sort of sorcery. You're taught this whole book of magic spells, that if you want to solve a quadratic equation, you invoke the quadratic formula. And you write some arcane symbols, and you solve the equation. But often you are taught to apply these rules without really understanding why they work. And as a consequence, maybe you're afraid to deviate. If you do anything which just doesn't follow the recipe, maybe it'll be a disaster. Mathematics gives you a way of solving problems. It's a way of thinking. It's a way of systematically taking a complicated problem, breaking it up into simpler pieces, working on each piece separately, and then putting them back together again, which is most effective for very abstract quantitative problems. But it's also a useful skill in the real world. [MUSIC PLAYING] Are there people who are naturally good at math and some people who are hopelessly bad at math? I don't think so. I think everyone has an innate mathematical talent. You can see it in children. They ask questions about numbers and shapes. There's a result in mathematics that all children or many children discover by themselves, and in fact they teach other children this one fact. And it's the fact that there is no largest number. And the way children realize this is at school they sometimes play this game, who can name the larger number. So they say oh, one million, and the other child says, one billion. But eventually they figure out that no matter what enormous number the other child names, they can just say plus 1. You get that? Whatever you said plus 1, and that's a bigger number. And once they realize that, they realize that there is actually no biggest number. And in doing so, they have actually discovered a very important technique in mathematics. It's called proof by contradiction. Proof by contradiction is when a proof is established by showing that if the opposite were true, it would lead to an impossibility or contradiction. If you want to show that something can't happen, for example, that there's no largest number, you assume that there is a largest number, and then you show that that leads to a contradiction. That if someone says, oh, the largest number is so and so, you just say plus 1. Okay. It is not the largest number. That is an example of a mathematical technique which is often very challenging for even undergraduate students to grasp when they're taught it formally. But children in schoolyards can actually pick up this concept just by playing a game. Everyone has an inbuilt mathematical intuition. It's obvious to everyone if you have a pizza and you share it among four people, everyone gets a smaller piece than if you shared it among three people. That's a very basic mathematical fact. And it's something that we all understand. The main reason why people think they are bad at math or they don't have the math gene, whatever, ...
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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World-renowned mathematician Dr. Terence Tao teaches you his approach to everyday problem-solving—without complex equations or formulas.Explore the Class