Science & Tech

Solving Problems With Story

Lesson time 09:34 min

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.

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Topics include: Solving Problems With Story Good Guys and Bad Guys Good Stories Come From Dumb Questions Good Narratives Bad Narratives Error Tolerance

Terence Tao

Teaches Mathematical Thinking

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

Preview

[MUSIC PLAYING] - One thing that surprised me, and I had to learn somewhat late in my medical career, is that the solution to mathematical problems often goes through narrative, through storytelling. I thought that mathematics was a very impersonal subject, where you just present equations and theorems and arguments without context. But actually the context is very important. The key is often to tell a good story about it. Mathematical narratives take abstract mathematical problems and add real-world context. It can help you see that your goal is more than just solving for x. Making a problem fit into the context of a relatable story can also give you insight or clues about it. It helps the viewer understand what's going on if there is a protagonist and an antagonist, if there is some goal to solve, there's some obstacle. Framing things in a way which has a narrative to it, it activates certain parts of your brain. [MUSIC PLAYING] If you want to develop your skills to find analogies to see connections, basically the most important thing is to ask questions. And the dumber the question, the better, really. So to give you one simple example from arithmetic, when you multiply two negative numbers together-- let's say, negative 3, negative 4-- you get a positive number, plus 12. But that's not very intuitive to many people. To many people, two negative numbers should combine to form another negative number. And so you can ask, is there some analogy you can use to pursue this? So you can maybe use an economic analogy. So if you want to multiply 3 times 4, you could say, okay, suppose I am being paid $3 an hour to do something and you work for 4 hours. So every hour you get $3. And after 4 hours, you get $12. Fine. But now suppose, instead of being paid $3 an hour, something is costing you $3 an hour. Maybe you're running water or something or electricity, and it's costing you $3 an hour. So after 4 hours, this will cost you $12. So this is why minus 3 times 4 is minus 12. So you can ask, how can I push this analogy further? So then you can ask, how do you interpret minus 3 times minus 4. Well, suppose your water is running or something, and it's costing you $3 an hour. But you manage to shut off the water for 4 hours, so you have saved 4 hours of expenses. And so you have saved $12. And this is why minus 3 times minus 4 is plus 12. So by exploring this analogy and just asking questions-- what does this mean, what does this mean in this analogy-- you can gain a sense of what multiplication of negative numbers really means. And your intuition is now better than it was before. [MUSIC PLAYING] It's actually very useful to anthropomorphize the mathematical objects you deal with. They're not just x's and y's. Often you will hear, if you listen to a mathematician talk about a problem, they might say that this is the enemy, and certain things are good guys. Maybe there's a certain powerful tool that we want to apply....

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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