Science & Tech

Choosing the Problem to Solve

Lesson time 11:50 min

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.

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Topics include: Choosing the Problem to Solve Asking the Right Question Problem-Solving and Rock Climbing Creating Bite-Size Problems Group Testing

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

[JAZZ MUSIC] - If I were to summarize what makes a good problem, it should just be beyond your current range of capability. It should have maybe just one difficulty that you don't quite know how to solve, but every other aspect, you have some idea of how to proceed. Hopefully, the question has some connection to some intuition that you already have. So like, many questions have a geometric flavor, and so you can use your special intuition. Some people are naturally very good at numbers, and so actually having a question with a lot of numbers in it, you can leverage your intuition. So it has to match your skill set. And it's not so much whether you succeed or fail at the question, but it's whether you can learn something from it. [JAZZ MUSIC] The ability to ask the right question and to frame it in the right way, I think, shows up all over human endeavor-- not just in mathematics. Just to give you one example, there was this airport that had received a lot of complaints about people having to wait for their luggage to arrive. So they tried to solve the question of shortening the time between the landing of the plane and the deployment of the baggage. But they found that the solutions they implemented didn't decrease customer complaints that much. And it turned out what they really didn't like was waiting at the carousel for the luggage to arrive. And actually, the solution was to take longer to walk from the airplane to the luggage carousel. So they put some partitions, so that they would feel like they are making more progress. And by the time they arrived at the carousel, the luggage would arrive shortly afterwards. And this reduced the complaints by quite a bit. So it is possible for your thinking to get stuck in a rut. You are so certain that a certain approach is going to work or a certain answer is going to be what you expect. So sometimes, asking the right question is key to actually getting a satisfactory answer. [JAZZ MUSIC] You don't want a problem that is too easy, that is too routine. You always want problems that are just barely out of reach of the known technologies. One analogy that many mathematicians use is to liken mathematical problem solving to climbing. In fact, many mathematicians are rock climbers. I myself am not, but many of my friends are. And actually, rock climbers-- they use some of the same language that mathematicians use. A difficult cliff is called a problem. And when you climb the cliff, you solve the problem. If you want to get from the bottom of a cliff to the top of a cliff, and you know, it's 30 feet high, you can't just go directly up there. That's not feasible. But you want to find some handhold or some ledge which is more feasible just almost within reach. You just need to stretch a little bit. And then once you're at that point, you identify the next step, which gets you closer to your goal-- but one which is just, again, just barely within reach. You ...

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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