Science & Tech
Finding Strength in Numbers
Lesson time 08:20 min
Math has evolved into a team activity, and being open to input from others is key to success. Terence explains how he leans on research from fellow mathematicians—and how students and peers interact with him in the same way through blogs.
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Topics include: Finding Strength in Numbers The Power of Collaboration Divide and Conquer Crowdsourcing The Erdos Discrepancy Problem Sharing Victory
[MUSIC PLAYING] - I think mathematics, like any other discipline, it's actually a very social discipline. In the past, maybe we were-- mathematics was conducted by isolated people in rooms, you know. We would just work for months or years on a problem. But nowadays, it's a much more social process. Problems in mathematics or in other disciplines are so interdisciplinary that we need to communicate with other people. One of the great advantages of working with someone who has a slightly different skill set than you is that you get to learn their toolbox. I didn't used to use numerical simulations very much in my work. I would much rather work things out by pen and paper than to write a little computer program to do things for me. But I've worked with people who are very, very good at simulations. And it was quite informative to actually see these graphs and figures come up, almost in real time. Some people were just extremely fast. That is the future of our field. Mathematics used to be a very individual activity. People used to just work in isolation. But nowadays, it's much more common to collaborate. I really enjoy collaborating with other mathematicians. It brings out, I think, certain modes of thinking that are more difficult to express when you're by yourself. It's good to explore complementarity. I like to say that a good collaboration should involve at least one optimist and one pessimist. The optimist keeps dreaming of new ideas and sort of these blue sky approaches to your problem. And the pessimist's job is to shoot down the crazy ones, the crazy ideas, but keep the sane ones. And if you have too many optimists or too many pessimists on a project, it doesn't work. A mix is good. Diversity is always good in a collaboration. Sometimes in a collaboration, you try to assign precise roles to people. But I find it's best-- just let things flow naturally. There were two famous mathematicians, Hardy and Littlewood, who wrote down what are called the Hardy-Littlewood rules of collaboration. One of them is that once you agree to collaborate, you do not try to ascertain whether the work was divided fairly. Everyone just does what they feel is appropriate. It's never very productive to try to ascertain, you know, oh, you did 30% of the work, you did 60%. If two people work on the same project, it's not like they get half the credit each. They each sort of get full credit for the paper, at least in principle. I think technology has really changed the way we can collaborate. But now we can crowdsource many types of mathematics. The problem can be split up into many, many different pieces. And you can have large groups of people work on each individual piece and almost have an assembly line. You see this phenomenon throughout science, actually. Amateur astronomers can discover comets. Biologists employ amateurs to try to solve protein folding problems. And we are just at the cusp in mathematics of also being able 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.
Featured Masterclass Instructor
World-renowned mathematician Dr. Terence Tao teaches you his approach to everyday problem-solving—without complex equations or formulas.Explore the Class