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Design Solutions Like a Mathematician: Watch and Practice

Po-Shen Loh explains how mathematicians boil a problem down to its essential elements.
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Ask the Cleanest Question: Design Solutions Like a Mathematician, with Po-Shen Loh, Associate Professor of Mathematics, CMU, and Founder & CEO, Expii Abstracting in Theory So mathematics is the art of asking this cleanest question. It’s actually the art of abstraction. I’m using that word because we’ve heard ‘abstract’ somewhere else before, too, in abstract art. Or if one even thinks about how art has moved or transformed, it’s actually had phases where people try to draw the essence of what’s happening. And this drawing the essence allows one to focus on what actually matters. If one works in say, design – I happen to work on the design of software products, the user experience design.
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When one thinks about this, one often goes through stages where you first have what’s called the low-fidelity design, where you just focus on what are the main components that should be there in the first place. And you do that first and keep working on that before you go eventually to the high-fidelity design, where you have all of the perfect graphics. And the reason for this is it can actually be a distraction early on to think about all of the frills and all of the additional pieces at the end. And if you go all the way out there on the wrong original construction, you’ve wasted an enormous amount of time. So when one is approaching a problem, often
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times the key questions are to ask: what are the main drivers? What are the main forces? What will cause success? What are the biggest impact factors? Of course, there might be a thousand impact factors, but maybe three of them are the biggest ones. And once you realize what are the most important ingredients, you start to think, well what can we do to most optimally address those components? And as you’ve built out the system then you’ve focused on the most important parts, and at the end you will create a solution which, ideally, addresses the other ones but in order of importance.
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Abstracting in Practice About three years ago I became the national coach of the United States International Math Olympian Team. I was very happy for a day, thinking this is very interesting. But the next day I started thinking maybe I should do something with this, and this is a responsibility to do something at the national scale. And I decided that I wanted to focus not only on training an elite group of students, but trying to do as much as I could to boost the baseline mathematics capability in this entire country.
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So after thinking for some time, I actually came to an idea which was based on using these core mathematical areas that I’d been working with to actually build a solution for education that could be delivered for free on every smartphone. This is actually the project I’m working on right now called Expii. And our principle is that actually you could turn that smartphone into a virtual tutor, which automates what a person would get if they hired a tutor. And this mathematical way of abstracting a problem is maybe also illustrated in the way that I chose to approach education, of saying, well, if we’re trying to deliver a virtual tutor, what are the real components inside?
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One is what are the concepts that people are going between, and the other is how much do they understand in each concept. And if you have both of these together, maybe you can turn it all into a math problem where you analyze those pieces. And yes, there will be all this other stuff like how the tutor talks to you, and what it looks like and what color it is, but those will go on afterwards after you have that core engine inside.

In this video, mathematician Po-Shen Loh explains how mathematicians boil a problem down to its essential elements. This approach can help you significantly in communicating with others about any complex problem and its possible solutions.

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  • What is Po-Shen Loh getting at with the example of abstract art? How does it relate to problem solving in general?

  • Consider a solution your company has implemented in the past. What were the core elements? The abstract skeleton? What were the secondary elements of the solution?

  • In the example above, did your company’s process follow the approach Po-Shen Loh outlines here? What were the results of the process you followed?

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