# How a Math Algorithm Could Educate the Whole World – for Free

## Mathematics professor Po-Shen Loh has created Expii, a free education tool that democratizes learning by turning your smartphone into a tutor.

**Po-Shen Loh**, PhD, is associate professor of mathematics at Carnegie Mellon University, which he joined, in 2010, as an assistant professor in the Department of Mathematical Sciences. As a Hertz Fellow, Professor Loh received his PhD in combinatorics of the Pure Math Department at Princeton University. His thesis discussed several original results that he discovered during his graduate study in joint projects with his advisor and other collaborators. Professor Loh studies questions that lie at the intersection of two branches of mathematics: combinatorics (the study of discrete systems) and probability theory.

Prior to his work at Princeton, Loh received the equivalent of a master's degree in mathematics from the University of Cambridge (United Kingdom) in 2005, where he was supported by a Winston Churchill Foundation Scholarship. He received his undergraduate degree in mathematics from Caltech in 2004, graduating first in his class, and his undergraduate thesis later received the Honorable Mention for the 2004 AMS-MAA-SIAM Morgan Prize.

In his spare time, Loh has maintained his involvement with the United States Mathematical Olympiad program. He is now the head coach of the national delegation, as well as a lead fundraiser for the organization. As a high school student, he won a silver medal at the 1999 International Mathematical Olympiad (IMO), and following his win continued to be active in the training of high school students at the U.S. national Math Olympiad Summer Program. In 2004, he served as the deputy leader for the U.S. team at the IMO in Athens, Greece, where our national team placed second. After completing his PhD, Loh again, served as deputy team leader for the United States at the International Mathematical Olympiad from 2010 to 2013. Afterwards Professor Loh was promoted to national head coach of the U.S.A. IMO team, and on his second attempt, Team U.S.A. won first place, in a competition with teams from over 100 countries represented.

Earlier this year, Loh received an NSF CAREER award, the most prestigious NSF award for junior faculty, which honors outstanding research combined with a commitment to teaching. Professor Loh is the founder of the educational technology startup expii.com, a crowd-sourced platform for the world to share interactive lessons in math and science.

**Po-Shen Loh:** 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 to think that maybe I should do something with this. 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.

Unfortunately I had no money, no connections and only one person. So the only thing I knew was mathematics, algorithms and this probability and network theory. 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 smart phone. This is actually the project I'm working on right now called Expii.

Our principle is that actually you could turn that smart phone into a virtual tutor which automates what a person would get if they hired a tutor. It wouldn't be as good as a tutor, but it could get very close. And if you could deliver a free almost tutor on every smart phone in the United States you might solve equity problems, you might be able to allow everyone, even if they live in a different ZIP Code, to be able to access this tutor, which previously had only been accessible to people who are quite wealthy. Because today the cost of a tutor is in the $30 an hour, $20 an hour, $50 an hour depending on how you look at it. If you can reduce that to zero dollars an hour you would actually open up this accessibility to everyone.

If we realize that what we're trying to build is this virtual tutor then you actually, again, can start to conceptualize well knowledge happens to be all of these concepts linked together in this network. Then the problem becomes if you have this network how do you mathematically analyze where a person should go next? That can be done by using probability and statistics to find new ways to measure how much each person understands about each concept. Statistics, because the way that one would measure this is by asking them questions.

The experience someone has is they indicate what they want to learn and then the system starts to pitch questions at them, questions that they would need to know how to answer in order to understand what they claim they want to understand. As the questions come, based on people's responses to the questions, the system adjusts the difficulty of the questions and where the next questions come from in the same way that a human tutor adjusts their line of questioning based on whether a person is successful or not successful at the previous question. If the student reaches a point where they are hopelessly confused, meaning they don't know how to do this question at all, then the system suggests that maybe they could read some explanations.

As you can see it turns the lesson flow upside down. It's not that the class comes first and then the homework and then the exam, the first thing that comes is the exam essentially followed by these practice problems, which adapt to you, followed by the class for anything that you don't know. The idea is that this should cure boredom at the high end and also cure confusion at the struggling end.

I actually started this with a brilliant Carnegie Mellon undergraduate student and then the two of us built this system together. But when you start with no resources you need to think of ways to actually generate all of this content in a way which doesn't cost enormous amount of resources. And we took inspiration from Wikipedia. Our system aggregates all of the questions and explanations that anyone in the world might want to contribute, uses voting like a website called Quora in order to find out which content is strong, and uses statistics, the algorithms, to figure out what questions are easy and difficult. So actually in the end it turns out that it sucks in all of this content, it licenses it all with the creative commons license like Wikipedia and then puts it all across on a platform that anyone with a smart phone can use.

So as we keep developing these mathematics and algorithms our goal is actually to deliver free education to all of the world using a system that self-organizes in the same way that mathematics self-organizes from its basic assumptions.

Po-Shen Loh is a Hertz Foundation Fellow, Princeton-educated mathematician, Carnegie Mellon professor, the head coach of the U.S. International Math Olympiad team, and now he’s adding start-up entrepreneur to his knock-out resume. Loh has created Expii, a math and science education tool that aims to turn every smartphone into a tutor. With the support of the Fannie and John Hertz Foundation, he pursued a PhD in combinatorics at the Pure Math Department at Princeton University.

The Hertz Foundation

mission is to provide unique financial and fellowship support to the nation's most remarkable PhD students in the hard sciences. Hertz Fellowships are among the most prestigious in the world, and the foundation has invested over $200 million in Hertz Fellows since 1963 (present value) and supported over 1,100 brilliant and creative young scientists, who have gone on to become Nobel laureates, high-ranking military personnel, astronauts, inventors, Silicon Valley leaders, and tenured university professors. For more information, visit hertzfoundation.org.# A new theory explains Jupiter’s perplexing origin

A new computer model solves a pair of Jovian riddles.

- Astronomers have wondered how a gas giant like Jupiter could sit in the middle of our solar system's planets.
- Also unexplained has been the pair of asteroid clusters in front of and behind Jupiter in its orbit.
- Putting the two questions together revealed the answer to both.

# Vikings unwittingly made their swords stronger by trying to imbue them with spirits

They didn't know it, but the rituals of Iron Age Scandinavians turned their iron into steel.

*Shutterstock*

- Iron Age Scandinavians only had access to poor quality iron, which put them at a tactical disadvantage against their neighbors.
- To strengthen their swords, smiths used the bones of their dead ancestors and animals, hoping to transfer the spirit into their blades.
- They couldn't have known that in so doing, they actually were forging a rudimentary form of steel.

# Develop mindfulness to boost your creative intelligence

Sharon Salzberg, world-renowned mindfulness leader, teaches meditation at Big Think Edge.

- Try meditation for the first time with this guided lesson or, if you already practice, enjoy being guided by a world-renowned meditation expert.
- Sharon Salzberg teaches mindfulness meditation for Big Think Edge.
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