# Practical Risk-Taking

listed in Fellows

One of mankind’s greatest strengths is our willingness and ability to take risks. Some of the risks are physical (mountain climbing, sky diving). Some risks are financial (buying a home, starting a business). And some are mental (developing a new product, innovating a better way to do something). The world would not be where it is today without risk takers willing to take a chance and try something different.

Mathematicians may not seem like risk-takers, but mathematical research actually focuses on challenging the foundational fabric of truth and reality. It may seem like everything there is to know about math is already known, but that isn’t true. Math offers a way to understand the logical framework of the world, which then contributes great insight to fundamentally transform other disciplines, such as physics and computing. And as our understanding of those areas grows and changes, so does our understanding of mathematical principles.

I’m a mathematician and a mathematics professor, and one of the things I’m most passionate about is helping to alleviate the fear, “I’m not a math person.” Math is all about decision making and analysis and everyone has those skills. The challenge with math is, that it’s based on a network of prerequisites. Math is one of those subjects for which the concepts are chained in sequences of dependencies, so if you miss a few concepts along the chain you can become completely lost. When there's this long chain of prerequisites, it makes the subject more fragile as you're learning it. I think everyone is—or can be—a math person. I believe that all that one has to do, is to go through the chain and fill in the gaps. If everyone was able to pick up those prerequisites then mathematics would change from being the hardest subject to the easiest subject.

As somebody who works on probability and statistics, I think about risks and risk taking—especially practical risk taking. I was driven to try practical risk taking through my connection with the Hertz Foundation. Once you are a Hertz Fellow you are forever a Fellow, and you stay connected to the Hertz Community. It’s an extraordinary group of people who provide an incredible amount of mentorship, guidance, and even encouragement to take whatever theoretical ideas you may have and turn them into reality for a practical impact. This is sometimes scary, especially if you're on the tenure track at a university, as I was.

The support of the Hertz Foundation and Fellows provided the encouragement as I launched a virtual mathematics tutor called Expii. Expii is an education solution that can be delivered for free on every internet enabled device around the world—to fill those gaps in mathematical knowledge and help even the learning playing field. Using algorithms that refine and personalize the learner’s experience, Expii is able to give anyone exactly the lesson they need at the time they need it. This personalization provides the learner with explanations or problems that are engaging and on their level, eliminating the common obstacles faced today when students are confused, but resource constraints do not allow them personalized attention. Expii works on all internet connected devices all over the world, crossing borders and overcoming barriers in education.

The Hertz Fellowship and connection with the Foundation, has always encouraged the importance of creative freedom, the power of the network, and the importance of choosing your own path, three tenets that guide my personal and professional life. I have always believed that you don’t need to “stay inside the lines” and follow the linear career paths of research, teaching, entrepreneurship, etc. Instead, you can combine different disciplines until you find what is right for you, as I did.

My own work in mathematics centers on an intersection of three fields: probability, theoretical computer science and algorithms, and combinatorics. I have applied the principles of combinatorics, which is the study of networks, such as social networks, the Internet, or networks of concepts, to education in novel ways which in turn established the theoretical foundation of Expii, emboldening me to take the practical risk of implementing the ideas for global scale.

If we don't take risks, we make only incremental progress as a human race. The least risky thing to do is to focus on incremental improvement instead of leapfrogging forward. In America, we are a culture that promotes risk taking. I think that's why we've made so many leaps because in this society it's actually okay to fail a few times before succeeding. The success is what leaves an imprint on future generations.

*Po-Shen Loh is an associate professor of mathematics at Carnegie Mellon University, which he joined in 2010. He is also the national coach of the USA International Math Olympiad Team, where he led the U.S. team to first place after a 21-year gap. Po-Shen Loh is the founder of expii.com, a free interactive website focusing on math and science in order to help students succeed. He has been recognized with several different awards, including an NSF CAREER award and the Morgan Prize Honorable Mention Award. He earned his undergraduate degree in Mathematics from Caltech, where he graduated first in his class. He earned his MA in mathematics from the University of Cambridge and his PhD in Combinatorics of the Pure Math Department at Princeton University.*