Math for the Real World

mathematician, Fred Roberts, real-world problems, applied mathematics — Fred Roberts

(Image credit: Carl Blesch, Rutgers University)

This ScienceLives article was provided to LiveScience in partnership with the National Science Foundation.

Fred Roberts is a professor of mathematics at Rutgers University and director of a center that employs data analysis to address homeland security threats. He is also director emeritus and senior advisor of an internationally renowned mathematical sciences research center established in 1989 to solve complex problems in information science and communication technology. Roberts' major research interests are in mathematical models in the social, behavioral, biological, environmental and epidemiological sciences, and in problems of communications, transportation and security. His first book, Discrete Mathematical Models, with Applications to Social, Biological and Environmental Problems, has been called a classic in the field and his books and articles cover a wide range of topics from energy modeling to mathematical psychology to biomath in the high schools.

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Under Roberts' leadership, DIMACS evolved beyond mathematics and computer science to encompass physical and life sciences, environmental sciences, social sciences, engineering, economics, agriculture and public policy. The interdisciplinary nature of the DIMACS faculty made it possible for researchers to see how mathematical solutions could be applied to problems such situations such as gene sequencing, evolutionary biology, epidemiology, sustainability, and homeland security.

In 2006, Roberts headed the first major DIMACS-hosted center to apply information science to maintaining homeland security. In 2009, he assumed his current position as director of the Command, Control and Interoperability Center for Advanced Data Analysis (CCICADA), a Department of Homeland Security University Center of Excellence with 17 partner organizations nationwide. His research interests in this field include stadium security, container inspection at ports, sensor management for nuclear materials detection, early warning of disease outbreaks and bioterrorist events, and homeland security aspects of global environmental change.

Well, the field has to be defined very broadly because although I was trained as a mathematician, I have a lot of hats that I wear and I work on all kinds of problems. I'm passionate about environmental problems. I'm interested in issues of sustainability and energy use and climate. I'm also very interested in connections between the mathematical sciences and the social sciences, so in my professional life I've worked on psychology and sociology and problems of how small groups work well together — or don't. I'm interested in issues of communication and transportation, and I've also gotten very much involved in issues of homeland security, natural disasters and protecting the safety of people. And, I'm passionate about applications and mathematics as the language of science. I was trained as a mathematician, I got interested in mathematics but I love it because of everything I can do with it.

Early on, my inspiration was as a child of Sputnik. It was launched when I was in high school, launched by the Russians and it was a big shock to the Americans because we thought we were first in science and first in space and so on. That had a lot of influence on us when we were high school kids and we were encouraged to go into science. I was inclined in that direction anyway, but certainly there was a little bit of a push from Sputnik. It didn't hurt that my high school math teacher knew some very distinguished mathematicians and, when I started looking for a college, I happened to find a college where one of those mathematicians was the chairman of the Math Department. That was Dartmouth College and so I went there thinking I would study mathematics and that's what I did. But, it wasn't the way I thought it was going to go — I got very excited while I was there about mathematics and its applications, particularly in the social sciences and ecology and so it took off from there.

If you're talking about advice about my scientific career, the best was "follow your passion and follow what you're really interested in" — and it's the same advice I give my kids. That is, you're spending a lot of the working and waking hours with the career that you choose, so if you don't choose a career you love, it doesn't matter how much money you make — that's not going to bring you happiness.

Well, I think that's the reason I'm doing research. I was one of the first people who worked on the growing demand for energy. We pinpointed all of the major sources and uses of energy and we looked at ways you might conserve — we looked at ways you might decrease our vulnerabilities because of the sources of energy that we have. I think that I've made a difference by focusing on environmental issues, whether it's the health of ecosystems or whether it's the changes in our climate. I think I've also made a difference in some of the security issues that we face. I've worked with a lot of government agencies, most recently the Federal Emergency Management Agency, which is concerned with disasters like the hurricanes that we just experienced, earthquakes and other disasters. I'm also working with the Coast Guard on preserving the fish populations off the coast of the Northeast. Most people don't realize that the Coast Guard is concerned with things like the health of fisheries, they think the Coast Guard is just a law enforcement agency. I've also worked with the Coast Guard in helping them figure out how to save money by allocating their resources better. For example, how many boats of different kinds do they need and where do they put them?

We've also worked with the National Football League on stadium security, and that's been a lot of fun. Most people don't realize that there may be as many as 30 different agencies that are involved in making sure that the stadiums they enter, after they buy a ticket, are safe. And there's a lot of mathematics involved in that. We've modeled how you evacuate a stadium — some of our models were actually used when there was a lightning storm in a national stadium — and we've modeled how you inspect people entering the stadium to make sure that they're not bringing in something that might hurt somebody else. It's actually been fun, because it's gotten me to meet all these great, interesting people and I actually got to try on a Super Bowl ring as a result. We've also worked with the NBA, the National Hockey League and Major League Baseball. I never thought as a kid — and I liked sports — that I was going to get to do those things by being a mathematician.

Well, I have to say at different stages of my career, different people have. In college, I had a couple of professors who were very, very influential in my life. One of them was John Kemeny. John Kemeny was a Hungarian refugee who did his post-doctorate internship with Albert Einstein. (As an aside, he told a story of how when he was courting his wife, the key was to take her on a date to meet Einstein.) So, I was lucky enough to meet John Kemeny when I was just a college freshman, and I did my senior thesis under his direction. And he introduced me to a lot of really interesting ideas. I also met a professor as an undergraduate, Bob Norman, who was the one who introduced me to mathematics and the social sciences. I never realized until I met Professor Norman that there was a way that you could use math to understand behavior, and you could understand how people learn and you could understand how people relate to the world around them, the things they perceive. I never understood how neuroscience might be relevant, so there were all these things that I learned that way. He became a good friend. He came to my wedding, and in fact, I'm still in contact with him and he and I still talk about the mathematics of voting, and the mathematics of how groups make decisions. When I got to graduate school at Stanford University, Professor Kemeny introduced me to Patrick Suppes. Patrick Suppes was a really interesting guy because not only was he a professor of psychology and a professor of philosophy, but he was also a professor of statistics and a professor of education. And he ran the Institute for Mathematical Studies in the Social Sciences. So I went there partly to meet Professor Suppes. I met him soon after I arrived and he certainly had a huge influence on me because of the diversity of things he was interested in. He introduced me to some very interesting people, including R. Duncan Luce, a psychologist. Really he was a mathematician who has a degree in mathematics but he studied psychology and I ended up doing a post-doctoral fellowship with him. He recently passed away, unfortunately. He had a tremendous amount of influence on my way of thinking.

Well, I think what would surprise people is all the variety of things that mathematics is usable and useful for. Most of us have studied math when they're a kid and you think it's about numbers and you think it's about addition and multiplication and division and subtraction. You might learn a little bit of algebra or geometry, but you don't really connect with what it's good for. One of the things I've gotten into, and I think this is very important, is an effort to see that the world is very interconnected as far as all the fields of science and mathematics go. So, we're starting to see multi-disciplinary approaches to the problems of science. And we've started a project that I'm very excited about, which is to introduce those ideas to students in high schools. The example in that project is the connection between biology and mathematics, and I think it would surprise most kids in high school that mathematics is useful for biology. And I think it would surprise you whether you were interested in math or bio, that there's a connection. What we've done is to go into the math and bio classes and introduce them to how to use math in ecology and how to use math to understand the human genome and genetics, and how you use math to understand the spread of disease and epidemics. It has been remarkable how people have related to that. The first response we got was from kids in the math class, "Are you kidding me? We're going to do bio here?" And we got the same kind of response from kids in the bio class; "I thought math was in the math class? What are we doing with equations?" But, then it really opens up their eyes to the fact that you can understand biology better if you know some math and you can really appreciate math more if you see that it's useful for bio.

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