Lifted by several grants, Rider University’s math department has been conducting premier mathematical research into fundamental problems that have intrigued scientists for decades. Two national research grants, from the National Science Foundation and the National Institutes of Health, gave Professor Ciprian Borcea new opportunities to explore one of his research interests, articulated systems related to crystalline and protein structures. The projects encompass several disciplines but much of the mathematical underpinnings stem from rigidity theory.
Mathematicians and scientists employ rigidity theory to help them understand the structure of natural materials and the behavior of linked systems. This fundamental theory has a double root. The first is purely mathematical, but the second is deeply practical, as it describes the relationship between structure and stability. The scale ranges from the atomic world of particles to the very human world of mechanical devices and buildings. Rigidity theory helps engineers understand why the frame of a house holds together and doesn’t collapse.
One grant is assisting Borcea tackle a problem of rigidity theory that James Clerk Maxwell, the Scottish physicist whose equations were the first to successfully describe electromagnetism, faced more than 150 years ago. Will Borcea and his students succeeding in solving this conundrum? That’s the hope, of course, but wrestling with the challenge produces its own rewards, Borcea says.
“If you don’t necessarily solve the problem you’re aiming at, the effort is still usually extremely fruitful," he says. "Failure in mathematics is oftentimes very productive. In research, you need perseverance. That’s another part of a student’s education.”
On April 4, Borcea organized a symposium at Rider that focused on the topics of his NIH grant. He was joined by his collaborator from Smith College, Dr. Ileana Streinu, and Dr. George Phillips of Rice University. In addition to the lectures, Borcea began a series of mathematical research seminars this month that also revolve around the grant projects. The seminars are aimed at highly motivated undergraduates.
Conducting such research on the undergraduate level can be challenging for students. “You are confronting the unknown and competing with all of the experts,” Borcea says, adding that, “Normally, you have to absorb a lot of mathematics to have techniques to even understand the problem, let alone solve it.”
That makes the way people appreciate math very different from, say, music. Enjoying a symphony doesn’t require a complex understanding of music theory, but appreciating a theorem usually springs from a specialized form of knowledge. “Math builds upon itself, layer after layer, and requires an abstraction and complexity that cannot be explained in a few lines,” says Borcea, who received his doctorate from the University of Bucharest in Romania.
The very idea of mathematical research can cause people to scratch their heads, Borcea says. “A picture exists of mathematics as something static and kind of boring where you have a formula to memorize and not much more, which is a completely misleading perception of the reality. The challenge for a mathematician is to convince a person not familiar with science or mathematics that there is evolving refinement and beauty and creativity in these fields.”
Grants also facilitate the exchange of ideas among peers. For example, Borcea attended the American Mathematical Society meeting at the University of Maryland in Baltimore on March 29 and 30 and a workshop at the Isaac Newton Institute for Mathematical Sciences in Cambridge, England, in February.
“You cannot just rely on publications,” says Borcean, who was a member of the Institute for Advanced Study in Princeton before joining Rider’s faculty. “It’s important to go out and see what people in other universities are doing.”