## 'Math Fascinates Me'

Professor Elena Nogina's research has been published worldwide.
October 13, 2009

Elena Nogina has been surrounded by numbers her whole life. Both of her parents had doctorates in chemistry and were devoted to scientific research. Raised in Moscow, Nogina says that growing up, she was surrounded by her parents’ academic friends—scholars she calls, “high-level Russian scientists,” including the president of the Russian National Academy of Science.

Although Nogina didn’t pursue a career in science like her parents, she took a similar academic path. She received a doctorate in mathematics from Moscow University and the Russian Academy of Sciences.

"I'm the first mathematician in the family, but not the last,” she says. “Both of my sons have doctorates in mathematics."

CUNY—a ‘leading center’ for the study of mathematics
Nogina’s specific areas of research are theory of computation and Mathematical logic. According to Nogina, Mathematical logic studies “the exact laws of reasoning—which were first known in their philosophical form since Aristotle.  It fascinates me because it tries to answer fundamental questions about mathematics, and on what principals it was built.”

She is also conducting research into the field of Justification Logic. According to Nogina, the mathematical theory of knowledge has been studied for decades, but has “lacked an essential component—the notion of justification.

Justification Logic is a family of logical systems that originated from the Logic of Proofs.  It offers a new approach to the theories of knowledge, evidence, and beliefs.

She further describes Justification Logic as a ‘GPS System’. “When the GPS tracking device first came out, you knew that you could get from point A to point B. But with the newer devices, we can build and track an exact route from A to B,” she says. “We can now build and compare different justifications, evaluate the size of justification and more.”

Nogina calls CUNY the “leading center” of studies in the area of Justification Logic, and she was recently awarded a grant of \$375,000 from the National Science Foundation to study Justification Logic, along with two other CUNY faculty members.

“CUNY and BMCC students are involved in the research,” she says. “Our group produces dozens of papers and conference presentations a year, attracting significant funding.”

Nogina also received a PSC CUNY research grant for 2009-2010 which, making this her ninth grant at BMCC.

Sixty-four published papers
This year, Nogina’s research paper "Logic of Strong Provability and Explicit Proofs" was published in The Bulletin of Symbolic Logic. This marks her 64th published study that pertains to mathematics.

Her first papers were written when she was a doctoral student in Moscow and were published in what Nogina calls, “the best outlets available in Russia at that time.”

Some of her earlier works were also published in international journals, such as Logik und Grundlagen der Mathematik.

Over the years, her recent works were published in national journals, such as Journal of Logic and Computations and Springer Lecture Notes in Computer Science.

Game Theory—a new mathematical interest
It’s been a busy semester for Nogina, who teaches courses such as Mathematics for Health Sciences and Introduction to Discrete Mathematics.

“I am looking forward to new exciting developments,” says Nogina. “I have just finished writing a new PSC CUNY grant proposal where I am extending my research interests to yet another area, Game Theory.”

Game Theory is defined as a branch of applied mathematics mostly used in the social sciences, such as economics, as well as in biology, engineering and more. Game Theory attempts to mathematically capture behavior in strategic situations, where an individual's success in making choices depends on the choices of others.

The importance of math
As a mathematics professor, Nogina is oftentimes faced with the daunting question, “Why is math so important?”

“Mathematics is amazingly efficient in the natural sciences and technology. Is mathematics a powerful tool in social sciences, too? The answer is ‘yes,’” she explains. “Mathematics is very relevant to making responsible financial decisions, securely paying bills online, choosing voting systems and even playing games."

Nogina says that mathematics was always close to her soul. “I’m fascinated by its abstract beauty and internal logic. I’ve found great teachers, wonderful friends and even my future husband among mathematicians,” she says.