A 16-year-old California boy won a premier high school science competition Monday for his innovative approach to an old math problem that could help in the design of airplane wings.

Michael Viscardi, a senior from San Diego, won a $100,000 college scholarship, the top individual prize in the Siemens Westinghouse Competition in Math, Science and Technology.

Viscardi said he's been homeschooled since fifth grade, although he does take math classes at the University of California at San Diego three days a week. His father is a software engineer and his mother, who stays at home, has a Ph.D. in neuroscience, he said.

"It's unbelievable," Viscardi said of his win. "It's so incredible that I'm in shock right now."

Viscardi tackled a 19th century math problem known as the Dirichlet problem, formulated by the mathematician Lejeune Dirichlet.

The theorem Viscardi created to solve it has potential applications in the fields of engineering and physics, including airplane wing design. He said he worked on it for about six months with a professor at UCSD.

"He is a super-duper mathematics student," said lead judge Constance Atwell, a consultant and former research director at the National Institutes of Health. "It was almost impossible for our judges to figure out the limits of his understanding during our questioning. And he's only 16 years old."

Anne Lee, 17, a senior at Phoenix Country Day School in Paradise Valley, Ariz. and Albert Shieh, 16, a junior at Chaparral High School in Scottsdale, Ariz., shared the $100,000 top prize in the team category. They improved computer technology that could help locate the genetic roots of some inherited diseases like Alzheimer's, autism and bipolar disorder.

Lee and Shieh met at the gene research center at which they both have internships. They were assisted on their project by members of the institute.

"I would have been happy with anything," Shieh said.

Lee said dissecting a cow's eyeball early in her academic career inspired and encouraged her to study science.

As part of the winners' celebration, they were to get to ring the closing bell at the New York Stock Exchange at the end of the business day Monday.

The Siemens Foundation, founded in 1998, aims to increase access to higher education among gifted students studying math, science and technology. The foundation distributes nearly $2 million annually in scholarships and awards.

Nineteen students competed in the national finals — six individuals and six teams. Besides the winners' prizes, finalists won scholarships ranging from $50,000 to $10,000. Team members share awards.