It pays to be curious, to ask questions and seek answers.

That's what Mary Masterman found out. From a very young age, Masterman, now 18, asked thought-provoking questions.

When she was in the eighth grade, her father gave her a telescope. When she looked at stars and galaxies, she wanted to know what they were made of. That led her to build her first spectrograph.

In March, Masterman, of Oklahoma City, won top honors in the Intel Science Talent Search — America's most prestigious pre-college math and science contest — for building a spectrograph with higher resolution.

Her Littrow spectrograph splits light, like a prism, and uses a camera to record the resulting Raman spectra — a specific vibrational fingerprint of the molecular compound being investigated. Using a laser as her light source, Masterman tested several household objects and solvents and compared her results with published wave numbers.

She found she could make relatively accurate wavelength measurements with her low-cost, homemade device. She built her spectrograph system for $300. Commercial units can cost $20,000 to $100,000.

For her efforts, Masterman earned a $100,000 college scholarship from the Intel Science Talent Search, a nationwide competition. Students submit their research reports by mail by mid-November. In January, 40 finalists are selected from 300 semifinalists. The 40 finalists receive a free trip to Washington, D.C., to attend the Science Talent Institute in early March.

Aiming For Work

Masterman says she's interested in pursuing a career in physics or chemistry. "I almost didn't enter, because I didn't think I would even get to the semifinals," she said.

She says she was intimidated by the caliber of the other contestants. But she had confidence in herself.

Sure, Masterman is smart. She's tops in her class of 658 at Westmoore High School and has won numerous science honors.

But being bright alone is no guarantee of success.

Masterman had drive, worked hard and refused to give up when obstacles arose with her physics project.

Those qualities typify the winners of the annual Intel talent search.

John Pardon, 17, of Chapel Hill, N.C., won second place and a $75,000 scholarship for a math project that solved a classical open problem in differential geometry.

Dmitry Vaintrob, 18, of Eugene, Ore., won third place and a $50,000 scholarship for his investigation of ways to associate algebraic structures with topological spaces.

Masterman credits having a broad science background and being self-directed for helping her win the Intel competition. "I've taken a lot of classes in different sciences, and that helped me," she said.

The fact that she did the project without a mentor helped too, she says. Mentors often overshadow the student's work, guiding everything, she says.

"I've done a project with a mentor before, and it wasn't really my research," Masterman said.

It was the researcher's field, and Masterman felt like she was just along for the ride.

But every project is different, she concedes. For instance, doing medical research requires access to laboratories with specialized equipment, and that can be obtained only through mentors.

"If you're just interested in something on your own, it's OK not to have (a mentor)," she said.

Some might think living in Oklahoma — far from research hot spots and top-tier universities — would be a drawback for Masterman. She doesn't see it that way.

"There's a misconception that if you don't go to some big university that you can't do good research, but you can do perfectly fine even at your house," she said.

Others might think doing science projects would be too complicated or too expensive. Masterman says those people worry too much.

Her main goal with the project was to build a spectrograph that was a lot cheaper than commercial ones, but that could still get the job done. She says she barely knew about the Intel Science Talent Search and ended up entering at the last minute.

Building the spectrograph wasn't so hard, but getting it to work properly was difficult, she says. Masterman had trouble with the delicate job of aligning all the parts with the laser. That led to frustration.

"For a few weeks, I really hated my project," she said.

But she didn't quit. "I had already put so much time into it that I didn't want to stop," she said. The project took Masterman six months, including research, to complete.

Masterman had to make sacrifices with her personal time to do the project. She had to put aside activities such as playing the piano, harp and flute, and painting.

Fellow Intel contest winners Pardon and Vaintrob say their big hurdle was writing papers on their math projects. Their proofs were technical and had to be explained to a larger science audience. "If it's written well, it should be understandable even to those people who are in different fields," Pardon said.

Pardon showed that a finite-length closed curve in a plane can be made convex in a continuous manner, and without bringing any two points of the curve closer together.

Vaintrob proved that loop homology and Hochschild cohomology — both of which have to do with topography — coincide for an important class of spaces.

Like Masterman, Pardon and Vaintrob have lots of extracurricular activities.

At Durham Academy, Pardon participates in track and cross country. He also plays cello in the Honors All State Orchestra.

"It seems healthy to do other things besides school," Pardon said.

He thinks there are side benefits to recreation that can help with intellectual pursuits. Athletic and creative activities can keep your mind fresh, he says.

Vaintrob, a student at South Eugene High School, enjoys running, Nordic skiing, foreign languages, classical literature and poetry. Born in Russia and fluent in the language, he participates in Russian theater.

Pardon and Vaintrob worked up to the Intel Science Talent Search by participating in other math and science contests.

A TopCoder Top Gun

Pardon was one of the top 25 algorithm writers in the TopCoder competition. He also received a gold prize at the 2005 and 2006 International Olympiads in Informatics.

He plans to study math and computer science in college.

Vaintrob has won numerous math honors. He received his state's top score in the American Math Competition two years running and was twice named one of 16 junior fellows at the Clay Mathematics Research Academy. He also won this year's Siemens Competition.

Vaintrob thinks about math problems when he's bored. "Some of the kids in my class would make fun of me for writing math formulas during lectures," he said.

The area he's concentrating on involves lots of math diagrams and pictures. "It's pretty hard to hold all of them in your head, so you have to write them down," he said.

Vaintrob plans to attend Harvard University and become a research mathematician.

BY PATRICK SEITZ