To her surprise, she excelled. Later, she was surprised by her surprise, because she had done well in math classes from elementary school through high school. But she had never considered studying math or science in college.

"It wasn't like I thought about it and thought, 'No, I can't do that,"' she recalled. "It just never occurred to me."

Next, she took the more complicated complex analysis course. The professor, Lincoln Chayes, invited her to enroll even though she had not taken all of the prerequisites. And then she had another class, real analysis, also taught by Professor Chayes.

She quizzed him with enough questions that he offered her and another student, Brandy Winn, the opportunity to tackle some original research, the first time he had given a research project to undergraduates.

For a simple model of magnetism, Professor Chayes thought that they might be able to prove a property that would indicate when the magnetic field would line up in a certain direction.

Professor Chayes tutored the two women for months on the background knowledge they would need. Then the students spent months more, up to 12 hours a day, working on the proof.

"I thought that the two were really, really first rate," Professor Chayes said.

Sometimes, they spent days on an approach before finding an obvious flaw. Other times, they thought they had finished, before Professor Chayes would find an error or oversight. And, finally, Professor Chayes found no more gaps.