By all accounts, he is one of the best math teachers in the country. The Mathematics Association of America has given him two national awards. He was appointed by the Bush administration to the National Mathematics Advisory Panel. For 25 years he has prepared middle-schoolers for the tough admissions standards at Thomas Jefferson High School for Science and Technology, the most selective high school in America.

Yet this year, when Vern Williams looked at the Jefferson application, he felt not the usual urge to get his kids in, but a dull depression. On the first page of Jefferson's letter to teachers writing recommendations, in boldface type, was the school board's new focus: It wanted to prepare "future leaders in mathematics, science, and technology to address future complex societal and ethical issues." It sought diversity, "broadly defined to include a wide variety of factors, such as race, ethnicity, gender, English for speakers of other languages (ESOL), geography, poverty, prior school and cultural experiences, and other unique skills and experiences." The same language was on the last page of the application.

"This is just one example of why I have lost all faith in the TJ admissions process," Williams said. "In fact, I'm pretty embarrassed that the process seems no more effective than flipping coins."

Last year, he said, Jefferson rejected one of only two eighth-graders in Virginia who qualified to take the USA Junior Math Olympiad test, six scary problems to be done in nine hours. At the same time, "students who had very little interest [or] motivation in math and science were admitted," he said. "Some admitted students had even struggled with math while in middle school."

Williams knows that the school board is concerned that less than 4 percent of Jefferson students are black or Hispanic. He is black himself and was born in the District. He is familiar with the failings of math education for low-income minorities, but he doesn't think rejecting top math students is the best way to make the school more diverse.

The solution, he said, is to "get rid of all warm and fuzzy math programs at the elementary school level and teach real academic content to all students." Textbooks are dumbed down, he said, to accommodate allegedly math-phobic children. Don't get him started on the overuse of calculators.

He showed me a copy of a Jefferson recommendation he filled out in 2004. It asked him to rate the candidate on "interest in math," "self-discipline" and "problem-solving skills." There was no mention of ethnic diversity. This year, recommenders are required to assess three qualities: intellectual ability, commitment to STEM [science, technology, engineering, math] and whether the applicant's background, skills and past experiences "contribute to the diversity of TJHSST's community of learners."

Last November, I wrote a column endorsing that approach. I said that if the school put more emphasis on character and less on math scores, more black and Hispanic applicants would have a chance. I still believe that. But I have been so taken with the power of Williams's teaching over the years that I feel obliged to present his contrary view.

He has run into several cases of Jefferson ignoring STEM commitment. Humanities types are being accepted, and stars of Mathcounts, the nerd equivalent of youth soccer, are being rejected.

"And yet how many minorities have this corrupt process scooped up? Barely any!" Williams said. "I usually write between 45 and 60 TJ recommendations and spend at least 75 minutes on each because I make them all totally unique. I felt like last year's effort was a total waste of time."

The Jefferson admissions committee's careful sifting produced last year's average senior class SAT score of 2233, the highest in the nation by far. That is impressive. But at least one gifted teacher who knows Jefferson well thinks it could do better finding the students who come for the love of math, not prestige.