It is a 58-page dissent, longer than the combined efforts of four other justices who wrote. The court’s first Latina justice directly took on Roberts’s view that the nation’s continued reliance on racial classifications hinders rather than promotes the goal of a color-blind society.

Sotomayor noted Roberts’s famous statement in a 2007 opinion that “the way to stop discrimination on the basis of race is to stop discriminating on the basis of race.”

Too simplistic, she said.

“This refusal to accept the stark reality that race matters is regrettable,” Sotomayor wrote. “The way to stop discrimination on the basis of race is to speak openly and candidly on the subject of race, and to apply the Constitution with eyes open to the unfortunate effects of centuries of racial discrimination.”

She added: “As members of the judiciary tasked with intervening to carry out the guarantee of equal protection, we ought not sit back and wish away, rather than confront, the racial inequality that exists in our society.”

Roberts responded with a short, sharp statement of his own.

“To disagree with the dissent’s views on the costs and benefits of racial preferences is not to ‘wish away, rather than confront’ racial inequality,” Roberts wrote.

“People can disagree in good faith on this issue, but it similarly does more harm than good to question the openness and candor of those on either side of the debate.”

Sotomayor, 59, has spoken extensively about how affirmative action was key to her rise from a public housing project where her parents spoke only Spanish. The search for minorities to diversify student bodies in the 1970s won her invitations and scholarship offers from Ivy League schools she had only just learned existed.

She excelled at Princeton, winning the top undergraduate prize, and went to Yale Law School. But she has drawn diametrically different lessons about the experience than Justice Clarence Thomas, the court’s only African American, who said affirmative action cheapened his Yale Law degree.

Thomas did not write separately in Schuette v. Coalition to Defend Affirmative Action. But Sotomayor, joined in the dissent by Justice Ruth Bader Ginsburg, devoted pages to the country’s “long and lamentable record of stymieing the right of racial minorities to participate in the political process.”

And she said her colleagues ignored “the importance of diversity in institutions of higher education” and the decision “reveals how little my colleagues understand about the reality of race in America.”

Sotomayor filled her dissent with a detailed history of the court’s decisions regarding political empowerment and efforts by majorities to dilute the strength of minorities. She reprinted pages of graphics showing the decline of minorities at top universities in California and Michigan since the states prohibited the use of racial considerations.

She even wrote that she was not going to use the term “affirmative action” because of its connotation of “intentional preferential treatment” such as quotas, because the court has outlawed such practices. Instead, she called it a system of “race-sensitive admissions policies.”

But the most striking part of the dissent was a rebuke to “the view that we should leave race out of the picture.”

“Race matters,” she wrote, to the minority teenager who sees “others tense up as he passes;” to the young person addressed in a foreign language although she grew up in this country; to the young woman who is asked “No, where are you really from?”

“Race matters because of the slights, the snickers, the silent judgments that reinforce that most crippling of thoughts: ‘I do not belong here,’ ” Sotomayor wrote.

Roberts repeated Sotomayor’s words before coming to the opposite conclusion.

“It is not ‘out of touch with reality’ to conclude that racial preferences may themselves have the debilitating effect of reinforcing precisely that doubt, and — if so — that the preferences do more harm than good,” he responded.

The debate provides a remarkable view of the court’s ideological split. But it is unlikely to change many minds — not of those who support what is a step-by-step effort by Roberts to remove racial classifications, or of those who support Sotomayor’s defense of what is clearly a minority view on the court.

Justices are not appointed by presidents “unless they have strong opinions,” said Michigan Attorney General Bill Schuette (R). “I think there are strong passions on each side of this argument.”