WASHINGTON — The implicit message, delivered by the Supreme Court majority in two of the most important decisions of the term that ended this week, is that racial discrimination is no longer as big a problem as we once thought.

Neither the voting rights case out of Texas nor the affirmative action hiring case out of New Haven, Conn., said that explicitly. But the link between the two is the assumption or assertion that this society has largely healed itself and does not need the race-conscious remedies that the previous generation of politicians thought necessary.

If that reading of the court’s majority is correct, then two things are clear. Judge Sonia Sotomayor will certainly challenge the prevailing view if she is confirmed by the Senate to join that bench. And over a longer period of years, President Obama is likely to find himself in conflict with the court on the question of race.

In the voting rights case decided on June 22, Chief Justice John Roberts signaled that he thinks time has run out on the remedy Congress concocted in 1965 to overcome the historical pattern of denying blacks access to the ballot box in much of the South. A central provision of the Voting Rights Act, passed originally for five years and repeatedly extended, requires covered jurisdictions to get approval from Washington for any change, no matter how trivial, to its voting procedures.

As Roberts wrote in his opinion, “the historic accomplishments of the Voting Rights Act are undeniable. . . . (But) things have changed in the South. Voter turnout and registration rates now approach parity. Blatantly discriminatory evasions of federal decrees are rare. And minority candidates hold office at unprecedented levels.”

Given all that, he said, it is hard to justify the constitutionality of treating one set of states differently from all the others. The Voting Rights Act was spared only by the court’s discovery that the statute could be interpreted in a way that gives the Texas district involved in the case a chance to be exempted from its terms. So the court deferred judgment on the constitutional question. Seven justices agreed with Roberts. The eighth, Clarence Thomas, wanted to rule it unconstitutional right now.

In the New Haven firefighters’ case, Justice Anthony Kennedy, writing for a 5-4 majority, ruled that protesting white firefighters had been victims of reverse discrimination when the city scrapped an exam on which none of the African-Americans scored well enough to win immediate promotion. In doing so, he put a new and severe limitation on the Civil Rights Act of 1964, passed to open the job market to blacks.

Justice Ruth Bader Ginsburg, in dissent, noted that New Haven, now estimated to be nearly 40 percent black, has only one African-American among its 21 fire captains. But, unlike in 1964, when blacks were being beaten for seeking their rights, the court—and perhaps the country — now shows as much or more sympathy for the white victims of the reverse discrimination it finds in affirmative action programs.

Injecting Sotomayor into this epochal debate when her hearings begin in a couple of weeks will introduce a passionate and committed advocate of affirmative action. In her professional life and in her many speeches, the woman who would be the first Hispanic justice has repeatedly signaled that she does not believe the wounds of racial discrimination are completely healed, or that the remedies of the past are no longer needed. In that, she is joined by Obama, who rejects the notion that his election signaled the advent of some “post-racial” age.

You have to believe that as Obama has the opportunity over time to reshape the Supreme Court, there will be more Sotomayors — and more of a challenge to those who wish to dispute the continuing damage that segregation has done to this country, and the continuing need for race-conscious remedies.