This is not your grandfather's America. Last night, America selected a Black president for the second time, elected the nation's first openly gay senator, approved same-sex marriage in two states, rejected a ban on gay marriage in another, defeated two anti-abortion Republican Senate candidates in deep red states, and legalized marijuana in two other states.

As the GOP clung to an old and outdated vision of America, it's no surprise they lost so badly last night. As ABC News's Matthew Dowd said, "The Republicans ran a Mad Men campaign in a Modern Family world."

How did this change happen? Do the math.

Start with former President Bill Clinton's speech at the Democratic Convention in Charlotte. "People ask me all the time how we got four surplus budgets in a row, What new ideas did we bring to Washington? I always give a one-word answer," Clinton said. "Arithmetic."

With that one word, Clinton explained not only the problem with recent GOP tax proposals but the fundamental problem facing the future of the Republican Party. Their math doesn't add up.

Perhaps this should come as no surprise from a party whose leaders have recently mocked science, questioned evolution, denied climate change, misunderstood a woman's reproductive process, derided "critical thinking," and dismissed the significance of college education. But Republicans have also campaigned and governed for years as though they were not bound by the ordinary rules of simple arithmetic.

Even as recently as Tuesday's Election Day, Republicans were still denying the basic math of the U.S. electoral map by claiming that Mitt Romney's alleged "momentum" would somehow magically carry him to victory in states where he had never led in the polls.

To make their case, Republicans viciously attacked New York Times polling expert Nate Silver, who had painstakingly reviewed and studied every major public opinion poll and developed a detailed algorithm to forecast the election. By election day, Silver gave President Obama a 90 percent chance of victory, a confident number that some Republican operatives could not believe. (It's important to note that Silver did not predict Obama would win 90 percent of the vote. He merely predicted Obama had a 90 percent chance of winning the election because the president had so many ways to reach the needed 270 electoral votes.)

The president's victory last night confirmed Silver's math and also revealed another statistical flaw for the Republicans. Mathematically speaking, they can't continue to win elections simply by winning the white vote, and certainly not by relying primarily on white men.

Democrats have lost the white vote in every presidential election since Lyndon Johnson, but as the share of white voters declines in each successive election, their relevance to the outcome diminishes as well. Last night, Obama won re-election with just 39 percent of the white vote. But he won 93 percent of the African American vote and 71 percent of the Latino vote. Obama also won 55 percent of women voters, a key element of victory in a nation where women make up the majority of the population.

At a time when the majority of people born in this country are not white and men are already the minority, Republicans have no hope for the future if they fail to reach out to women and minorities. Putting a turncoat like Artur Davis on stage at the GOP convention and running a few Black Republicans like Allen West in Florida and Mia Love in Utah is no substitute for a serious effort to address the genuine needs and concerns of millions of women and minorities, and that may explain why both West and Love lost on Tuesday.

The conservative activists in the Republican primary process pushed their presidential nominee so far to the right this year that they alienated Blacks, Hispanics, women, gays, and just about anybody else who is not a straight white man.

Now the Republicans have to re-think who they are, and GOP strategist Mike Murphy predicts a battle for the soul of the party between the "mathematicians" who can count and the devout "priests" who can't.

This is not rocket science, folks. It's basic math. You don't get to 270 electoral votes by subtracting and dividing 47 percent of the country, as Mitt Romney famously did, or by ignoring the concerns of the groups that now make up the majority of the country. You get there by adding and multiplying.

Math is a difficult subject for some to master, but it's results are undeniable. And in the end, math always wins.

Keith Boykin is a New York Times best-selling author and former White House aide to President Clinton. He attended Harvard Law School with President Barack Obama and currently serves as a TV political commentator. He writes political commentary for BET.com each week.

The opinions expressed here do not necessarily reflect those of BET Networks.

BET Politics - Your source for the latest news, photos and videos illuminating key issues and personalities in African-American political life, plus commentary from some of our liveliest voices. Click here to subscribe to our newsletter.