Sen. Rand Paul, (R-Ky.), who announced he's running for president in 2016, is known for his belief in limited government. Here his take on Obamacare, the Constitution and more, in his own words. (Julie Percha/The Washington Post)

Rand Paul announced that he is running for president in a speech in Louisville on Tuesday. The Republican senator from Kentucky and the son of the libertarian icon Ron Paul is calling himself "a different kind of Republican leader." In some ways, the younger Paul really would be different.

To be sure, Paul agrees with his fellow Republicans on many issues. He thinks states should be free to prevent gays from marrying. He thinks that climate change is real and that humans are causing it, but that view hasn't stopped him from opposing President Obama's regulations on carbon dioxide emissions, which Paul says will damage the economy. Paul has consistently argued for more lenient federal marijuana policies, but even on this controversial issue, most of his potential rivals for the GOP nomination agree with him that states should be free to write their own laws on weed.

Still, there are a few areas in which Paul's previous statements suggest he may have some real disagreements with other likely Republican candidates. And there are other areas in which Paul's opinions seem to have changed. Either Paul will further adjust his views as the campaign progresses to align himself with his opponents, or these disagreements will define the primary phase of the campaign for him.

Surveillance

The clearest difference between Paul and his party is probably on the question of how much information the government should be able to collect from Americans' phone calls and digital communications.

A bill to reform the National Security Agency failed last year because of Republican opposition. They worried that restrictions on the agency's ability to gather massive amounts of data could blind the country to a terrorist plot.

Like the rest of his party, Paul voted against the bill, but for the opposite reason. He felt it didn't go far enough to constrain surveillance, and that a vote in favor would have been a vote for spying on Americans.

That vote sets Paul apart from just about everyone in his party, including establishment figures who want to keep the government's surveillance powers as well as others who are sympathetic to Paul's views, but more willing to compromise. Sen. Ted Cruz (R-Tex.), a presidential candidate who sponsored last year's bill, criticized Paul's refusal to vote for it last week, saying the bill would have passed the Senate with Paul's crucial support.

The military

Paul's views on snooping are clear. By contrast, how he thinks about America's military power might be the largest unanswered question in his campaign. As a libertarian, Paul used to argue against using military force in foreign countries. Before joining the Senate, he denounced the Bush administration's aggressive foreign policy, saying that Vice President Richard B. Cheney had supported the invasion of Iraq because it would benefit his former employer, Halliburton.

Paul has said repeatedly he would oppose war with Iran, including in an interview last year on ABC's "This Week." He said then he thought war with Iran was "a dumb idea," and he also talked about the military budget, saying it shouldn't be "a blank check." These statements set him at odds with most other Republicans.

More recently, though, he's taken a harder line on Iran, joining the rest of his caucus in signing a controversial letter on the negotiations over that country's nuclear program. In an apparent shift away from his previous skepticism about military spending, he proposed a $190 billion increase in the Pentagon's budget last month.

The schools

Many libertarians worry that the federal government is impinging on locally elected school boards' authority over classrooms. In particular, they're upset about the Common Core, a national set of standards designed to ensure that a high school diploma means more or less the same thing in every state.

Paul shares this concern, and he's been talking to voters about it. On a recent visit to New Hampshire, he said that the national system threatens to stifle new ideas in education and that the federal Department of Education should be eliminated.

The Common Core began as the brainchild of a few activists, governors and state education officials, not with bureaucrats in Washington, D.C. Still, the standards might not have been adopted so widely and so quickly without the support of the Obama administration.

He's also claimed the standards contain "revisionist history that ignores the faith of our Founders." (The standards do not address history, only math and reading.)

The Republican field is divided on the question of the Common Core. Some likely candidates are on Paul's side, while others agree with former Florida governor Jeb Bush, an outspoken supporter. Bush has dedicated his time since leaving office to advancing the standards through his private foundation.

The economy

Another major question for Paul is what he thinks about the Federal Reserve and the recent financial crisis. The Fed's decisions about where to set interest rates have profound consequences for the national economy, so it will be important for voters to figure out exactly what Paul thinks about this issue.

Most Republicans have argued that the Fed has gone too far in its efforts to support the economy since the crisis, risking a sudden, drastic increase in prices. So far, prices have hardly budged, and there's no reason to think that they will.

Despite the stability of prices, however, Paul has gone even farther than some of his Republican colleagues, speaking approvingly of the gold standard. On the gold standard, a dollar was worth a fixed weight in gold, which at least ensured that the prices of other things wouldn't change much over the long term.

"We need to think about our currency that once upon a time had a link to a commodity, and I think we should study it," he said in 2013. He did not, however, advocate for a return to the gold standard, but only for a commission to study the idea.

If there are any economists on the commission, they'll probably reject it. Economists disagree about a lot of things but not the gold standard. Just about all of them think it's a terrible idea, according to one recent survey.

Whether Paul, as president, would ask Congress to restore the gold standard remains to be seen. The possibility that he might makes him "by far the most dangerous candidate in the 2016 field," Danny Vinik argues at the New Republic.