The proposal is the centerpiece of President Obama’s new strategy against climate change, following his inability to push through Congress a proposal during his first term to put a price on CO2 emissions. Perhaps most important, it is supposed to be a sign, after decades of dithering, that the United States is ready to lead the world’s effort to put limits on the heat-trapping gases that, experts agree, are changing the climate.

“It really does send a signal to the rest of the world,” said Kevin Kennedy, head of the United States Climate Initiative at the World Resources Institute, a research organization devoted to sustainable development. “It reinforces for many international players that the United States is going to be a serious player.”

Once one gets past the initial enthusiasm, however, the proposal falls far short of the standard scientists have set. The numbers, to put it in Professor Jackson’s terms, don’t quite add up.

The new rules call for a 30 percent reduction in emissions of carbon dioxide by the nation’s power plants by the year 2030, compared with a base in 2005.

It is not a number to dismiss easily, particularly given the political and economic challenges that stand in the way of achieving it. Power plants are the biggest carbon polluters in the country. But the number is also not as big as it looks. For starters, half the job has been done already. By 2012, the recession and the electricity industry’s switch from coal to less-polluting natural gas had cut power generators’ emissions by almost 16 percent from their level in 2005.

What’s more, on their own, the new targets fall short of the promise President Obama first made at the world’s climate summit in Copenhagen five years ago and pledged formally at a summit in Cancún, Mexico, the following year: that by 2020 the United States’ total greenhouse gas emissions would be 17 percent lower than in 2005.

In its assessment of paths toward climate change mitigation, published in April, the Intergovernmental Panel on Climate Change pointed out, in its usual understated way, that “the current trajectory of global annual and cumulative emissions of greenhouse gases is inconsistent with widely discussed goals of limiting global warming at 1.5 to 2 degrees Celsius above the preindustrial level.” It added: “the assumptions needed to have a likely chance of limiting warming to 2 degrees are very difficult to satisfy in real-world conditions.”