"We will not just meet but we will exceed the level achieved at the height of the space race," he said.
Obama said the investments he is proposing would lead to breakthroughs, such as solar cells as cheap as paint and green buildings that produce all the energy they consume.
The pursuit of discovery a half century ago fueled the nation's prosperity and success, Obama told the academy.
"The commitment I am making today will fuel our success for another 50 years," he said. "This work begins with an historic commitment to basic science and applied research."
He set forth a wish list for the future including "learning software as effective as a personal tutor; prosthetics so advanced that you could play the piano again; an expansion of the frontiers of human knowledge about ourselves and world the around us.
"We can do this," Obama said to applause.
The president drew chuckles when he added: "I want to be sure that facts are driving scientific decisions, not the other way around."
Obama said his administration would double the budget of key agencies, including the National Science Foundation and the National Institute of Standards and Technology.
"At such a difficult moment, there are those who say we cannot afford to invest in science. That support for research is somehow a luxury at a moment defined by necessities. I fundamentally disagree," Obama said.
"Science is more essential for our prosperity, our security, our health, our environment, and our quality of life than it has ever been," he said.
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