The medal, presented by the Smithsonian Institution and struck in the 200th anniversary year of the birth of its founder, is awarded to "persons who have made distinguished contributions to the advancement of areas of interest to the Smithsonian," the institution said in a statement.
Hawking is known for his groundbreaking theories about black holes, the Big Bang and the conditions permeating the very early universe. His book, "A Brief History of Time," published in 1988, became a worldwide best seller.
"It has been a glorious time to be alive," Hawking said, speaking through a computerized voice synthesizer. Hawking, 63, has suffered from amyotrophic lateral sclerosis for more than 40 years. The disease has left him paralyzed and unable to speak except through the synthesizer.
"People really do want to understand where we came from -- that is why I appeared on 'The Simpsons,'" Hawking said, referring to his guest appearance on the popular television series, a comment that brought applause and cheers by the standing-room-only crowd attending the awards ceremony.
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