The disease reduced his bodily control to the flexing of a finger and voluntary eye movements but left his mental faculties untouched.
He went on to become his generation’s leader in exploring gravity and the properties of black holes, the bottomless gravitational pits so deep and dense that not even light can escape them.
That work led to a turning point in the history of modern physics, one that played itself out in the closing months of 1973 on the walls of his brain when Dr. Hawking set out to apply quantum theory, the weird laws that govern subatomic reality, to black holes. In a long and daunting calculation, Dr. Hawking discovered to his befuddlement that black holes — those mythological avatars of cosmic doom — were not really black at all. In fact, he found, they would eventually fizzle, leaking radiation and particles, and finally explode and disappear over the eons.
Nobody, including Dr. Hawking, believed it at first — that particles could be coming out of a black hole. “I wasn’t looking for them at all,” he recalled in an interview in 1978. “I merely tripped over them. I was rather annoyed.”
That calculation, in a thesis published in 1974 in the journal Nature under the title “Black Hole Explosions?,” is hailed by scientists today as the first great landmark in the struggle to find a single theory of nature — to connect gravity and quantum mechanics, those warring descriptions of the large and the small, to explain a universe that seems stranger than anybody had thought.
The discovery of Hawking radiation, as it is known, turned black holes upside down. It transformed them from destroyers to creators — or at least to recyclers — and wrenched the dream of a final theory in a strange, new direction.
“You can ask what will happen to someone who jumps into a black hole,” Dr. Hawking once said in an interview in 1978. “I certainly don’t think he will survive it.
“On the other hand,” he added, “if we send someone off to jump into a black hole, neither he nor his constituent atoms will come back, but his mass energy will come back. Maybe that applies to the whole universe.”
Dennis W. Sciama, a cosmologist and Dr. Hawking’s thesis adviser at Cambridge, called Hawking’s Nature paper “the most beautiful paper in the history of physics.”
Edward Witten, a theorist at the Institute for Advanced Study in Princeton, said: “Trying to understand Hawking’s discovery better has been a source of much fresh thinking for almost 40 years now, and we are probably still far from fully coming to grips with it. It still feels new.”
In 2002, Dr. Hawking said that he wanted the formula for Hawking radiation to be engraved on his tombstone.
He was a man who pushed the limits — in his intellectual life, to be sure, but also in his professional and personal lives. He traveled the globe to scientific meetings, visiting every continent, including Antarctica; wrote best-selling books about his work; married twice; fathered three children; and was not above appearing on “The Simpsons,” “Star Trek: The Next Generation” or “The Big Bang Theory.”
He celebrated his 60th birthday by going up in a hot-air balloon. The same week, he also crashed his electric-powered wheelchair while speeding around a corner in Cambridge, breaking his leg.
In April 2007, a few months after his 65th birthday, he took part in a zero-gravity flight aboard a specially equipped Boeing 727, a padded aircraft that flies a roller-coaster trajectory to produce fleeting periods of weightlessness. It was a prelude to a hoped-for trip to space with Richard Branson’s VirginGalactic company aboard SpaceShipTwo.
Asked why he took such risks, Dr. Hawking said, “I want to show that people need not be limited by physical handicaps as long as they are not disabled in spirit.”
A longer obituary will appear shortly.